CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit under 35 U.S.C. § 119(e) of U.S. provisional application serial number 61/701,264, filed September 14, 2012, the disclosure of which is incorporated by reference in its entirety.

FIELD

[0002] Disclosed embodiments are related to systems and methods for detecting position and/or trajectory of an object.

BACKGROUND

[0003] Lines of a playing surface, like a tennis court, are typically marked by visible lines. However, in some instances, an automated line calling system including sensors placed on, or embedded in, a playing surface is used to help determine whether a ball lands in or out of bounds during play. Sensors placed on and near boundary lines of sports games, such as tennis, have typically included pressure based sensors to detect the physical force from a ball impacting the sensor, though other types of sensors have also been used. These pressure based systems have been combined with various additional sensors such as sound detectors as well as information regarding the status of the game including, for example, serving to which side and singles versus doubles tennis, to aid in determining if a ball has been hit in or out and if the detected signal was due to a foot fall from a player.

SUMMARY

[0004] In one embodiment, a sensor system may include three or more parallel conductors adapted to be arranged on a ball playing surface. The three or more conductors may be adapted to detect an electrical signal induced in at least two of the three or more conductors by a ball. The sensor system may also include a processor electrically

communicating with the three or more conductors that is configured to receive the electrical signal and output at least one of a trajectory and position of the ball.

[0005] In another embodiment, a method of detecting a position and/or trajectory of a ball includes: inducing an electrical signal in three or more parallel conductors arranged on a ball playing surface with the ball; sensing the induced electrical signal; and processing the sensed signal to determine at least one of a trajectory and position of the ball.

[0006] It should be appreciated that the foregoing concepts, and additional concepts discussed below, may be arranged in any suitable combination, as the present disclosure is not limited in this respect. Further, other advantages and novel features of the present disclosure will become apparent from the following detailed description of various non- limiting embodiments when considered in conjunction with the accompanying figures.

BRIEF DESCRIPTION OF DRAWINGS

[0007] The accompanying drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures may be represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawing. In the drawings:

[0008] Fig. 1 is a schematic representation of a sensor including four conductors disposed on top of a substrate;

[0009] Fig. 2 is a schematic representation of a sensor including four conductors embedded in the top surface of a substrate;

[0010] Fig. 3 is a schematic representation of the sensor including four round conductors embedded in the top surface of a substrate;

[0011] Fig. 4 is a schematic representation of a sensor including four conductors with a tennis ball impacting the sensor;

[0012] Fig. 5 is a schematic representation of a sensor including four conductors with a tennis ball passing over the sensor;

[0013] Fig. 6 is a schematic representation of a sensor including three conductors with a tennis ball impacting the sensor;

[0014] Fig. 7 is a schematic representation of a sensor including three conductors with a tennis ball passing over the sensor;

[0015] Fig. 8 is a schematic representation of a sensor including combined separate sensor segments;

[0016] Fig. 9 is a schematic representation of a flexible printed circuit including portions of two separate sensors; [0017] Fig. 10 is a schematic representation of a pattern of sensors attached to a plurality of flexible printed circuits arranged on half of a tennis court;

[0018] Fig. 11 is a schematic representation of a pattern of separate sensors arranged on half of a tennis court; and

[0019] Fig. 12 is a schematic representation of one embodiment of an amplifier; and

[0020] Fig. 13 is a schematic representation of another embodiment of an amplifier.

DETAILED DESCRIPTION

[0021] While pressure based sensors are capable of detecting ball impacts, they still suffer from several drawbacks. Specifically, the inventors have recognized that the accuracy of where the sensor was struck, for example, on the sensor circuit versus before or after the circuit, can only be fully assessed using a secondary means such as a sound based approach, an additional force absorption approach, or additional sensors to determine which sensor was hit first. Additionally, and without wishing to be bound by theory, the pressure wave from a tennis ball impacting a playing surface can travel in both the forward and reverse direction. The degree of travel of the pressure wave through the playing surface is dependent on many factors including the speed of the ball, the angle of the ball, the spin of the ball, and surface material. Given that the pressure wave travels both forward and backwards from the point of impact, the sensor may detect a hit even when the ball does not impact the sensor thus diminishing the accuracy of a call. Another factor complicating analyzing whether a ball has struck inbounds or out of bounds, is that a ball does not impact a single point on the playing surface. Instead, a compliant ball such as a tennis ball will hit a surface, compress, skid, and then decompress as it leaves the surface all within a short amount of time of about 4 ms to 5 ms. In view of the noted limitations, the inventors have recognized the need to replace the pressure sensitive sensor approach currently used for detecting the location of a ball impacting a playing surface with a more accurate type of sensor.

[0022] In view of the above, the inventors have recognized the benefits associated with providing a sensor capable of generating a signal based on the proximity of the tennis ball to the sensor instead of the amount of force applied to the sensor. More specifically, the inventors have recognized that a sensor based on induction of an electrical signal in the sensor by the ball may offer a more accurate approach to detecting whether a ball has struck a playing surface in a particular location as compared to other types of sensors. Without wishing to be bound by theory, such a sensor may be viewed as an application of sensing the induced electric field by a point charge in an infinite metal plane. By applying such a concept, a significant reduction in electrical signal strength is observed between direct hits and nearby hits. In addition there is also a significant reduction in electrical signal strength observed from forces applied to the sensor by objects other than a tennis ball, including player footfalls, due to these objects not being charged to the same degree and/or having different shapes and movements. Thus, the proposed type of sensor noted above, and described in more detail below, may offer both improved detection accuracy as well as improved detection discrimination with regards to player footfalls. Additionally, due to the natural tendency of a tennis ball to become charged during play, the proposed sensors do not require the use of a modified tennis ball to generate the above-noted electronic signals.

Instead, the sensors described in more detail below may use a standard tennis ball as is currently approved by the relevant authorities. These sensors may also be used to detect other types of objects that are capable of inducing an electric charge in the sensor.

[0023] In one embodiment, the sensor includes at least three parallel conductors spaced from each other and extending along a length of the sensor. For example, the sensor may include three parallel conductors, four parallel conductors, or any appropriate number of conductors as the current disclosure is not so limited. The conductors may be located in the same plane in order to help minimize variations in the induced electrical signal in the conductors based on differences in the height of the conductors. However, embodiments in which the sensors are not located in the same plane are also possible. Depending on the particular embodiment, the sensor may be adhered to the top of the playing surface or embedded in the playing surface as the current disclosure is not so limited. Further, the individual conductors of the sensor may be positioned on the playing surface individually, or they may be assembled on a separate substrate that is then positioned and/or attached on the playing surface.

[0024] The three or more parallel conductors may be provided in any appropriate form. For example, the conductors may be embodied by Flat Flexible Cables (FFC), Flexible Printed Circuits (FPC), or Polymer Thick Film Circuits (PTF). Alternatively, the conductors could be provided as individual wires or thin elongated sheets of conductive material as the current disclosure is not limited to any particular form of the conductors. In some embodiments, it is desirable to provide a small vertical profile for both the conductors and the sensor to minimize both the appearance of the sensors as well as any impact on play.

Consequently, in some embodiments, the conductors can be very thin on the order of several thousandths of an inch in thickness. However, it should be understood that any appropriate thickness, including thicker conductors, might be used. In embodiments where the conductors, and the resulting sensor, are thicker, it may be desirable to embed the sensor in the playing surface as noted above and/or apply one or several layers of coloring to minimize the visibility of the sensor. In addition to the above, in some embodiments, the cross- sectional profile of the conductors and resulting sensor may be substantially flat to further minimize the impact of the sensor on play. However, it should be understood that other cross- sectional shapes are also possible. For example, the conductors might have a circular, ovular, square, or any other appropriate cross-sectional shape.

[0025] As noted above, the three or more parallel conductors are spaced from one another. This spacing can be viewed as a pitch of the conductors. Without wishing be bound by theory, the pitch will affect both the area the sensor is capable of monitoring as well as the accuracy of the sensor. For example, larger pitches will result in conductors that are spaced further from one another and thus are able to monitor a larger area. However, larger pitches will also result in decreased accuracy as to the detected position of a ball relative to the sensor. Therefore, when selecting the pitch of the conductors, the desired area as well as the desired sensitivity should be considered. While any appropriate pitch might be used, in one embodiment, the pitch of the conductors may be less than or equal to a desired sensitivity of the sensor. For example, in tennis the required accuracy for an automated line calling system is 5 mm. Therefore, the pitch of the conductors in such a system might be less than or equal to about 5 mm, 4 mm, 3 mm, 2 mm, 1 mm, or any other appropriate distance.

[0026] While in some embodiments, the individual conductors may be equally spaced and have similar sizes, in other embodiments, the individual conductors may be spaced at different distances from one another and/or have different sizes. Such an embodiment may offer multiple benefits. For example, and without wishing to be bound by theory, by providing different sizes of conductors and/or different distances between the conductors, the resulting electrical signal induced in the conductors by a charged ball either passing by, or contacting the conductors will be different and may enable analysis of the signal to more precisely locate the position of the ball relative to the conductors. [0027] In addition to the geometry and spacing of the conductors, it should be understood that the above-noted conductors may be made from any appropriate material. For example, the conductors may be made from copper or any other appropriate conductive material capable of having a tennis ball induce an electric field therein. Additionally, in some embodiments, it is desirable to coat the conductors with another metal that is resistant to corrosion to enhance the corrosion properties of the sensor. Appropriate metals for coating the conductors include, but are not limited to, tin, gold, or other similar metals capable of resisting corrosion.

[0028] As noted above, while the conductors may be directly attached to the playing surface of the court, in some embodiments, the conductors are either attached to, or embedded in, a substrate. The use of a substrate may offer multiple benefits including, for example, easier installation of the final sensor on a playing surface because the substrate is relatively easy to position while maintaining the conductors in the desired positions and orientations. The conductors may be attached to the substrate in any appropriate fashion including pressure, adhesives, bonding with the substrate material during formation, an interference fit, or any other appropriate method. After forming the one or more sensors including the three or more parallel conductors and the associated substrate, the sensors can be assembled onto, or embedded in, a playing surface using adhesives and/or pressure, though other appropriate methods might also be used. The one or more sensors can be arranged in any appropriate pattern as described in more detail below. It should be understood that any appropriate substrate could be used including, but not limited to, a dielectric layer. In some embodiments, the substrate is flexible to facilitate both storage of the sensor as well as positioning of the sensor during installation. In instances where the substrate is both flexible and includes an adhesive, the substrate may function as a line tape that can be easily applied to acrylic "hard" courts, PVC carpet courts, grass courts, clay courts and other appropriate types of courts. Additionally, in some embodiments, the playing surface itself might be considered the substrate.

[0029] In some embodiments, the conductors are insulated from one another to prevent direct conduction between the conductors. Therefore, in one embodiment, the individual conductors are insulated. For example, insulated wires might be used.

Alternatively, an insulating layer may be provided on top of the conductors to provide the desired insulation. Appropriate insulating layers can include, but are not limited to, appropriate plastics, rubbers, insulating varnishes such as enamels, or other appropriate materials with an appropriate resistivity. Depending on the application, the resistivity of the material may be greater than about 10 ¹⁰ Ohm*cm. However, embodiments in which the resistivity material is less than 10 ¹⁰ Ohm*cm may also be possible. The thickness of the insulation on the wires and/or the insulating layer may be less than about 0.3 mm, 0.1 mm, or any other appropriate thickness as the current disclosure is not so limited. In embodiments where the conductors are either embedded in, or coated with, an insulating material, it is preferable that the insulating material coating the sensor be appropriately colored to avoid applying separate paint to the sensor. However, depending on the thickness of the paint and the insulation, embodiments in which a separate paint is applied to an already insulated sensor are also possible.

[0030] While the above embodiment describes the use of insulation on the individual conductors and/or in insulating layer to prevent direct conduction between the conductors, in some instances a sensor may be provided without insulation or an insulating layer on at least a top surface of the conductors. Such an embodiment may be appropriate for use in a playing surface that is made from, painted with, or coated by a material with an appropriate resistance since this material can provide the desired insulation between the conductors. It is desirable that the material coating the sensor have a resistivity that is greater than or equal to 10 ¹⁰ Ohm*cm though other resistivities may also be possible. In one embodiment, a sensor excluding the above-noted insulation and/or insulating layer may be painted with an epoxy- based tennis line paint with an appropriate resistance. For example, the epoxy insulating enamel R-831-S; from the company "Jiaxing Rota-Ropa insulating material Co. Ltd", China could be used. The resistivity of this insulating enamel is equal to 10 13 Ohm* cm in normal (dry) conditions and is equal to 10 ¹⁰ Ohm*cm in wet conditions (after immersion in water for 24 hours). In another embodiment, a simple acrylic coloring can be used to paint the playing surface and/or the sensors. Examples of acrylic colorings that might be used include

"Plexipave" by California Paints and "Nova Acrylic" by Nova. In yet another embodiment, the sensor including uninsulated conductors could be assembled on an acrylic "hard" court such that it is covered by an acrylic surface coating, an acrylic line paint, or an acrylic glue.

[0031] After positioning one or more sensors in a desired pattern on a playing surface, the one or more sensors can be connected to an amplifier in order to amplify the signal induced in the sensors by a tennis ball. Depending on the embodiment, the amplifier can be a low noise amplifier including one or more appropriate filters. It should be understood that the various characteristics of the amplifier such as the gain coefficients, the bandpass filter frequencies, as well as other characteristics, may be optimized for any particular sensor design and installation pattern. In one embodiment a bandpass filter may be used that filters frequencies less than about 1 kHz to 10 kHz and frequencies greater than about 10 kHz to about 100 kHz. The high frequency filter value should be greater than the low-frequency filter value. In another embodiment, the bandpass filter may filters frequencies less than about 2.0 kHz to about 5.0 kHz and greater than about 100 kHz.

[0032] As discussed in more detail below, the amplifier can be used to facilitate two separate modes of sensor operation. These modes of operation include a contact sensor mode where a detected signal corresponds to a ball contacting the sensor and a trajectory sensor mode where a detected signal corresponds to a ball passing near, but not contacting, the sensor. These modes of operation may either be performed individually or simultaneously as the current disclosure is not so limited. As discussed in more detail below, in some embodiments two sensors may be used to act separately as the contact sensor and the trajectory sensor. In such an embodiment, two separate amplifiers may be used with the separate sensors.

[0033] The one or more amplifiers are connected to one or more appropriate processors in order to process the output signals and determine whether or not a ball has struck inbounds or out of bounds. The processor may be embodied by any appropriate system including, but not limited to, a computer processor, processors integrated with one or more components of the sensor, or any other appropriate device capable of processing the signals. It should understand that the specific signal processing conducted by the processor to determine whether a ball had struck inbounds or out of bounds will depend on the specific sensor used as described in more detail below. After determining whether a ball has struck inbounds or out of bounds, the processor may activate one or more appropriate indicators such as a light and/or sound indicator. For example, during a tennis match, appropriate signals such as a sound signal in an ear-phone or a green lamp light signal could be given in real-time to a linesmen and/or chair umpire when a ball hits on or near a line. The linesmen and the chair umpire could then use this information to make a final decision. In the case of a home court or a tennis club court, an appropriate sound signal could be given in a loud form and/or a light signal could be given when the ball hits on or near the line. The players could then use this signal to make a decision such as whether or not to continue to play the game. In addition to indicating that a ball is "in" or "out", in some embodiments, the processor may also have the ability to determine, and output, a confidence level based on the detected signal, or signals, used to make the determination of the ball being "in" or "out".

[0034] In view of the above, the various embodiments of a sensor disclosed herein identify signals resulting from the induced electrical signal in three or more conductors from a charged ball, or other object, based on the position and velocity not force. As a result, the ability to accurately detect the proximity and location of a ball relative to the sensor is significantly increased relative to conventional sensors. Thus, the described sensors are appropriate for detecting signals from very soft shots as well as very hard shots while maintaining a desired accuracy.

[0035] Turning now to the figures, several nonlimiting examples of the currently disclosed sensors as well as their methods of operation and incorporation into a playing surface are described. However, it should be understood that the current disclosure is not limited to only the embodiments shown in the figures. Instead, various modifications might be made to the depicted embodiments, or various features of the depicted embodiments might also be combined with one another.

[0036] For the sake of clarity, the depicted sensors do not include an insulating layer, insulation on the conductors, or any other insulating coating. However, it should be understood that the depicted sensors can include any of the various types of insulation noted above. Additionally, for the sake of clarity, the embodiments described herein are also directed to sensors detecting the position and/or trajectory of a charged ball, but the disclosed sensors and their methods of use could also be used to detect the position and/or trajectory of other charged objects as well. It should also be understood, that while the embodiments and figures describe sensor systems for use on a tennis court playing surface, the sensor systems disclosed herein could be used with any appropriate ball playing surface or other surface where it is desirable to track the position and/or trajectory of a charged object.

[0037] Fig. 1 depicts an embodiment of a sensor including a substrate 2 and four conductors 4-10 disposed on the top surface of the substrate 2. The depicted conductors 4-10 have flat cross- sectional profiles extending in a direction L corresponding to a long axis of the sensor. The conductors 4-10 and are also depicted as being parallel to one another and arranged in the same plane. The conductors 4-10 are connected to an amplifier 12 at one end of each conductor. While the same ends of the conductors have been depicted as being connected to the amplifier 12, embodiments in which different ends of the various conductors are connected to the amplifier are also possible. In the depicted embodiment, the conductors 4-10 are not connected to one another. While straight conductors have been depicted, it should be understood that the conductors might be arranged in another pattern including, for example, a serpentine pattern.

[0038] Similar embodiments of a sensor are depicted in Figs. 2 and 3. In these embodiments, the sensor again includes a substrate 2 as well as four conductors 4-10.

However, in Fig. 2 the conductors 4-10 are embedded in the substrate 2. Additionally, as noted above while flat elongated conductors 4-10 have been depicted in Figs. 1 and 2, as depicted in Fig. 3, the conductors 4-10 may also have different shapes such as a circular cross sectional shape.

[0039] As illustrated in Fig. 1, the conductors 4-10 are spaced from one another by a pitch D measured from centerline to centerline and have a thickness t as well as a width w. The sensor may have an overall height H. Without wishing to be bound by theory, in some embodiments, it is desirable to minimize the distance between the conductors 4-10 of the sensor and a playing surface to improve the accuracy of the sensor. For example, with regards to a sensor for use on a tennis court, the conductors may be spaced less than or equal to 1 mm from the playing surface or between 0.1 mm to 0.2 mm inclusive. Therefore, in an embodiment in which the substrate is disposed on the playing surface, the height H may be less than or equal to 1 mm or between 0.1 mm to 0.2 mm inclusive. Additionally, the pitch D may be between or equal to 0.1 mm to 10.0 mm. For example, the pitch might be between or equal to 0.5 mm to 1.5 mm for a contact sensor. Alternatively, the pitch D could be between or equal to 3 mm or 5 mm for a trajectory sensor. In instances where a sensor is used as both a contact sensor and is a trajectory sensor, the pitch D might be between or equal to 1 mm to 2 mm. In embodiments where the combined sensor including a substrate 2 and conductors 4- 10 is used as a line sensor a thickness t of the conductors may be between or equal to 50 μιη to 100 μιη. In some embodiments, the width of the conductors is between or equal to 0.6 to 0.8 times the pitch D. While particular values and relationships are given for the dimensions noted above, it should be understood that the pitch D, thickness t, width w, and height H will be different for different applications and that the current disclosure is not limited to only the dimensions described above. [0040] It should be understood that the conductors 4-10 may be connected to the amplifier in any number of different fashions. For example, in one embodiment, the two exterior conductors 4 and 10 might be connected to the positive inputs of the amplifier and the two interior conductors 6 and 8 may be connected to the negative inputs of the amplifier. In such an embodiment, the sensor may be viewed as two combined sensors both including two conductors. In another embodiment, the two interior conductors 6 and 8 may be connected to the positive and negative inputs of the amplifier and the two external conductors 4 and 10 may be connected to ground. Operation of this particular embodiment is described in more detail below.

[0041] Without wishing to be bound by theory, the physical mechanism of the signal generation in the four conductor sensor is as described below in regards to Figs. 4 and 5. The relative sizes of the ball and sensor in these drawings are not to scale. Generally, the signal of the four conductor sensor is produced as a result of electrostatic induction of the conductors 4-10. More specifically, the electrical charges induced in the conductors 4-10 of the four conductor sensor are induced by the electrical charges that are located on the ball 14 and/or on the court surface, not depicted. The electrical charges on the ball 14 and on the court surface appear as a result of a triboelectric effect when the ball 14 rubs against the court surface and electrical charges of opposite sign are generated on the court surface and the ball 14. The ball 14 can also become electrically charged through interactions with other objects such as a racket, a person's hand, and the air to name a few.

[0042] In general, the generation of electric charges on the ball and/or on the court surface during any given ball bounce or impact plays no significant role in signal generation. Instead, a ball is usually already electrically charged up to saturation level through previous interactions with the various objects noted above. For this reason the electrical charge of the ball does not vary significantly during any single bounce or impact and can be treated as constant. Therefore, the signal produced by the sensor can be assumed to be due to an electrically charged ball that is charged to the saturation level. It is possible that a ball might not be charged to saturation level in some instances. For example, the electrical charge of the ball might be low before the bounce if the ball was "grounded" for a long enough time and the resulting signal might be of a different form and/or a lower value. However, after several strokes and bounces (or after interaction with other objects) the ball would be charged and normal sensor detection would be restored. While the ball is generally considered to be at the saturation charge, it should be understood that the current disclosure is not limited to only considering signals generated by balls, or other objects, that are charged to the saturation level. Instead, a sensor system might also include considerations to account for conditions that might result in a ball that does not charge to the saturation level.

[0043] Without wishing to be bound by theory, the amplitude of the signal induced in the conductors 4-10 is dependent on the ball speed, the value of electrical charge located on the ball, and the distance of the ball relative to the conductors. Signal generation during a contact event between the ball and the sensor is discussed with regards to the Fig. 4. A more complete discussion of the physical phenomenon is provided in the examples below. In the figure, a ball 14 has either impacted, or skidded onto, the conductors 4-10 of the sensor. The ball 14 has compressed such that its "footprint" contacts multiple conductors while it is on the ground. The resulting signal induced in the conductors 4-10 due to contact with the footprint of the ball 14 is produced due to the electrical charges located on the balls surface contacting the sensor between the external wires of the four conductor sensor. The value of the resulting signal is proportional to the difference between the electric currents induced in the two internal conductors 6 and 8 of the four conductor sensor. Due to the approximately constant surface density of electrical charge on the ball noted above, the form of the induced signal versus time is mainly determined by the behavior in time of the ball footprint. More specifically, there are two sharp peaks in the induced signal corresponding to the when the edges of the footprint cross the sensor edges. These two peaks may be above a preselected threshold that is greater than a signal associated with a ball that does not contact the sensor. The influence of charges located in areas outside of the sensor may be shielded by the external wires 4 and 10 of the four conductor sensor which are connected to ground.

Additionally, the sensor may also be combined with a differential amplifier to further reduce the detected signal associated with charges located outside of the sensor area.

[0044] As noted above, in some embodiments, the sensor is shielded from charges located outside of the sensor. Consequently, in embodiments where the sensor is included in a line, the sensor may be located on an outside border of the line. Therefore, a contact signal will only occur when the ball footprint has contact with at least an outer edge of the line. This may be of particular benefit when the sensor is used in the game of tennis where contact with an outer edge of the line by the footprint of the ball is sufficient to make an "in" or "out" ruling. [0045] As noted previously, the accuracy of a sensor is determined by the distance between the conductors in the sensor, i.e. the pitch D, and by the distance between the conductors and the court surface, i.e. the height H. More specifically, and without wishing to be bound by theory, both the pitch D and the height H may be minimized to improve the accuracy the sensor. For example, to provide a desired accuracy in ball position

determination of about 1 mm to about 2 mm, a four conductor sensor used to detect ball contacts might have a pitch D of about 1 mm and a height H of less than about 1 mm or 0.1 mm - 0.2 mm.

[0046] While the signal generated by the sensor is generated mainly when the ball 14 hits the sensor. The signal of the sensor could be also generated by a player foot, not depicted, that hits the sensor, or moves near the sensor, due to charges that have accumulated there as well. The signal of the ball when it is not in contact with the sensor can also be a source of interference with detecting a contact. However, the amplitude of the signal generated by the moving ball and by the moving player can be substantially reduced by the appropriate signal processing and/or filters such that the signal from these sources is much lower than the signal from a ball 14 that hits the sensor as depicted in Fig. 4. The signal from a ball 14 that hits the sensor may be differentiated from the signal from a moving ball and from a signal from the moving player using appropriate threshold values, the form of the signal, and/or signals from other sensors. Because of this accuracy, the sensor may be used to confirm whether the ball hits the line or not when it is operated in a contact sensing mode.

[0047] In addition to providing a contact sensor, a separate sensor, or in some embodiments the same sensor, can be operated as a trajectory sensor to sense a trajectory of a ball 14 that does not contact the conductors 4-10 of the sensor as depicted in Fig. 5. As described in more detail below, the induced electric signal in the conductors can be used to determine if the ball rebound place is located in the "in" region or in the "out" region.

[0048] When operated as a trajectory sensor, the conductors 4-10 are again arranged and monitored as noted above. However, in this embodiment, the electric charge is induced in the conductors 4-10 by a ball 14 that has a trajectory as indicated by the arrow that does not contact the sensor, see Fig. 5. If the amplitude of a detected signal is higher than a predetermined threshold value (Ul _th ) the signals received from the trajectory sensor are both measured and recorded for a predetermined amount of time. It is desirable that the threshold value Ul _th be set as low as possible but high enough to exclude expected noise in the signal. For example, the threshold value might be equal to 10 ^" x Ulm; where Ulm is the amplitude of the signal from the trajectory sensor when the ball rebound is located close to the sensor but the ball does not hit the sensor and the measurement duration might be up to about 50 milliseconds. However, other durations and threshold values might be used as well.

Additionally, in some embodiments, a signal from a contact sensor may also be measured and recorded at the same time.

[0049] Without wishing to be bound by theory, the sign of the signal received from a sensor acting in a trajectory mode will be different for the balls located in the "in" and in the "out" regions. For example, in the current embodiment, the signal of the sensor operating in a trajectory mode depends only on the position of the ball with respect to the sensor and is not dependent on the ball speed. Since the signal is determined based on the difference of the induced signal between the two interior conductors 6 and 8, the signal is equal to zero when the center of the ball is located just opposite the sensor and is equidistant to the two interior conductors 6 and 8 as depicted in Fig. 5 because the signal induced in each conductor is equivalent at that point. Therefore, as a ball approaches the midpoint of the sensor from either side, a magnitude of the induced signal will increase until it reaches a peak and then decrease to zero as the ball 14 reaches a location corresponding to the midplane of the sensor. As the ball continues to the other side of the sensor midplane, the sign of the signal will reverse and grow in magnitude until another peak is reached and the signal then decreases in magnitude as the ball moves out of range of the sensor.

[0050] It should be understood that the sign of the detected signal will depend on the arrangement of the conductors. For example, conductors 6 and 8 might be arranged as positive negative or negative positive. However, for the sake of clarity, an embodiment in which the induced signal is positive when the ball is located in the "in" region and the signal is negative when the ball is located in the "out" region is discussed below. Additionally, while a particular arrangement of the conductors and pattern of signals is discussed below, embodiments in which other arrangements and/or signal processing strategies are used are also possible.

[0051] In view of the above, the sign of the signal may be used to indicate the side on which the ball is located and the magnitude can be related to the distance of the ball from the sensor. Therefore, monitoring the shape and magnitudes of the signal can be used to determine the trajectory of the ball and whether or not the ball bounce location is in the "in" or "out" regions. Specific types of trajectories and the expected signals are discussed further below.

[0052] In one instance, a ball crosses the sensor. Due to the ball 14 approaching the sensor from one side, passing over the middle of the sensor corresponding to zero signal, and then moving away from the sensor on the other side, the expected signal may correspond to a sinusoidal wave. Therefore, the signal will have two peaks of different sign in the first and in the second half of the signal respectively. The amplitude of the "positive" signal in one half of the signal may differ in terms of the absolute value from the amplitude of the "negative" signal in the other half of the signal. Depending on the specific embodiment as well as the position and trajectory of the ball, this difference may be about a factor of 1.5, but it might be higher if the ball is located close to the sensor. Additionally, this difference in magnitude of the peaks may be used to determine in what direction the ball was travelling.

[0053] Again assuming that a positive signal corresponds to the "in" region, if the amplitude of the "positive" signal is lower in magnitude than the amplitude of the "negative" signal, it means that the ball was located closer to the sensor, and thus at a lower height, as it passed into the "out" region. Assuming that the ball originated from the "in" region this corresponds to a ball having a downwards trajectory over the sensor and into the "out" region. This type of signal would correspond to an "out" signal. If such a sensor was combined with a contact sensor, and no signal was detected from the contact sensor, this would indicate that the ball was "out" and also did not contact the line. If instead the signal from the contact sensor indicated a contact had occurred, the ball would be ruled as "in" independently of the signals from the trajectory sensor. Somewhat similar to the above, if the amplitude of the "positive" signal is higher in magnitude than the "negative" signal, it means that the ball was located further from the sensor, and thus at a greater height, as it passed into the "out" region. Assuming that the ball originated from the "in" region this corresponds to a ball having an upwards trajectory over the sensor and into the "out" region. This type of signal would correspond to an "in" signal.

[0054] In other instances, the trajectory of the ball does not cross the sensor, or it crosses the sensor at a large height H where the induced signal is below the detection threshold of the sensor. In these types of instances, the signal induced in the sensor will be unipolar (only "positive" or only "negative"). Assuming a detection limit of about 10 cm and velocity of about 20 m/sec the detected signal may be on the order of about 5 msec in duration, though depending on speed and detection limits other durations are possible. In view of the above, a unipolar peak of an appropriate duration can be interpreted as the ball impacting the ground on one side of the sensor and depending on whether it is positive or negative, the impact location can be determined as being "in" or "out".

[0055] Without wishing to be bound by theory, if the ball 14 directly hits the conductors 4-10 of the sensor depicted in Fig. 5 acting as trajectory sensor, the detected signal could be several times, for example up to 10 times, higher than the signal from a ball that misses the sensor. This information could be used to affirm that the ball is "in". It should also be noted that it may be difficult to use a trajectory sensor to discriminate between a ball that hits the sensor and a ball that has a near miss relative to the sensor. Thus, in some embodiments, and as noted above, it may be desirable to also use a separate contact sensor, or a sensor capable of acting as both a contact and trajectory sensor, to give more reliable results. However, embodiments in which a trajectory sensor is used alone are also possible.

[0056] Similar to a contact sensor detecting a signal from a footfall, a sensor acting as a trajectory sensor may also detect signals generated by the moving foot of a player that are very similar in amplitude and form. Therefore, it may be difficult to differentiate a signal from the moving ball and a signal from the moving foot of the player in the case of a trajectory sensor for all possible variations of the ball movement and the player movement. Consequently, in some embodiments, trajectory sensors may not be used to control the entire game when a player could be located somewhere near a line. However, embodiments where a trajectory sensor is used by itself are also possible. For example, a trajectory sensor could be used to control the service boxes in tennis when the ball is served because in this case there is no player located near the line. Additionally, when the trajectory sensor is used in combination with a contact sensor as noted above, the trajectory sensor may help to differentiate the signal from a ball that hits the sensor and a signal from a foot that hits the sensor.

[0057] In another embodiment, the sensor includes three parallel conductors 4-8 disposed on, or embedded in, a substrate as depicted in Figs. 6 and 7. Again these sensors may correspond to a contact sensor as depicted in Fig. 6 and/or a trajectory sensor as depicted in Fig. 7. In the depicted embodiments, the internal conductor 6 is connected to the input of an amplifier and the two external conductors are connected to ground. However, other arrangements are also possible. Similar to the embodiment described above, the conductors 4-8 are parallel to each other and are preferably located in the same plane on the playing surface. Additionally, the conductors may either be individually insulated, or an insulating layer may be disposed on top of the conductors and the top surface of the substrate 2. The insulating coatings and/or layers are not depicted in the figures for the purposes of visualization. The conductors 4-8 may be made from the same materials as noted above for the four conductor sensor. The conductors 4-8 may also be any appropriate shape or size and may be spaced from each other by any appropriate distance for the intended application. In one embodiment, and as depicted in figures, the conductors 4-8 may be flat conductors embedded in the underlying substrate 2. While it may be possible to use the three conductor sensor as a contact sensor, it may be preferable to use the three conductor sensor as a trajectory sensor. When used as a trajectory sensor, the pitch D for the three conductors 4-8 may be between about 10 mm to 20 mm inclusively, though other pitch distances are also possible.

[0058] Without wishing to be bound by theory, the physical mechanism of the signal generation in a three conductor sensor used as a trajectory sensor is as follows. Similar to the description above, the signal is again produced as a result of electrostatic induction in the conductors 4-8 by the charges located on the surface of ball 14. Also, the three conductor sensor can again be used to determine the relative position and trajectory of the ball with respect to the playing surface to determine whether a ball is "in" or "out". The generated signal will have an amplitude that is inversely proportional to the square of the distance between the ball and the sensor (i.e. the height of the ball with respect to the court surface). The signal will also have two peaks of different sign in the first and in the second half of the signal respectively when the ball crosses the sensor. The magnitude of the signal in the first half of the signal generally differs from the magnitude of the signal in the second half of the signal and is usually about 10% or 20%, though other differences in magnitude are also possible. In instances where the ball does not cross the sensor, or impacts on one side and passes over the sensor at a height greater than the detection limit, the signal will be unipolar similar to that described above for a four conductor sensor. Typical amplitudes of the detected signals may be on the order of about 0.5 V to about 5 V. For the purposes of tennis, the typical duration of the signal may be on the order of T = H/V, where H is the detectable height of the ball and V is the speed of the ball. For H = 10 cm and V = 20 m/sec the expected value of T is about 5 milliseconds. [0059] Without wishing to be bound by theory, the sensitivity of the depicted sensor

(the detectable amplitude of the signal) increases with the increasing value of the distance between the conductors, is proportional to the speed of the ball, and is inversely proportional to the square of the height. So, if the height of the ball near the sensor is about 5 cm when the ball has a bounce within 20 cm to 50 cm from the sensor, the signal will be about 9 times higher than in the case when the height of the ball near the sensor is about 15 cm when the ball has a bounce within 60 cm to 150 cm from the sensor.

[0060] Turning now the types of signals that might be detected, if the signal includes two peaks of opposite sign, the ball has passed over the sensor. If the amplitude of the signal in the first half is lower (in absolute value) than the amplitude of the signal in the second half, the height of the ball is decreasing in time as it passes over the sensor. Consequently, the ball trajectory most likely corresponds to a contact with the court in the "out" region. In contrast to the above, if the amplitude of the signal in the first half is higher (in absolute value) than the amplitude of the signal in the second half, the height of the ball is increasing in time as it passes over the sensor and the ball most likely contacted the court in the "in" region.

[0061] If the ball moves in the opposite direction, for example, from the "out" region to the "in" region as might occur for the side line in tennis, the sign of the sinusoidal like signal from the sensor will be changed. In this case, another but similar algorithm of signal processing could be used to determine whether the ball was "in" or "out". If the amplitude of the signal in the first half is lower (in absolute value) than the amplitude of the signal in the second half, the height of the ball is decreasing in time as it passes over the sensor and as a consequence the ball likely contacted the court in the "in" region. Correspondingly, if the amplitude of the signal in the first half is higher (in absolute value) than the amplitude of the signal in the second half, the height of the ball increases in time as it passes over the sensor and as a consequence the ball likely already contacted the court in the "out" region.

[0062] With regards to dealing with unipolar signals, the sensor may be operated in a fashion similar to that described above with regards to the four conductor sensor.

[0063] Without wishing be bound by theory, it should be noted that there are several mechanisms that may result in the generation of a false signal in the above described sensors. These mechanisms are described in more detail below together with the difference between the true signals associated with the ball impact and false signals associated with other things. Generally, the desired signals can be discriminated from these false signals through the use of the signal duration, the signal form, and/or the correlation between the signals from different sensors.

[0064] In the case of a contact sensor, the moving ball can produce a false signal in the sensor when it passes close enough even though it does not contact the court surface where the contact sensor is located. This false signal can be substantially reduced using the symmetric conductor layout scheme noted above for the four conductor sensor and through the use of a differential amplifier. Therefore, this false signal will have a lower amplitude and will vary in time more slowly in comparison with the true signal. Further, this false signal will not have very short pulses in the beginning and in the end of the signal like a ball contact signal. The false signal will instead have likely have two maximum values during the middle portions of the signal. Therefore, the contact sensor may discriminate these false signals based on the duration of the pulse, the location of the peaks in the signal, and/or the amplitude of the peaks.

[0065] In another instance, electric break down can occur between the ball and the playing surface resulting in an electric discharge (a spark) in the air between the charged ball and the charged court surface since they have charges of opposite sign. Usually the electric discharge may appear just after or soon after the ball leaves the court surface, near the end of the true signal. This electric discharge in air may produce a very high magnitude and very short duration current in the sensors as compared to the true signal. This false signal is usually unipolar and has an amplitude that is several orders of magnitude higher than the true signal and the duration is less than about 1 ms at the input of the amplifier. This signal may also be detected substantially simultaneously on multiple, and sometimes all of the sensors, located both close to the ball and further away from the ball. At the output of the amplifier this signal generally has reached the saturation amplitude of the amplifier output

(approximately equal to the power supply voltage) and a duration approximately equal to the characteristic time of the amplifier output. Such a signal output from the amplifier can be easily discriminated from the various types of outputs noted above from the true signal based on the magnitude, duration, shape, and/or number of simultaneously activated sensors.

[0066] Another possible source of a false signal includes signals induced by sources of electromagnetic interference such as sources with frequencies of about 50 Hz, though other frequencies are also possible. This interference can again be minimized through the use of the symmetric scheme of the four conductor sensor noted above and the use of a differential amplifier as the first input stage of the amplifier. Frequency filters can also be used to further reduce this interference if necessary. Appropriate threshold values can be used to distinguish this type of false signal.

[0067] As noted previously, a false signal can also be produced by a player's moving foot. However, this signal generally has a duration that is longer than the true signal associated with a ball. For example, the signal associated with a player's foot may be on the order of about 50 ms or longer as compared to 10 ms or less for a true signal. Additionally, the signal form induced by the movement of a player's foot may have more than two oscillations corresponding to the more complicated contact area behavior between various forms of shoe soles and the sensor. Consequently, the duration of this type of false signal as well as its shape and information from other sensors can be used to discriminate signals from a player's foot.

[0068] A false signal can also be cause by air bubbles located between the court coating material and the court surface. To avoid generation of such a false signal, it is desirable that the sensor be fixed to the surface of the court over its entire length without air bubbles between the court coating material and the court base. Therefore, care should be taken to minimize the presence of bubbles at least near the sensors. However, it should be understood that the use of the currently disclosed sensors are not limited to instances where no bubbles are present.

[0069] Having described both the sensors and their methods of use above contact sensors and trajectory sensors, it should be understood that these sensors can be used either separately or in combination. Additionally, the combination of a contact sensor and a trajectory sensor, either as separate sensors or as a single sensor acting in both modes, allows the resulting sensor system to provide comprehensive monitoring and control of the game with the use of real-time signals indicating whether a ball was located in an "in" or "out" region.

[0070] The contact sensors and trajectory sensors both have limitations with regards to their ability to sense the position of a ball. Further, and without wishing to be bound by theory, generally, the signal from a ball that hits a sensor is higher than the signal from the ball that misses the sensor. Therefore, as noted above, in some embodiments, it is desirable to use one or more trajectory sensors and one or more contact sensors to monitor the position of the ball. However, when monitoring multiple signals, it is necessary to decide when a ball is in or out based on those multiple signals when the signals do not agree. Therefore, in one embodiment, if the processing of the signals for one of the sensors results in the conclusion that a ball is "out" then the processor can make the determination that the ball is "out", even if some other sensors indicate that the ball is "in". Correspondingly, if the processing of the signals for all the sensors indicate that the ball is "in" then the ball is "in".

[0071] In addition to making determinations when the conflicting signals are provided by multiple sensors, the detection areas and accuracy of the multiple sensors, and/or a single sensor constructed to act as both a trajectory and contact sensor, can be selected based on the requirements of the game. For example, a sensor system can be designed to monitor a desired sensing area around the lines on a court. Without wishing to be bound by theory, the sensitivity of a sensor as described above is proportional to the pitch squared (D ).

Therefore, as noted above, the conductors of a trajectory sensor may have a pitch D that is between or equal to about 3 mm to 5 mm. This pitch would permit the sensor to have sensitivity sufficient to monitor a controlled zone up to about 50 cm to 60 cm wide. While it should be understood that the contact sensors and trajectory sensors may have any appropriate dimensions as noted above based on various design considerations and application, in at least one embodiment a pitch D between 3 mm to 5 mm is used for a trajectory sensor. Because such a sensor would likely be unable to discriminate between a ball that hits a sensor and a ball that misses the sensor a corresponding contact sensor may have a smaller pitch D as noted previously.

[0072] In view of the ability to create a large controlled area using a single sensor, it is possible to provide sensors that are located only in the lines of a court, though other positions are as possible. Therefore, installation of sensors in the other parts of the court within the "in" and/or in the "out" regions may not be needed. The need to use fewer sensors offers multiple benefits such as simplified sensor layouts, reduced installation costs, and reduced system costs. Additionally, in embodiments where the sensors are simply adhered to the playing surface, the sensors do not change the court surface, and instead simply change the lines of the court slightly. Also, the currently disclosed sensors offer improved signal generation and help to eliminate problems such as shorting of sensors powered by batteries and coated with acrylic paints, or other electrically conductive paints because the sensor is totally insulated and in some embodiments is not covered by a court surface coating material, such as an acrylic paint. All of these benefits promote the usability of these sensor on acrylic ("hard") courts, PVC courts, grass courts, clay courts, and other types of courts as well. The sensors are also appropriate for home courts, club courts, and official tournaments.

[0073] In one embodiment, a combined sensor system installed in a court may include two sensors for monitoring the position of a ball relative to a line. The two sensors may include a three conductor trajectory sensor located near the internal edge of the line and a four conductor contact sensor located near the external edge of the line. By appropriately selecting the dimensions of the sensors, it may not be necessary to include other sensors in the "in" and/or in the "out" region of the court as noted above. However, it should be understood, that other arrangements with a single sensor or more than two sensors as well as sensors with different numbers of conductors are also possible.

[0074] The above described sensors may be installed in a court in any appropriate manner. For example, one or more sensors may be affixed to a playing surface by an adhesive, or by using another appropriate attachment method, along substantially its entire length. In some embodiments, the one or more sensors may also be fixed in position relative to the surface coating material located either above or below the sensor. In embodiments where the one or more sensors are installed in an acrylic court, the material located just above (i.e. opposite) the sensor may be a material other than the acrylic coating material of the court. For example, a polyurethane material might be used to coat the sensor. This approach may be of particular use in locating the sensor in the line of a court where the line paint may be a polyurethane enamel, nitrocellulose enamel, or some other kind of paint or enamel with appropriate electrical resistivity. While the sensors may be located in the lines of a court, the sensors may also be located in the "in" and/or "outs" regions of the court as well as the disclosure is not so limited. In such an embodiment, the coloration of the material applied to, or coating, the sensors may be appropriately selected to match that of the court.

[0075] If the conductors of a particular sensor are made from uninsulated material, and the sensor is installed in an acrylic court, the sensor could be covered by an acrylic glue, the acrylic court surface coating material itself, or an acrylic line paint. However, in instances where a sensor is covered by the above-noted acrylic materials, it is preferable that the conductors associated with the sensors not be covered by an initial layer of non-acrylic materials with a high value of electrical resistivity such as polyurethane or epoxy materials. In addition to the above, if a sensor including uninsulated conductors is installed in an acrylic court and a fiberglass mesh is used to fix the sensor in place, it is desirable that the fiberglass mesh be rare enough so that the acrylic court surface coating material used to cover the mesh may have sufficient electrical contact with the conductors of the sensor. For example, the fibers of the fiberglass mesh may be distanced from one another with a dimension that is greater than a dimension of sand particles in the court surface coating material. If glue is used to fix the fiberglass mesh on the surface of the conductors of the sensor embedded in the acrylic-based court, is preferable that the adhesive be the acrylic glue, not polyurethane glue or other similar glue with a high value of electrical resistivity. It should be understood that other adhesives are also possible.

[0076] As noted previously, and without wishing to be bound by theory, in order to provide a high accuracy measurement with the sensors, it is desirable that the distance between the conductors of the sensor and the court surface be minimized in areas such as in the lines of a court. The distance between the conductors and the court surface may be equal to 1 mm or less or in some embodiments between about 0.1 mm to 0.2 mm inclusively. To further aid in the accuracy and sensitivity of the sensor, in some embodiments, the sensor is not covered by the court surface material and is instead covered using a special line paint or pre-applied insulating coating with an appropriate coloration.

[0077] In embodiments where a contact sensor is located in a line, the contact sensor may be arranged such that an external conductor of the contact sensor is arranged adjacent to an external edge of the line. The other conductors of the contact sensor could then be located in the "in" region with respect to the line edge. However other arrangements, including the use of contact sensors and trajectory sensors in multiple locations both in and outside of lines on a court, are also possible.

[0078] It should be understood that the contact and trajectory sensors described herein may be laid out in any appropriate pattern. This pattern may include multiple sensors arranged in linear patterns or one or more sensors laid out along a serpentine path.

Additionally, a single sensor could be defined by combining multiple segments of sensors together in multiple ways to define a single electronic circuit. Without limitation, this could include multiple parallel sensors 20 that are connected to a primary sensor 22 as depicted in Fig. 8. This incorporation of multiple parallel sensors may be done using appropriate analog circuitry or any other appropriate method. It should be understood that each of the sensors 20 could have been provided as a separate circuit and connected via any appropriate connection to merge the signals into a single analog circuitry. However, by combining the sensors 20 with a primary sensor 22, an action on any portion of the combined circuit would be as if primary sensor 22 had sensed the impact or trajectory of the ball. In addition to acting as a single circuit, the multiple parallel sensors 20 and/or the primary circuit 22 may be integrated with a flexible printed circuit FPC to aid in positioning, connecting, and installing these sensors on a playing surface. Such an embodiment is shown in Fig. 9 where sensors 24 and 26 are combined in a flexible printed circuit 28. Therefore, a single section of FPC could include multiple portions of different unconnected circuits, and/or interconnected circuits, such that when differing areas are connected to other sub-circuits, multiple separate and complete circuits may be defined.

[0079] Fig. 10 depicts multiple sensors positioned on half of a tennis court which are connected using flexible printed circuits in order to simplify installation. As depicted in the figure, a plurality of flexible printed circuits 30 are connected to a corresponding plurality of sensors 32 that are laid out in straight lines between the flexible printed circuits 30. In some embodiments, the plurality of sensors 32 might simply be cut from a roll of sensor material, positioned on the playing surface, and attached to the appropriate flexible printed circuit 30 in order to install the sensors. The particular pattern in which the flexible printed circuits 30 are arranged is selected to permit the interconnection of sensors in appropriate locations on the playing surface. However, it should be understood that other patterns of the flexible printed circuits 30 and/or the sensors 32 are also possible.

[0080] Fig. 11 also depicts multiple sensors positioned on top of the tennis court.

However, in this particular embodiment, nine separate sensors 34-50 are positioned in a serpentine pattern on the court to define the areas. These individual sensors 34-58 are connected to one or more output circuits 52 that may either be attached to separate amplifiers or a single amplifier depending on the embodiment. The output signals can then be processed individually or together as the disclosure is not so limited. Additionally, the sensors may either be all contact sensors, all trajectory sensors, a combination of the two, or all of the sensors could incorporate both contact and trajectory sensing capabilities. While a particular layout has been depicted in the figure, it should be understood that other configurations are also possible.

[0081] Several examples regarding the theory of how the sensor functions as well as possible embodiments of various components associated with a sensor system are described below. However, it should be understood that the following descriptions and explanations are by way of example only and are not intended to limit the current disclosure in any way.

[0082] Example: Trajectory Sensor

[0083] Without wishing to be bound by theory, the theoretical model of the sensor signal generation is based on the well-known solution of the physical problem related to the electric field induced by the point charge in the infinite metal plane.

[0084] The induced electric field is given by the equation

[0085] E = 2 Q _b z (x ² +y ² +z ² ) ^"3/2 (1)

[0086] Where Qb is the value of the point charge; "z" is the vertical coordinate of the ball (height); "x" is the horizontal coordinate in the direction transverse to the sensor

(conductor); and "y" is the horizontal coordinate in the direction along the wire. The center of the coordinate system is taken in the center of the sensor.

[0087] The conductor is considered as the part of the plane (infinite strip) that has a width D in the x-direction. It is assumed that the electric field from the ball is uniformly charged on the surface and is equivalent to the electric field from a point charge located in the center of the ball with the same total charge. Therefore, we can find the following.

[0089] Where R _b is the radius of the ball and σ^, is the ball surface charge density

(K/m ). The induced electric field only has a vertical (z) component.

[0090] The surface charge density induced in the metal plane is given by the equation

[0091] σ = Ε/4 π (3)

[0092] Therefore, the total charge generated (induced) in the conductor is given by the equation:

[0093] Q = D J Cb dy = (Q _b / π) z (z ² +x ² ) ^-1 (4)

[0094] When the ball moves near the wire the electric charge varies in time (t). If the conductor is connected to the ground through a resistor "R", for example an input resistor of an amplifier, the voltage applied to the resistor is given by the equation:

[0095] V _in = R dQ/dt (5)

[0096] The signal at the output of an associated amplifier is given by the equation:

[0097] V _out = V _in G (6)

[0098] Where G is the gain coefficient of the amplifier. [0099] If a three-wire sensor is used the "width" of the conductor used in the equation

(4) will be given by the distance between the two external conductors of the sensor.

[00100] If a four conductor sensor is used the signal of the sensor will be given equation:

[00101] V _4i „ = D dVi _n /dx (7)

[00102]

[00103] If the derivative of (dQ/dt) in equation (5) is taken, the following equation results:

[00104] V _in = - R D (Q _b / π) (dz/dt (z ² - x ² ) (z ² +x ² ) ^"2 + dx/dt 2 x z (z ² +x ² ) ^"2 ) (8)

[00105] Or in nondimensional form using the notations:

[00106] U = x/z; V _z = dz/dt; and V _x = dx/dt (9)

[00107] The following results:

[00108] Vi, R D (Q _b / π) z ^"2 (V _z (1 - U ² ) (1 ² +U ² ) ^"2 + V _x 2 U (1 +U ² ) ^"2 ) (10)

[00109] Where V _z is the vertical component of the ball speed and V _x is the horizontal component of the ball speed in the direction perpendicular to the sensor.

[00110] In the vast majority of cases V _z « V _x and a simpler equation may be used:

[00111] Vi _n = - R D (Q _b / π) z ^"2 V _x 2 U (1 +U ² ) ^"2 (11)

[00112] In this approximation for a four conductor sensor the following equation results:

[00113] V _4in = - R D (Q _b / π) z ^"2 V _x (D/z) (1 - 3U ² ) (1 +U ² ) ^"3 (12)

[00114] It is seen from equation (12) that the signal of a four conductor sensor is reduced by the factor (D/z) in comparison with a three conductor sensor (in the order of value). The function dependent on U in equations (10 - 12) is of the order of 1 when U varies from minus infinity to plus infinity.

[00115] This supports the concept of using of a four conductor sensor with a relatively small pitch D value in order to discriminate between a ball that hits the sensor and a ball that misses the sensor. For example, when D = 1 mm and z = R _h = 33 mm the factor (D/z) = 0.03 (relatively a very small value). So the signal from the ball that misses the sensor would be reduced by approximately 30 times when a four conductor sensor with these dimensions is used. However, embodiments in which a three conductor sensor is used in this manner, and/or where a four conductor sensor is used to measure the trajectory are also possible. [00116] Turning to the three wire sensor operation, the case when V _z « V _x is addressed. In this case the form of the signal (in time) is given by the equation

[00117] F(U) = U (1 +U ² ) ^"2 (13)

[00118] The above is derived from received from equation (11). When the form of the signal is sinusoidal like, the function (13) has two extremums (max and min) at:

[00119] U = +/- 3 ^"1/2 ~ 0.6; F(U) ~ 0.3

[00120] So, the signal has two extremums at x ₁ = - 0.6 z and x ₂ = 0.6 z; when the center of the ball is displaced with respect to the sensor on the value Δχ = +/- 0.6 z.

[00121] When U = 0 (x = 0) the signal is equal to zero.

[00122] The amplitude of the signal in extremums is approximately given by the equations:

[00123] V _in (min/max) = - R D (Q _b / π) z ^"2 V _x 0.6

[00124] IVin(min/max)l = R D (Q _b / π) z ^"2 IV _X I 0.6

[00125] Note that the minimum (maximum) value of the signal is proportional to z ^"2 .

Because the minimum and maximum of the signal are received at different positions of the ball (xl = -0.6 z and x2 = +0.6 z) the value of the ball height zl and z2 are different at these two positions. Near the sensor the height of the ball is approximately constant and could be given by the equation:

[00126] z = z0 (l + x tg(c0)

[00127] where "a" is the angle between the ball trajectory and the court surface, tg(a)

« 0, and "zO" is the height of the ball at x = 0 (just opposite the sensor). So,

[00128] zl = zO (l - 0.6 tg(cO)

[00129] z2 = z0 (l + 0.6 tg(a))

[00130] Therefore, the signal at point xl is given by:

[00131] IV1I = R D (Q _b / π) zl ^"2 IV _X I 0.6 = R D (Q _b / π) zO (1 - 0.6 tg(a)) ^"2 IVxl 0.6

[00132] Respectively the signal at point x2 is given by:

[00133] IV2I = R D (Q _b / π) z2 ^~2 IV _X I 0.6 = R D (Q _b / π) zO (1 + 0.6 tg(a)) ^"2 IV _X I 0.6

[00134] The ratio IV1/V2I is given by the equation:

[00135] IV1/V2I = (1 - 0.6 tg(a)) ^"2 /(l + 0.6 tg(a)) ^"2 = (1 + 0.6 tg(a)) ² /(l - 0.6 tg(a)) ²

[00136] The point xl corresponds to the moment of time

[00137] Tl = xl/V _x = -0.6 z0/V _x

[00138] The point x2 corresponds to the moment of time [00139] T2 = x2/V _x = 0.6 zO/V _x

[00140] The time T is measured from the point x = 0 that corresponds to the center of the signal. Additionally, if tg(a) > 0, the height of the ball increases near the sensor and the ratio of VI to V2 is given by:

[00141] IV1/V2I > 1

[00142] If tg(a) < 0, the height of the ball decreases near the sensor and the ratio of VI to V2 is given by:

[00143] IV1/V2I < 1

[00144] If tg(a) = 0.1 (V _z = 0.1 V _x , approximately corresponds to the serve: V _z = 5 m/s; V _x = 50 m/s)

[00145] IV1/V2I = 1.3

[00146] If tg(a) = 0.25 (V _z = 0.25 V _x , approximately corresponds to the base line: V _z =

5 m/s; V _x = 20 m/s)

[00147] IV1/V2I = 2.8

[00148] If zO = 5 cm (the ball has a contact with the court near the sensor) and V _x = 20 m/s (base line)

[00149] The moments of time are about:

[00150] Tl = -1.5 msec

[00151] T2 = +1.5 msec

[00152] If V _z is not much smaller than V _x , as might occur for some side line shots into this, the more complicated equation (10) could be analyzed.

[00153] Example: Design of a Trajectory Sensor for Specific Tennis Court Lines

[00154] When the above sensors are integrated into a tennis court, the lines may be grouped into two groups. Group 1 may consist of the service line, and group 2 may consist of the sidelines and the line between the service course. How these groups are monitored, will depend in part on what portion of the court is "in" or "out" for service and regular play.

Without wishing to be bound by theory, when the ball moves near the lines of group 1 the component of the ball speed transverse to the line (Vx) is usually very high on the order of about 40 m/s to 60 m/s in the many cases. The vertical component of the ball speed (Vz) is also usually about 10 m/s. Therefore, the ratio z/x is usually on the order of about 0.2. So, if the signal from a ball that is moving near the sensor is measured at an altitude H = 10 cm (when the ball is located just opposite the sensor, it can be determined that the ball that has a rebound point at a distance of about x = +/- 50 cm from the line. Similarly, when the ball moves near the lines of group 2 the component of the ball speed transverse to the line (Vx) may be about 10 m/s to 20 m/s such as when the ball moves near the side line. In this case, the ratio z/x might be on the order of about 1. When the ball moves near the central line between the service boxes the component of the ball speed transverse to the line (Vx) could be approximately equal to zero. In this case the signal would be determined by the vertical component of the ball speed (Vz). In view of the above, sensors located in the lines of group 2 may monitor a controlled zone with an area equal to about 20 cm if the pitch value of the trajectory sensor is equal to about D = 1 mm. It should be noted that the signal to noise ratio is equal to about 10 ^" (0.001) or lower for such a sensor when it is used with the amplifier depicted in Fig. 14 and as described below.

[00155] Example: Contact Sensor

[00156] Again without wishing to be bound by theory, the signal generated when a ball hits the sensor is now described in more detail. When the ball hits the sensor (hits the court), the ball is deformed. More specifically, the bottom part of the ball may be considered as a flat part in the shape of a discus for example. The main part of the signal of the sensor in this case is determined by this charged bottom part of the ball (i.e. charged discus). Therefore, the electric charges that are induced in a metal plane by an electrically charged discus of radius R _< j having a surface charge density aa located at distance h from the plane is described below.

[00157] It is known that induced surface charge density in a corresponding metal plane will be equal to the discus surface charge density.

[00158] σ = σ _ά (3.1)

[00159] However, for the deformed ball the signal will be approximately two times higher because the electric field within the ball is approximately equal to zero. This is due to the electric field within the non-deformed round ball being exactly equal to zero. Therefore the induced charge can be described by the equation:

[00160] c = 2 c _b (3.2)

[00161] Note that c _b = c _d .

[00162] This equation (3.2) is valid within the discus area, when x/R _d < 1. "x" is the coordinate measured from the center of the discus. For x/R _< j > 1 the induced electric charge reduces very rapidly with the characteristic scale on the order of h. So the electric charge induced in the conductors of the sensor of with pitch D will be given by the equation:

[00163] Q = σ L

[00164] where L is the length of the part of the sensor that is located opposite the ball and where the induced charges exist. The following equation can be derived from the geometry:

[00165] L = 2 (R _d ² - x ² ) ^1/2

[00166] So in nondimensional form (U = x/R _d )

[00167] Q = 4 c _b R _d D (l - U ² ) ^1/2 (3.3)

[00168] If the discus (i.e. the deformed ball) moves with a constant speed V in the horizontal direction perpendicular to the sensor the signal of the sensor can be given by the equation:

[00169] Vi _n = R dQ/dt = - 4 R c _b D V U (1 - U ² ) ^"1/2 (3.4)

[00170] It should be noted, that R is the value of the input resistor of an associated amplifier as noted above. Further, equation (3.4) is valid for lUI < 1. For lUI > 1 the value of Vi _n falls to zero with the characteristic scale on the order of h/R _d . It should also be noted that (formally) the value of the signal (V _m ) is infinitively high if U = 1. However, near the point lUI = 1 the equation (3.4) is not valid. Therefore, the equation (3.4) might only be used up to lUI = 1 - h/R _d (in order of value). So the maximum signal magnitude could be given by the equation:

[00171] V _in = R dQ/dt = - 4 R c _b D V (2h/R _d ) ^~1/2 (3.4)

[00172] The maximum signal magnitude is realized when the edge of the discus (the edge of the ball footprint for a real ball) touches the sensor during the first and the last moments the ball is in contact with the sensor.

[00173] For a four conductor sensor the maximum magnitude of the signal will be given by the same equation (3.4) because the edge of the ball footprint is present only in one half of the sensor and is absent in the other half of the sensor when the maximum signal is attained.

[00174] The ratio of the signal from the discus to the signal of the round ball (the discrimination factor between the ball that hits the sensor and the ball that miss the sensor) is given by the equation:

[00175] V _d /V _b = 2 ^"1/2 (R _b /D) (R _d /D) ^1/2 [00176] This equation is obtained by dividing of equation (12) on equation (3.4). The dependence on "U" is ignored and "z" is taken as being equal to R _b the minimum value of z for a round ball.

[00177] Example: Amplifiers

[00178] As noted previously, the one or more sensors described above may be associated with an amplifier such as a low noise amplifier. Such an amplifier may be of benefit when a single sensor is used in two modes of operation, for example, as a contact sensor and as the trajectory sensor simultaneously. However, two different amplifiers could be used if two different sensors are used as separate contact and trajectory sensors. Other types and schemes of amplifiers could also be used. For example, two possible embodiments of an amplifier scheme are depicted in Figs. 12 and 13. The output associated with these amplifiers could be processed by a processor or by multiple distributed processors. These one or more processors may be of any type suitable for the intended installation location and available technical resources, and may include one or more of general purpose computers, special purpose computers, microprocessors, digital signal processors (DSPs), application specific integrated circuits (ASIC), multi-core processors, or any other appropriate processor.

[00179] Without wishing to be bound by theory, the main concept of the amplifier depicted in Fig. 12 and of the appropriate signal processing is as follows.

[00180] The first stage of the amplifier works mainly as a current to voltage converter.

The output signal of the first stage is given by:

[00181] Ul = (11-12) * R2

[00182] The signal is slightly integrated at the frequencies ω > (R2C1) ^"1 .

[00183] The second stage of the amplifier for the contact sensor portion works mainly as a differentiator. The output signal of this stage is given by:

[00184] U2c = (dUl/dt) * R5C3

[00185] The second stage of the amplifier for the trajectory sensor portion works mainly as the integrator. The output signal of this stage is given by:

[00186] U2 _T = (iUldt) * (R7C5) ^"1

[00187] A standard variable gain amplifier could also be used in combination with the depicted low noise amplifier to obtain the necessary total gain coefficient. [00188] Without wishing to be bound by theory, the main concept of the amplifier embodiment depicted in Fig. 13 and of the appropriate signal processing associated with such an amplifier is as follows.

[00189] The first stage of the amplifier works as a current to voltage converter. The output signal of the first stage is given by:

[00190] Ul = (11-12) * R2

[00191] The second stage of the amplifier is the Variable Gain Amplifier (VGA) that adjusts the amplitude of the signal to the characteristics of the ADC (DSP). It is assumed that 14 bit ADC is used. Therefore, the output can be give as:

[00192] U2 = G * Ul

[00193] where G is the gain coefficient of VGA. A Numerical Filter F _c may be used to obtain the signal for the contact sensor. Another Numerical Filter F _T may also be used to obtain the signal for the trajectory sensor.

[00194] Without wishing to be bound by theory, the main approach to the filter design is as follows.

[00195] Fc = Kc * Fci * F _C2 * F _C3

[00196] The filter Fci is used to reject the low frequency signal. That is the high-pass filter having the frequency cutoff cocl = (0.5 - 1) * 10 3 c - ^" 1. This filter could be of the second order or higher.

[00197] The filter F _C2 is used to differentiate the signal. For example filter F _C2 could be a filter where:

[00198] F _C2 (oo) = ω/(1 + (oo/ooc2) ² ) ^1/2

[00199] That is the filter may have a frequency cutoff coc2 = (1 - 3) * 10 ⁴ c ^"1 .

[00200] The filter F _C3 can be used to reject high frequency signals. That is the low- pass filter having the frequency cutoff coc3 > coc2. This filter could be of the second order or higher as well. Kc is the gain coefficient of the filter (if necessary).

[00201] Filter F _T can be setup in a manner somewhat similar to the above. Specifically

F _T may be viewed as below:

[00202] F _T = K _T * F _T i * F^ * F _T3

[00203] The filter F _T I is used to reject the low frequency signal. That is the high-pass filter having the frequency cutoff cotl = (0.5 - 1) * 10 ¹ c ^"1 . This filter could be of the second order or higher. The filter F _T2 is used to integrate the signal. For example it may be of a filter of type

[00204] FreCoo) = 1/(1 + (ω/ωί2) ² ) ^1/2

[00205] This corresponds to a filter with frequency cutoff of cot2 = (1 - 2) * 10 ¹ c ^"1 .

The filter F _T3 is used to reject the high frequency signal. That is the low-pass filter having the frequency cutoff cot3 = (1 - 3) * 10 3 c - ^" 1. This filter could be of the second order or higher. Κχ is the gain coefficient of the filter (if necessary).

[00206] While specific filters are described above and in the figures, other types of filters could be used.

[00207] While the present teachings have been described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments or examples. On the contrary, the present teachings encompass various alternatives, modifications, and equivalents, as will be appreciated by those of skill in the art. Accordingly, the foregoing description and drawings are by way of example only.

[00208] What is claimed is: