Field of the Invention

[0001] The present invention relates to multilateration (MLAT) systems and methods that calculate target position by incorporating kinematic modeling of targets into conventional range and time-difference-of-arrival (TDOA) MLAT systems.

Background of the Invention

[0002] In a multilateration system used for the purpose of aircraft navigation, a signal receiver that receives multiple signals from synchronous sources can determine its own location through means of multilateration (MLAT) using signals transmitted on the Secondary Surveillance Radar (SSR) frequencies of 1030±5MHz and

1090±5MHz bands, the Distance Measuring Equipment (DME) frequency bands, Universal Access Transceiver (UAT) frequency bands and GPA frequency bands. Generally, two types of approaches are involved in the MLAT process. The first type of MLAT approach, generally known as the TOA MLAT or rho-rho navigation technique, assumes the transmission time is known to or can be inferred by the receiver hence the range to the transmitter can be calculated from the signal propagation time based on the time of arrival (TOA) of the signal. Given multiple ranges to different ground transmitters the position of the receiver can be solved as the intersection of the range-derived spheres. The second type of MLAT approach, generally known as the time difference of arrival (TDOA) MLAT technique, assumes the exact time of transmission of the signal is unknown to the receiver, but the relative transmission time is known or can be inferred by the receiver. In most cases, the signals are transmitted simultaneously, but in other cases known delays are purposely introduced to stagger the time of transmission to avoid synchronous garbling of the signals at the receiver. In either case, the receiver uses the signals, TOAs and any known transmission delays to calculate the range difference of the received signals from pairs of transmitters. The position of the receiver is then calculated as the intersection of the range-difference derived hyperboloids. [0003] On the other hand in a multilateration system used for the purpose of aircraft surveillance, surveillance systems require a signal transmitted by an aircraft to be received and a time of arrival (TOA) determined at each receiving unit. Analogous to the case of MLAT navigation, if the signal transmission time is known to or can be inferred by the surveillance system, TOA MLAT approach can be used and if the transmission time is unknown to the surveillance system TDOA MLAT approach can be used.

[0004] In either of the two cases (i.e., MLAT navigation and MLAT surveillance), geographic topography, weather conditions and RF interference can interfere with signal reception, which may cause the MLAT system to be unable to determine the position of the aircraft. What is needed is a system and method that augments the ability of existing MLAT navigation and surveillance systems to determine an aircraft position in the NAS (National Airspace System) even when the above conditions are present.

Summary of the Invention

[0005] According to a first aspect of the present invention, there is provided a method of augmenting a multilateration system in determining a position of a target, the method comprising determining a plurality of signal time-of-arrival (TOA) measurements of a target at a plurality of observation times, determining a plurality of signal time-differences-of-arrival (TDOAs) of the target using the TOA

measurements, constructing a range difference equation for each of the TDOAs as a function of the target position at a first observation time and the kinematics of the target over the plurality of observation times, constructing a set of target equations by combining the range difference equation and additional target equations constructed using at least one of additional target positional measurements and additional target kinematics measurements, and computing the position of the target at the first observation time and the kinematics of the target over the plurality of observation times by solving the set of target equations. [0006] In some embodiments of the present invention, the kinematics of the target include at least a three dimensional velocity of the target. In other embodiments, the kinematics of the target include at least a three dimensional velocity and a three dimensional acceleration of the target.

[0007] In some embodiments, the additional target kinematics measurements and the set of target equations include one or more range difference rate measurements and equations. In some of these embodiments, the range difference rate measurement is obtained by measuring the signal frequency difference of arrival (FDOA). In other of these embodiments, the range difference rate measurement is obtained by tracking the TDOA measurements over time using Kalman Filtering.

[0008] In some embodiments, the additional target positional measurements and the set of target equations include one or more range measurements and range equations. In some of these embodiments, the range measurement is obtained by the target by interrogating a DME transponder. In other of these embodiments, the range measurement is obtained by a ground interrogator interrogating the transponder on the target.

[0009] In some embodiments, the additional target kinematics measurements and the set of target equations include one or more range rate measurements and range rate equations. In some of these embodiments, the range rate measurement is obtained by tracking the range measurements over time using Kalman Filtering. In other of these embodiments, the range rate measurement is obtained by measuring signal Doppler frequency shift. In other embodiments, the additional target positional measurements and the set of target equations include one or more range sum rate measurements and range sum rate equations.

[0010] In some embodiments, the additional target kinematics measurements and the set of target equations include one or more range sum rate measurements and range sum rate equations. In other embodiments, the additional target positional measurements and the set of target equations include azimuth vector measurements and azimuth vector equations. In yet other embodiments, the additional target kinematics measurements and the set of target equations include horizontal velocity measurements and horizontal velocity equations.

[0011] In some embodiments, the additional target positional measurements and the set of target equations also include vertical position measurements and vertical position equations. In other embodiments, the additional target kinematics

measurements and the set of target equations also include vertical speed

measurements and vertical speed equations.

[0012] In some embodiments, the set of target equations are solved by minimizing a cost function that is a function of the residual error of each of the target equations of the set of target equations evaluated at the solution. In some embodiments, the horizontal velocity measurements are obtained from an inertial sensor unit. In other embodiments, the horizontal velocity measurements are obtained by measuring the ground speed and heading of the target.

[0013] In some embodiments, the ground speed of the target is computed from the indicated and true airspeed of an aircraft target. In other embodiments, the heading of the target is obtained from the reading of magnetic compass of the target.

[0014] In some embodiments, the vertical position measurements are obtained from the reading of a barometric altimeter of the target. In other embodiments, the vertical speed measurements are obtained by tracking the vertical position

measurements over time using Kalman Filtering.

[0015] In some embodiments, the multilateration system is part of a navigation system of the target, and the signal used for detemiining a TOA is transmitted from a reference transmitter whose position at the time of transmission is known to the target and the signal is received by the target and the arrival time of the signal is the TOA.

[0016] In some embodiments, the reference transmitter is a GPS or WAAS satellite. In other embodiments, the reference transmitter is a DME transponder.

In yet other embodiments, the reference transmitter is a ADS-B ground based transceiver (GBT) unit. In some embodiments, the target position and kinematics is computed at the target. [0017] In some embodiments, the multilateration system is part of a target surveillance system, and the signal used for deteπnining a TOA is transmitted by the target and the signal is received by the plurality of receivers whose positions at the time of receiving the signal are known.

[0018] In some embodiments, the target is an aircraft and the signal is the aircraft transponder signal. In other embodiments, the target is an aircraft and the signal is the aircraft ADS-B signal. In some embodiments, the receiver is a multilateration ground receiver that receives at least the Mode-A/C/S aircraft transponder signals.

In other embodiments, the receiver is a ADS-B ground based transceiver (GBT) unit. In some embodiments, the TOA measurements and additional measurements received at the plurality of receivers are transmitted to a central processor and the central processor computes the target position and kinematics.

[0019] In some embodiments, the receivers are time synchronized or the relative time biases of each receiver of the plurality of receivers are known. In other embodiments, the receivers are frequency synchronized or the relative frequency biases of each receiver of the plurality of receivers are known.

[0020] According to a second aspect of the present invention, there is provided a system for a target to determine its own position using a reference transmitter, the system comprising at least one target and at least one reference transmitter, wherein the at least one reference transmitter transmits a signal over a plurality of observation times, and wherein the at least one target determines a plurality of time-of-arrival (TOA) measurements for the signals transmitted by the reference transmitter over the plurality of observation times, determines a plurality of time-difference-of-arrivals (TDOAs) using the TOA measurements, constructs a range difference equation for each of the TDOAs as a function of the target position at the first observation time and the kinematics of the target over the plurality of observation times, constructs one or more target equations by combining the range difference equation and additional target equations constructed using additional target positional measurements and additional target kinematics measurements, and computes the position of the target at the first observation time and the kinematics of the target over the plurality of observation times by solving the set of target equations.

Brief Description of the Drawings

[0021] For a fuller understanding of the nature and objects of the invention, reference should be made to the following detailed description of a preferred mode of practicing the invention, read in connection with the accompanying drawings in which:

Fig. 1 illustrates determining a time-derivative TDOA (dTDOA) using TDOA observations of a target over time in one embodiment of the present invention;

Fig. 2 illustrates tracking observed TDOAs over time and deteπriining dTDOA from the slope of the smoothed track at a given point in time in one embodiment of the present invention;

Fig. 3 illustrates tracking range measurements over time and determining dTDOA from the slope of the smoothed track at a given point in time in one embodiment of the present invention;

Fig. 4 illustrates two range circles derived from range measurements to a target from a reference station at different times in one embodiment of the present invention;

Fig. 5 illustrates one method for deteπnining the initial position of the target using the intersection of the three circles in one embodiment of the present invention;

Fig. 6 illustrates two hyperbolas derived from the range-difference or TDOA measurements from a target to a pair of reference stations at different times in one embodiment of the present invention;

Fig. 7(a) illustrates one example where the position of the target is determined by using three TDOA hyperbolas;

Fig. 7(b) is an enlargement of the upper crossing area of the three TDOA hyperbolas of Fig. 7(a);

Fig. 7(c) is an enlargement of the lower intersection of the three TDOA hyperbolas of Fig. 7(a); and Fig. 8 illustrates an example using WAAS satellites as reference stations in one embodiment of the present invention.

Detailed Description of the Invention

[0022] When a surveillance system, such as an MLAT system, determines the position of a target (e.g., aircraft) over a period of time, the surveillance system forms a target track that includes heading, altitude and speed information.

[0023] The first embodiment of the present invention uses one or more of heading, altitude and speed information from aircraft track information to create a target kinematic model and combines data determined from the target kinematic model with asynchronous observations of positional measurements (e.g. single range and time- difference-of-arrival (TDOA) measurement) of a target to determine the position of the target at a point in time.

[0024] In one embodiment, the basic form of target kinematic modeling involves modeling the velocity of a target as a time-invariant vector such that any position in space at a given time can be related to an initial position at time zero by a

displacement equal to the velocity times the elapsed time. In another embodiment, the target kinematic modeling includes target accelerations and higher-order kinematic parameters. In these embodiments, all of the target positions during the observation period are modeled as a function of the initial position and kinematics parameters so that observations at different times can be combined to determine the position of the target at any given time.

[0025] In addition, by modeling target kinematics, the time derivatives of the positional measurements are utilized to provide additional information that is used to determine the position of the target. Further, by modeling target kinematics, unconventional information such as target airspeed and frequency difference of arrival (FDOA) are incorporated into MLAT formulations to provide new ways of estimating target positions.

[0026] The first embodiment of the present invention computes (i) a time- derivative TDOA (dTDOA) using Frequency Difference of Arrival (FDOA) or (ii) a TDOA determined from the slope of a smoothed track of TDOA measurements, and combines the computed TDOA with one or more range measurements or TDOAs from an MLAT system to determine the position of the target. This can be done in cases where the range measurements or TDOAs alone would be insufficient to determine the position of the target.

[0027] In a second embodiment of the present invention, a time-derivative measurement of range (dR) is computed by (i) directly measuring the Doppler frequency shift due to the range rate induced by the target movement, or (ii) by tracking the range measurement over time, and deteπnining the time derivative from the slope of the smoothed track, and combines the computed dR with one or more range or TDOAs from an MLAT system to determine the position of the target.

[0028] In a third embodiment of the present invention, the known velocity of a target is used with at least two range measurements to a reference station to determine the position of a target.

[0029] In a fourth embodiment of the present invention, the known velocity of a target is used with range-difference or TDOA measurements to two reference stations to determine the position of the target.

Time Derivative Measurements of TDOA and Range

[0030] In the first embodiment of the present invention, a time-derivative TDOA (dTDOA) is determined using TDOA observations of a target over time, as shown in Fig. 1. The dTDOA is determined using the following equation:

C -dTDOA^ C ™ ⁰ ^

¹² dt

₌ (X ₀ + VJ-X ₁ )V _x + (y ₀ + V _y J -Y ₁ )V _y (X ₀ + VJ-X ₂ )V _{x +} Jy ₀ + V _y t-Y ₂ )V _y

A(O R ₂ (t ⁾ Where the target's x y positions are functions of time and velocity is expressed as:

[0031] In one embodiment, the present invention measures the Frequency

Difference of Arrival (FDOA) of the signal transmitted by the target and received by two receivers (sensors in Fig. 1). Based on the Doppler frequency shift that results from the movement of the target, the difference in the received frequency of the signal at the two receivers is determined. The FDOA is related to dTDOA using the following equation:

= C- dTDOA _u

or

J c

[0032] The FDOA is determined by subtracting the frequencies of the RF signals at the two receivers. In another embodiment, FDOA is determined by measuring frequency shifts from the normal center frequency at a single receiver (or each receiver) and then computing the difference in frequency received at the receiver over time. In the above embodiments, the two receivers need to be time synchronized so that, if local oscillators are used, no artificial frequency shifts due to inter-site frequency incoherence is added to the measured frequencies.

[0033] Alternatively, dTDOA is determined by observing TDOAs over a period of time and dTDOA is simply computed from the slope of the smoothed track at a given point in time, as shown in Fig. 2. The slope of the smoothed track is typically readily available in a tracking algorithm such as Kaman Filter (KJF).

[0034] In the second embodiment, the time-derivative measurements of range (dR) is determined by (i) directly measuring the Doppler frequency shift due to the range rate induced by the target movement, or (ii) by tracking the range measurement over time and determining the time derivative from the slope of the smoothed track, as shown in Fig. 3. In the present invention, when a TDOA from two receivers and a range from one of the receivers are available, the range from the other sensor can be derived, such that the ranges and range rates from all receivers can be derived if the range from a common RU of all TDOA measurements is known.

Positioning Based on Known Target Velocity

[0035] In the third embodiment of the present invention, the known velocity of a target is used with at least two range measurements to a reference station to determine the position of a target. Different methods for estimating velocity used in this embodiment of the present invention are discussed below.

[0036] Fig. 4 illustrates two range circles derived from range measurements to a target from a reference station at time t and time t+dt. The center of the circles is the location of the reference station and the target positions at time t and time t+dt are on the two circles at the respective observation times. Since no intersection occurs between the two circles, it is clear that the position of the target cannot be determined from the circles alone in Fig. 4.

[0037] In one embodiment, the present invention uses the known velocity of a target to determine the target position because the only positions on the circles that will satisfy the known velocity of the target is a pair of positions having the

displacement indicated by the velocity, as shown in Fig. 4. Note that two solutions are determined in the example in Fig. 4 due to ambiguity; however, the ambiguity can be removed using prior knowledge of the target position.

[0038] Alternatively, in another embodiment, the position of the target is determined by using range measurements and a known velocity in accordance with the following equations:

R ₁ = ^{x _ϋ + V _x t -X _λ γ + {y _ϋ + V _y t-Y _x f

R _t+Λ = ^x ₀ + V _x (t + dt) -X _x f + {y _o +V _y {t + dt) -Y _l ) ² which is interpreted as two circles one with radius R ₄ with center at

(X _r V _x t, Yi-V _y t) and the other with radius R _t+dt with center at (X _r V _x t+dt),

Y _r V _y t+dt)).

[0039] An example is illustrated in Fig. 5 where three range circles at times tl, t2, t3 are plotted. In Fig. 5, each circle has a displaced center in time and radius equal to the range measurement. As a result, the intersection of the three circles occurs and indicates the initial position of the target (marked by '+'). Thus, when the target velocity is known, the position of the target is determined using the distance between the target and a reference station that is being tracked. The determined position of the target may have an ambiguous solution but the erroneous position can be logically excluded using prior knowledge of target position.

[0040] In the fourth embodiment of the present invention, the known velocity of a target is used with range-difference measurements or TDOA measurements to two reference stations to determine the position of the target.

[0041] Fig. 6 illustrates two hyperbolas derived from the range-difference or TDOA measurements from a target to a pair of reference stations at time t and time t+dt. The foci of the hyperbolas are the location of the reference stations and target positions at time t and time t+dt are on the two hyperbolas at the respective

observation times. Since no intersection occurs between the two circles, it is clear that the position of the target cannot be determined from the hyperbolas alone in Fig. 6.

[0042] In this embodiment, the present invention uses the known velocity of a target to determine the target position because the only positions that will satisfy the velocity is a pair of positions having the displacement indicated by the velocity, as shown in Fig. 6. Note that two solutions are determined in the example shown in Fig. 6 due to ambiguity; however, the ambiguity can be removed using prior knowledge of the target position.

[0043] Alternatively, in another embodiment, the position of the target can be determined by using range-difference or TDOA measurements in accordance with the following equations: C TDOA ₁ = ^(x ₀ + V _x t - X ₁ ) ² + (y ₀ + V _y t -Y ₁ Y -^x _{0 +} VJ - X ₂ ) ² + (y _Q + V _y t- Y ₂ ) ² C -tDOA _t+ώ = ^x _o + V _x (t + dt) -X ₁ ) ² +(y _o + V _y (t + dt) -Y ₁ ) ²

-p _o + V _x (t + dt)-X ₂ ) ² + (y ₀ + V _y (t + dt) -Y ₂ ) ^T which is interpreted as two hyperbolas, one with range difference C* TDOA ₁ with foci at (X _r V _x t, Yi-V _y t) and (X ₂ -V _x t, Y ₂ -V _y t) and the other with range difference

C*TDOA _t+dt with foci at (X _r V _x( t+dt), Y _r V _y( t+dt)) and (X ₂ -V _x( t+dt), Y ₂ -V _y( t+dt)).

[0044] An example is illustrated in Fig. 7(a), where three TDOA hyperbolas at time tl, t2, t3 are plotted. Each hyperbola has displaced foci positions in time and range difference equal to the range-difference measurement. As a result two intersections of the hyperbolas occur but only one intersection of the three hyperbolas indicates the initial position of the target (marked by '+').

[0045] Enlarged views of the intersection areas are shown in Figs. 7(b) and 7(c). In Fig. 7(b), it is clearly shown that the three hyperbolas do not intersect at the upper crossing area shown in Fig. 7(a), therefore, this solution is the ambiguous solution. In Fig. 7(c), it is clearly shown that the three hyperbolas intersect at a single point in the lower crossing area shown in Fig. 7(a), therefore, this is the correct solution for the initial position of the target. Thus, when the target velocity is known, the position of the target is determined unambiguously using the range difference between the target and two reference stations that is being tracked.

Measuring Target Velocity

[0046] A closed-form (non-iterative) method is used in one embodiment of the present invention to estimate the velocity of a moving target using range or quasi- range measurements.

[0047] As used in this disclosure, a range measurement is the measurement of the distance between the target and an observation station and a quasi range is the derived range from a range-related measurement such as TDOA (time difference of arrival) and TSOA (time sum of arrival). For example, a range of the target to reference j can be determined when the range from the target to reference i is known based on the following equation:

TDOAij * C = ΔR

where: C is the speed of light; and

ΔR is the difference of the two ranges.

This method requires the range rates (the rate of variation of range, or time-derivatives of the range measurements as functions of time) to be known.

[0048] Where only ranges or quasi-ranges are known, the range rates need to be derived from the smoothed tracks of the range/quasi range measurements. If Doppler frequency shift measurements and FDOA are known the range rates can be derived directly from such measurements.

[0049] Given range and range rates from a target to multiple stations, one can estimate the velocity of the target using the following equations (for simplicity, the equations assume a 2-dimensional problem; however, this method can be extended easily to include 3-dimensional cases):

The range from target to station i is expressed as;

R ₁ = ^(X ₀ +VJ-Xf + (y _o + V _y t-Y _i ) ²

And the range rate is the time derivative of the above equation as shown below;

One may rearrange the above equation to obtain the following;

R ₁ Ri = (X ₀ +Vj-X ₁ )V _x +(y _o + V _y t-Y _i )V _y

Similarly the range or quasi range measurements obtained from station j and k are;

R _J R _J = (x _o +Vj -X _j )V _x +(y _o +V _y t-Y _J )V _y

R _k Rt = (*„ +Vj-X _k )V _x +(y ₀ +V _y t-Y _k )V _y

If one takes the difference between the first equation and the later two equations, the following results; R _I R,-R _J R _J = (X _J -X _l )V _x +(Y _J -Y _ι )V _y

R ₁ R ₁ -R _t Rt = (X _k -X ₁ )V _{x +} (Y, -7,)V,

Now, the target velocity can be solved linearly as;

[0050] If more than 3 range/quasi range measurements are available, one embodiment of the present invention uses a pseudo-inversion technique to solve the linear equation to determine the position of the target. This is known as a redundant case because the additional observation stations provide redundant measurements which supplement the minimum number of measurements necessary to determine the position of the target. This method is generally known as the least-squares (LS) method. More elaborate methods model the error of the observations and use weighted least squares (WLS) method to determine more accurate solutions for the position of the target.

[0051] When the measurement errors are normally distributed, one embodiment of the present invention uses an optimal weighting matrix, which equals the covariance matrix of the measurements, to provide the optimal solution for the position of the target based on Maximum-likelihood estimation theory. These techniques for solving the above equations are well known in the art and are not discussed further in this disclosure. Details on these techniques can be found in most detection and estimation text books. The formulations and descriptions provided are considered sufficient for anyone who is familiar with the field to derive the necessary details for implementing an optimal estimator.

[0052] Note that for 3 -dimensional cases, where target vertical position is also of interest, the formulations need to be expanded to include the vertical components, (i.e. the Z terms). In such case a fourth range/quasi range measurement is required to produce the velocity estimate. One exception is when the target's vertical position and velocity are derived directly from the observed barometric altitudes such that they can enter the 3-D formulations either as a known value or as independent measurements that produce more measurement equations for determining the position of the target. Since target altitudes are generally known, target altitude should be included in the equations to reduce the minimum number of observation stations required, such as a minimum of three observations which give three range observations or one range and two TDOA or TSOA observations can be used to estimate the target velocity.

Estimating the Target Position Given Velocity

[0053] Where target velocity and a range measurement or TDOA are known, target position can be determined by solving a set of non-linear equations and would most likely involve iterative techniques, such as Newton-Raphson or Simplex Downhill, for example. However, in some cases a linear approach is used when conditions permit in a closed-form (non-iterative) solution in which the calculations are significantly simpler than the calculations of the iterative techniques.

[0054] When a sufficient number of observation stations exist, a closed-form solution can be used to determine the position of the target. For simplicity, the following example is based on a 2-dimensional problem. However, this can be easily extended to include the third dimension, the vertical component, by persons familiar with the art.

[0055] Assuming the target velocity is known, given at least two TDOA rate observations, either obtained directly from FDOA measurements or derived from smoothed TDOA tracks, the target position is determined by solving the following relatively simple equations in a linear form. The following equation denotes the TDOA (times C, in distance units) observed from two observation station, i and j:

D _f = fa + rj -Xi) ² + (y _o +v _y t-Y _i ) ² -J( ^χ _o +v _x t -x,) ² +0 ^; ₀ +py-r _y ) ² the time-derivative of the TDOA or the TDOA rate can be written as

= ip _o + ^v _* t -X ₁ ) ² +(y _o +Vj-Yf -j-J(x _o +Vj -XJ ₊ U _{0 +} Vj-TJ dt dt

or ₊ C _1J

where:

V _r

u

R, R. vv = R. R,

and t = 0 if the time of observing the TDOA rate is the time of observing the position of the target.

[0056] Similarly for observation stations i and k, a TDOA rate equation can be written as:

[0057] The linear equations are formed, in matrix form, as:

[0058] The least squares solution of the position of target is solved using the following equation: [0059] As previously stated other estimation approaches including redundant cases, and the 3 -dimensional extensions can also be used and will not be elaborated here. Anyone familiar with this field can derive the necessary equations with the provided information.

A New Navigation Positioning Backup Approach

[0060] The methods discussed above in the first through fourth embodiments of the present invention are very useful in navigation applications where target velocity can be derived by the target from its own sensors including barometric altitude, measured indicated airspeed, compass heading, and inertial sensing data, thereby enabling a target, such as an aircraft, to conduct self-position estimation using multiple range measurements from one or more reference stations such as a DME transponder, or multiple range-difference or TDOA measurements from two reference transmitters, such as GPS satellites, WAAS satellites, Loran transmitters, or any synchronous heart beat or time transmitters. The disclosed methods enable targets to determine their own position using one less reference station than conventional methods, thereby enabling a self-position determination capability without adding more reference stations.

[0061] For example, the navigation positioning backup plan in the NAS is for OMEfDME MLAT to be the positioning backup method for aircraft when GNSS is unavailable. The DME/DME MLAT method requires at least two simultaneous ranges from DME transponders, assuming barometric altitude is used, or at least three simultaneous ranges from DME transponders if barometric altitude is not used. To achieve the desired coverage for DME/DME MLAT additional DME transponder stations need to be installed. In addition, DME/DME MLAT also requires expensive scanning DME avionics to be installed on aircraft. In comparison, the disclosed known-velocity and range positioning methods of the third and fourth embodiments of the present invention only require a single DME transponder. Thus, the potential benefit of the present invention in reducing infrastructure investment can be realized. [0062] Alternatively, for TDOA based position determination approaches, such as GPS positioning, at least two GPS satellites are required to determine a target position, assuming barometric altitude is used, or at least three GPS satellites are required if barometric altitude is not used. Whereas, the known-velocity and range- difference positioning methods of the present invention only require determination of a single TDOA over time or TDOAs from any two reference stations from which a target can determine TDOA. Other potential reference station include WAAS satellites, as shown in Fig. 8, Loran-C transmitters or any transmitters that transmit synchronous heart-beat or time signals.

[0063] From the above equations, which assume a constant target velocity for the entire observation period, one may easily expand the disclosed equations to include acceleration when available to the aircraft. The equations including acceleration are written as follows:

R ₁ = J(x _o + V _x t + O.5a _x t ² -X,) ² + (y ₀ +V _y t + 0.5a _y t ² -F ₁ ) ²

C ^■ TDOA ₁ = J(x ₀ + VJ + 0.5a _x t ² -X ₁ ) ² + O ₀ + V _y t + 0.5a/ - F ₁ f

-J(X ₀ + V _x t + 0.5a _x t ² -X ₂ ) ² + (y ₀ + V _y t + 0.5a/ -Y ₂ ) ²

[0064] In one embodiment, the range based and TDOA-based known- velocity positioning methods are integrated to provide more robust target position

determination solution. In this embodiment, ambiguity is removed by mathematical redundancy and the resulting position determination has greater accuracy than either method provides standing alone. The following provides an example of determining a target navigation position based on one DME, two WAAS satellites, barometric altitude and airspeed. The measurements observed over time include:

[0065] In this embodiment, the equations used to determine target position are as follows:

^(X ₀ + Vj ₁ + 0.5aJ ² -X _W2 f + (y ₀ +V _y t, +Q.5a _y t _λ ² -Y _W2 f +(Z ₁ -Z^ ₂ ) ² +

⁸ A

R, ⁼ V< ^X - ₀ +VJ ₂ + 0.5a J ₂ x _D ) ² + (y _» + v _y t ₂ + 0.5α/ ₂ ^■ Y _D f +(z ₂ -Z _D ) ² +e R ₂

Z ₁ = Z ₁ + e _z

z ₂ =z ₂ +e ₂

V ^γ x =V ^y x +^e ^c vx

V ' y =V ' y +e *vy

a _x =a _x +e _m

a _y =a _y + e^

where: (X _D , Y _D , Z _D ) is the position of DME transponder;

(X _W i, Y _W i, Z _W i) and (Xwi, Ywb Z _W1 ) are the positions of WAAS satellites; and

the 'e' terms are measurement error terms which are normally modeled as Normally distributed random variables.

Note that the DME transponder at time 0 and time t ₂ are the same DME transponder in this example, but two different DME transponders can be used.

[0066] The target horizontal position (also vertical position and kinematics) at time 0 is determined by solving the above equations. To solve these equations, the present invention determines the set of unknown parameters (xo.yo _? Zo, Z _\ , Z ₂₅ V _x , V _y , V _z , a^ a _y , a _z ,) that best fit the above equations using a Maximum Likelihood (ML) parameter estimation approach to derive the optimal solution where ML estimation is implemented by minimizing the weighted least squares (WLS) cost which is a - function of the residual errors of the above equations evaluated at a given of solution. The weighting matrix of the WLS cost function is determined as the inverse of the covariance matrix of the residual errors of the equations based on a Gaussian error distribution assumption to attain ML equivalency.

[0067] Note that the measurement set can be expanded to include more ranges and TDOAs from longer-time observations as long as the acceleration model can describe the actual target movement within a predetermined error tolerance. It can also be expanded to include more than one range contributor (such as additional DME transponders or any ranging transponder that receives target interrogations and replies with information enabling a target to calculate its range to the object) and more than one pair of TDOA contributor (such as a third WAAS satellite, Loran-C transmitter, or any transmitters that transmit synchronous or pseudo-synchronous heart-beat or time signals, or even GPS satellites). The more measurements used to determine the position of the target the greater the accuracy of the determined position solution.

Generalized Kinematic MLAT Method

[0068] In many situations the position of a target may be estimated based on a mixture of prior knowledge and observations collected over a period of time. Such observations, or measurements, may include all or any of the following:

• range;

β time difference of arrival (TDOA);

• time sum of arrival (TSOA);

• doppler frequency shift;

• frequency difference of arrival (FDOA);

• direction of arrival (DOA) or azimuth vector information from a reference location to the target;

• target barometric altitude;

• target magnetic heading; β target indicated and true airspeed;

β target iπertial measurement; and

• meteorology data.

[0069] In the present invention, the aforementioned data is condensed and the measurements are re-interpreted into the following data categories:

« range;

β range rate;

• range difference;

• range-difference rate;

® range sum;

• range-sum rate;

« azimuth vector;

® target horizontal velocity;

• target vertical position; and

® target vertical speed.

[0070] All or part of the information in these categories is used to determine the position of a target using one of the methods disclosed in the present invention or other conventional methods. The key difference between the disclosed methods and conventional methods is the synchronization of the measurements. Conventional methods require a single snapshot measurement to determine target position. The disclosed kinematic model MLAT methods use the time derivatives or observation over time to determine a target position.

[0071] One embodiment of the equations for determination of target position using time derivatives or consecutive-time observations are presented below. Assuming the position of a target is of interest at a point of time, observation information regarding the position of the target is made at a time, t, which is later than the time of interest.

[0072] A range at time t, relative to reference platform i, is expressed as follows:

R ₁ = ^+ V _x t + 0.5a _x t ² -Xf + iy _o + V _y t + 0.5a _y t ² -Y ₁ ) ² + (z ₀ + V _z t + 0.5a _z t ² -Z ₁ ) ² + e _R [0073] In the following equations, β denotes the measurement of the information β , e _β denotes the error of β , and X, Y, and Z represent the position of a reference platform at the time of observation. Note that the t in each information equation may represent a different time from the t of another equation.

[0074] The range rate information at any time t, relative to reference platform i, is expressed as follows:

R, = ±-[(V _x + ajχx _o + V _x t + 0.5a _x t ² -X ₁ ) + ...

(V _y +a _y t)(y _Q + V _y t + Q.5a/ -Y,) + (V _Z +a _z t)(z ₀ + V _z t + 0.5af -Z ₁ )] + e.

R

[0075] A range difference information at any time t, relative to reference platforms i and j, is expressed as follows:

A, = p ₀ + V _x t + 0.5a _x t ² -X ₁ ) ² + (y ₀ + V _y t + 0.5a/ -T ₁ Y ₊ (Z ₀ + V _z t + 0.5a _z t ² -Z ₁ ) ² - ^(X ₀ + V _x t + 0.5a _x t ² -X _j ) ² + (y ₀ + V _y t + 0.5a/ -Y _j ) ² + (z _o + V _z t + O.5a _z t ² -Z _j ) ² + e _D

[0076] The range-difference rate information at any time t, relative to reference platforms i and j, is expressed as follows:

Dy = ^[(V _x + a _x t)(x ₀ + V _x t + 0.5a _x t ² -X ₁ ) + ...

(V _y + a _y t)(y ₀ + V _y t + 0.5a _y t ² -7,) + (V _t + a _z t)(z ₀ + V _z t + 0.5a _z t ² -Z ₁ )]-

^-[(V _x + a _x t)(x ₀ + V _x t + 0.5a _x t ² -X _y ) + ...

(V _y + a _y t)(y ₀ + V _y t + 0.5a/ - 7 _y ) + (V _z + a _z t)(z ₀ + V _z t + 0.5α/ - Z ₁ )] + e .

[0077] A range sum information at any time t, relative to reference platforms i and j, is expressed as follows:

S ₉ = p _o + V _x t + O.5a _x t ² -X ₁ ) ² +(y ₀ +V _y t + 0.5a/ -Y ₁ ) ² +(z ₀ +V _z t + 0.5a _z t ² -Z ₁ ) ² + ,1(X ₀ +V _x t + 0.5a _x t ² -X _j ) ² + (y ₀ + V _y t + 0.5a/ -Y _j ) ² + (z ₀ + V _z t + 0.5a _z t ² -Z _j ) ² + e _s

[0078] The range-sum rate information at any time t, relative to reference platforms i and j, is expressed as follows: Sy +"J)(X ₀ +V _x t + 0.5a _x t ² -X ₁ ) + ...

(V _y + a _y t)(y ₀ + V _y t + 0.5a/ - Y ₁ ) + (V ₂ + a _z t)(z ₀ + V _z t + 0.5a _z t ² - Z ₁ )] + + a/fr _o +V _x t + 0.5a _x t ² -X _j ) ₊ ...

(V _y +a _y t)(y ₀ +V _y t + 0.5a/ -Y _j ) + (V _Z +a _z φ _o +V _z t + 0.5af -Z _j )] + e.

[0079] The (horizontal) azimuth information at any time t provides the direction vector information between the target and a reference platform i, is expressed as follows: u _xi =±-[x ₀ +V _x t + 0.5a _x t ² -X ₁ ^e _11x

Kyi - ^γ ih ^e uy

[0080] Within the entire observation epoch, or time 0 < t≤ t _obs , the target kinematics is assumed to be a function of time and the initial velocity V _x , V _y ,V _z and constant acceleration a _x ,a _y ,a _z . Using constant acceleration model, the set of target kinematic information results in the following equations.

V ^y x =V ^y x + ^τ e ^e Kc

V y =V y +p Vx

a _y =a _y + e^

More detailed assumptions will assume acceleration as function of time to include higher order time derivative terms as well.

[0081] For example, a target's vertical position at any time t is given explicitly, such information is formulated as:

z(t) = z _o +V _z t + O.5a _z t ² +e _z [0082] The disclosed generalized Kinematic MLAT demonstrates that any number or combination of range, range rate, range difference, range-difference rate, range sum, range-sum rate information can be used in conjunction with the target kinematic and vertical position information to solve target position, as long as the information included provides a non-under-determined solution of target position. Note that any of the target kinematic information and the vertical position information can be treated as a known prior truth (e.g., 'e' terms reduced to zero) or as an error-prone

measurement. In the later case the kinematic and vertical position terms are solved with the horizontal position as unknown parameters. For steady-state kinematic estimations where a target is moving with a constant velocity, all acceleration terms are reduced to zero.

[0083] The determination of target position is solved by finding the parameters that are the best fit in the disclosed information equations. One method for determining the best fit is to use weighted least squares (WLS) criterion. When the error terms are zero-mean normally distributed the criterion converges to Maximum Likelihood criterion such that the solution is deemed optimal. Detail derivations of the solution estimation are not provided here as the information provided above is deemed sufficient for anyone who is familiar with the field to derive the necessary details.

[0084] In summary, the present invention uses kinematic parameters of a target to provide enhanced performance of conventional MLAT in terms of:

• reduced requirements on the number of receivers or reference platforms for providing TDOA, TSOA, FDOA, range, or DOA measurements;

® improved position accuracy and update rate;

® allowing the use of asynchronous measurements; and

• allowing deep integration of different types of measurement system.

[0085] The present invention also provides a more flexible and powerful MLAT method for deteiπiining target position. For example, in the context of finding backup Navigation service in lieu of GPS, an aircraft can combine one or more of the following currently available information to multilaterate its own position:

• range to a single DME transponder; β range rate to a single DME transponder;

® barometric altitude;

• indicated airspeed derived true airspeed; and

β declination-corrected magnetic azimuth heading.

[0086] The present invention also incorporates the following types of information to determine the position of a target:

β range to additional DME transponder;

β range rate to additional DME transponder;

• inertial sensor derived velocity and accelerations;

• TCAS derived DOA to SSR 1030/1090 ground transmitters;

β TDOA with respect to two WAAS satellites;

® TDOA rate (or FDOA on Ll and/or L2 signals) with respect to two WAAS satellites;

® TDOA with respect to two Loran C transmitters;

® TDOA rate with respect to two Loran C transmitters;

® TDOA with respect to two surviving and functioning GPS satellites; and

® TDOA rate (or FDOA on L 1 , L2 and/or L5 signals) with respect to two

GPS satellites.

[0087] For ground surveillance applications, such as the ATCRB S/MODE-S/UAT Wide-area MLAT (WAM) system, a target position can be solved with aircraft altitude and two or more TDOAs. The present invention provides improvements in position accuracy when TDOA rate and range or TSOA rate information are incorporated for calculating target position and kinematics.

[0088] While the present invention has been particularly shown and described with reference to the preferred mode as illustrated in the drawings, it will be understood by one skilled in the art that various changes in detail may be effected therein without departing from the spirit and scope of the invention as defined by the claims.