FIELD OF THE INVENTION

The invention relates to processing of acceleration measurement and in particular to a processing device for determining a direction of movement of portable acceleration sensor.

BACKGROUND OF THE INVENTION

Monitoring of motion of persons or animals is used in various applications. One use is for activity monitoring of persons, for example monitoring of a person's physical activity related energy consumption. Other uses include monitoring the motion route of a walking person.

Monitoring of a person's energy consumption may under- or overestimate energy consumption if the type of physical activity is not known. For example, energy consumption of cycling may be underestimated. This may be improved by taking into account activity context information. For instance, knowing the velocity cycling could be better distinguished from other locomotive activities like walking since cycling velocity is normally faster than walking.

Thus, there is a need to determine the velocity of person in the direction the person is moving.

Monitoring of a motion path or route of a person requires information of the motional direction of the person. Accordingly, there is a need to determine the direction of motion.

Global positioning systems (GPS) provide instantaneous information about speed direction and location. However, such systems may be too expensive to be used in certain types of consumer products. Besides, a GPS device does not work in a tunnel or like locations where the satellite signal is not available.

US2003191582 discloses a walking direction detection apparatus having an azimuth detection unit and acceleration detection unit. After a vertical direction with respect to the ground based on the detection direction of a gravitational acceleration component, a periodic up/down pattern of the absolute value of acceleration is detected. A value where the acceleration component in the horizontal direction becomes maximal or minimal is detected at a predetermined timing at which the acceleration component in the vertical direction transits from a maximal value to minimal value. The direction of the apparatus is corrected based on the direction of the acceleration component in the horizontal direction of that value. Based on these correction results, the walking direction of the movable body is detected.

Since the apparatus of US2003191582 is based on analyzing a certain motion pattern, the apparatus may not be applicable e.g. for cycling. Accordingly, it may be seen as an object to provide an apparatus capable of detecting motion parameters for general types of motion. It may also be seen as an object to improve US2003191582 with respect to reliability and accuracy of the detected motion values and it may also be seen as an object to provide an apparatus which is less expensive and has a simpler construction.

SUMMARY OF THE INVENTION

Accordingly, the invention preferably seeks to mitigate, alleviate or eliminate one or more of the above mentioned disadvantages singly or in any combination. In particular, it may be seen as an object of the present invention to provide a method and processing device that improves the solution of the prior art by providing a method for determining the motional direction of different types of motion.

This object and several other objects are obtained in a first aspect of the invention by providing a processing device for determining a direction of movement of a portable acceleration sensor comprising two or more sensor-directions, the processing device comprising: an input for receiving at least two vector acceleration measurements from the acceleration sensor where the measurements are separated in time, a processor for determining the direction of movement under the constraint of minimizing a sum or average value of lateral displacements determined from the vector acceleration measurements, where the lateral displacements are defined in a lateral direction perpendicular to the direction of movement and where the lateral direction and the direction of movement lie in a horizontal plane substantially perpendicular to an Earth-gravity direction.

The invention is particularly, but not exclusively, advantageous for obtaining a processing device capable of determining a direction of motion of an object.

The constraint of minimizing a sum or average value of lateral displacements should be understood broadly and comprises any mathematical method which ensures that lateral displacements, lateral velocities, lateral acceleration or in general lateral motion are minimized. Minimizing may be understood as a mathematical minimizing method or an algorithm which makes the accumulated averaged lateral displacements approach zero.

It is understood that the horizontal plane need not be perfectly perpendicular to the Earth-gravity direction. Thus, a small deviation in the perpendicular orientation of the horizontal plane may result in a small deviation of the estimated moving direction, and in sequence a small deviation of the estimated velocity, but the accuracy may already suffice, at least for activity recognition. In this case, a deviation of a few degrees, for example five or ten degrees is allowable.

The processing device may be applicable with acceleration sensors having two or more sensor-directions or sensor-axes. It is understood that the processing device may be wire or wirelessly connected with the acceleration sensor.

It may be advantageous to determine the direction of movement under the constraint of minimizing a sum or average value of lateral displacements determined from the vector acceleration measurements since this approach may be applicable to different types of motion since the approach is only based on values of measured accelerations.

The processing device according to the first aspect may be advantageous since the processing devices only requires a connectable acceleration sensor and, therefore, may enable a simple and cost effective device for determining motion parameters.

In an embodiment, the horizontal plane is perpendicular to an average vector acceleration determined by the processor from the at least two acceleration measurements.

It may be advantageous to determine the average vector acceleration from the at least two acceleration measurements, since the average vector acceleration provides an equivalent to the Earth-gravity direction. Thereby, the average vector acceleration defines the horizontal plane. Furthermore, it may be advantageous to determine the average vector acceleration from acceleration measurements, since this may allow the acceleration sensor to be oriented arbitrarily relative to the Earth-coordinate directions. The average vector acceleration may be determined by averaging, summing or filtering acceleration measurements.

In an embodiment the processor is configured for determining: an average vector acceleration from the at least two acceleration measurements, at least two inertial vector accelerations by comparing the average vector acceleration with the at least two vector acceleration measurements, at least two horizontal vector accelerations from the inertial vector accelerations, so that the horizontal vectors lie in the horizontal plane perpendicular to the average vector acceleration, and the direction of movement under the constraint of minimizing a sum or average value of lateral displacements determined from the at least two horizontal vector accelerations, where the direction of the lateral displacements is constrained to be perpendicular to the average vector of movement and to lie in the horizontal plane.

It may be advantageous to determine the direction of movement from horizontal vector accelerations when the acceleration sensor has three or more sensor directions since the horizontal vector accelerations lie in the horizontal plane and, thereby, enables derivation of the direction of movement, since the horizontal plane is at least approximately perpendicular to the Earth-gravity direction.

In an embodiment, the at least two horizontal vector accelerations are determined by decomposing the inertial vector accelerations into vertical vector accelerations being parallel with the average vector acceleration and horizontal vector accelerations being perpendicular to the average vector acceleration.

In an embodiment of the processing device the input comprises an analogue- to-digital converter for sampling vector acceleration measurements from the acceleration sensor and for converting the sampled values into digital values.

It may be advantageous to use an analogue-to-digital converter in the processing device since it enables use of acceleration sensors with analogue output.

In an embodiment, the processor is further configured for determining a velocity in the direction of movement, by projecting a vector of acceleration measurements, a vector of inertial vector accelerations or a vector of horizontal vector accelerations onto the vector of movement and integrating over a time period.

It may be advantageous to determine the velocity in the direction of movement, since the velocity enables calculation of travelled distance, energy consumption of the object carrying the acceleration sensor and characterization of the type of motion.

In an embodiment, the processing device is further configured for determining an absolute direction of movement relative to the Earth coordinate system by comparing the direction of movement relative to a reference direction of the Earth coordinate system.

It may be advantageous to determine an absolute direction of movement relative to the Earth coordinate system since this enables the processing device to map the route of the object carrying the acceleration sensor. In an embodiment, the reference direction of the Earth coordinate system is determined from an auxiliary direction sensor. Since the processing device does not provide an absolute reference direction relative to the Earth, it may be advantageous to determine the reference direction from an auxiliary direction sensor such as a compass. Alternatively, the reference direction may be provided by the user by entering a reference direction, for example by entering Earth north direction via a calibration button on the processing device.

In a second aspect the invention relates to a portable sensor system for displaying information of motion, the portable sensor system comprising the processing device according to the first aspect, an acceleration sensor for providing acceleration measurements to the processing device and a display for displaying information of motion determined by the processing device on basis of acceleration measurements.

In a third aspect the invention relates to a method for determining a direction of movement of a portable acceleration sensor comprising two or more sensor-directions, the method comprising: receiving at least two vector acceleration measurements from the acceleration sensor where the measurements are separated in time, determining the direction of movement under the constraint of minimizing a sum or average value of lateral displacements determined from the vector acceleration measurements, where the lateral displacements are defined in a lateral direction perpendicular to the direction of movement and where the lateral direction and the direction of movement lie in a horizontal plane substantially perpendicular to an earth-gravity direction.

The first, second and third aspect of the present invention may each be combined with any of the other aspects. These and other aspects of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter.

In general the invention relates to a device and a method for determining a direction of movement of a person carrying a portable acceleration sensor. The direction of movement characterizes the motion direction of the person's movement at certain points in time. By utilizing that the person's movement in directions other than the direction of movement averages to zero over a given time interval, the forward direction of movement can be determined. The direction of movement can be determined under the constraint of minimizing the displacements in a direction perpendicular to the direction of movement or by ensuring that the accumulated displacement perpendicular to the direction of movement approximates zero or is below a given threshold value. BRIEF DESCRIPTION OF THE FIGURES

The present invention will now be explained, by way of example only, with reference to the accompanying Figures, where

Fig. 1 shows a device for determining a direction of movement of a portable acceleration sensor,

Fig. 2A shows the motion pattern of an object,

Fig. 2B shows an arbitrary oriented acceleration-sensor,

Fig. 2C shows an acceleration-sensor orientated with respect to the Earth coordinates,

Fig. 3 illustrates acceleration vectors used for determining the direction of movement vector,

Fig. 4 illustrates the vectors of the direction of movement and the lateral direction,

Fig. 5 illustrates steps according to the method for determining the direction of movement,

Fig. 6 illustrates a possible implementation of the method for determining the direction of movement.

DESCRIPTION OF AN EMBODIMENT

Fig. 1 shows a processing device 100 for determining a direction of movement of a portable acceleration sensor 110 which is wire- or wirelessly connectable to the processing device via an input 120.

The acceleration sensor is designed to be carried by a person, animal or other objects such as vehicles. When the acceleration sensor moves due to movement of the person or object, the acceleration sensor generates an output signal corresponding to the current acceleration of the person or object and, thereby, the acceleration of the acceleration sensor 110.

The acceleration sensor 110 may have two sensor-directions Al and A2, three sensor-directions Al -A3, or the acceleration sensor may have more sensor-directions, for example four sensor-directions for a specific application. The sensor-directions Al -A3 are illustrated as coordinate axes of the sensor coordinate system 111. The accelerations sensor 110 is capable of generating accelerations signals corresponding to the accelerations in the directions of each of the sensor-directions Al -A3. Thus, a coordinate sensor 110 with three sensor directions Al -A3 generates acceleration signals for each of the three directions. The acceleration signals may be analogue or digital signals, and may be combined into a single analogue or digital signal. The individual acceleration signals or the combined acceleration signal is supplied to the processing device via a wired or a wireless connection 121.

The processing device 100 comprises a processor 101 for processing signals from the accelerations sensor 110. The processing device 100, alternatively the processor 101, may comprise an analogue-to-digital converter 102 for sampling values of the acceleration signal and for converting the sampled values into digital values. The processing device 100 may further comprise a display 103 for displaying information processed by the processor 101. The processing device 100 may be portable in order to be carried together with the accelerations sensor. The processing device 100 and the acceleration sensor may be integrated into a single sensor device, for example a portable sensor system 140.

A portable sensor system 140 for displaying information of motion generally comprises the processing device 100, the acceleration sensor 110 and the display (103).

The sensor-directions Al -A3 may be seen relative to the directions G1-G3 of the Earth-coordinate system 190. Accordingly, when the acceleration sensor 110 is carried by an object or user, the sensor directions Al -A3 may have any angular orientation relative to the Earth-coordinate directions G1-G3. The Earth gravity direction is given by the Earth- coordinate direction G3. For example the Earth gravity direction may point in the negative direction of the G3 coordinate.

Fig. 2A shows the motion pattern 201 of an object, for example a person walking along a path 202. As the person moves forward along the path 202 the person will normally also generate sideways motion displacement LAT as indicated by the motion pattern 201 alternatively shifting from side to side of the average path 202.

The averaged motion of the person, i.e. the average of the motion pattern 201, corresponds to the average motion path 202. The direction of movement DOM, indicated as directional vectors DOM along the path 202, corresponds to the averaged direction of movement of the walking person. The lateral displacements LAT are caused by the person's sideways motions in the directions vLAT which can be described as lateral motion vectors vLAT perpendicular to the direction of movement DOM.

From Fig. 2A it is clear that summing or averaging the lateral displacements LAT along the alternating lateral directions vLAT will result in a zero net-displacement, at least when the summing or averaging is performed over a period of time ΔT or a section of the path 202 that is, on one hand, sufficiently long so that a sufficient number of lateral displacements LAT along alternating lateral directions vLAT are averaged or summed, and on the other hand, not too long so that in this period of time the DOM does not change. Thus, the averaging period of time ΔT must be chosen so that alternating lateral displacements LAT are averaged to approximately zero and so the direction of movement DOM reflects the average direction of movement of the object. For example, if the object moves in a circle the averaging time ΔT should be chosen so that lateral displacements perpendicular to the periphery of the circle are averaged to zero and so that the direction of movement reflects the circular motion. For example, if the selected averaging time ΔT is too long, the direction of movement will not reflect a circular motion but a polygonal motion. As an example, if the averaging time ΔT is one third of the time for performing a single circular path, the direction of motion will not reflect a circular path but a triangular path.

Thus, summing or averaging lateral displacement values LAT obtained from a number of acceleration samples 203 within the time interval ΔT along the path 202 will give a value which equals or approximates zero. To hold this statement, a properly chosen ΔT along with a high enough sampling frequency is needed. A high enough sampling frequency means ΔT covers a sufficient number of sampling periods ΔTs. For example, the sampling frequency may be chosen to be at least twice the motion frequency of alternating lateral movements. Then, this can be utilized for determining the direction of movement DOM by minimizing a sum or average value of lateral displacements LAT.

Fig. 2B shows an example where the acceleration- sensor 110 having three sensor-directions Al -A3 in the sensor coordinate system 111 is arbitrary oriented with respect to the object or person 220 and, thereby, the Earth coordinate system 190.

Fig. 2C shows an example where the acceleration- sensor 110 with two sensor- directions A1-A2 is orientated so that a static sensor-direction AS of the sensor is oriented perpendicular to the ground. Thus, the static sensor-direction is an imaginary sensor-direction perpendicular to the two sensor-directions A1-A2, i.e. the static sensor-direction does not provide any measurements. The static sensor-direction AS, which may be marked on the acceleration sensor 110, is perpendicular to the horizontal plane HOZ (not shown) spanned by the two sensor directions A1-A2. Thus, the two-coordinate acceleration sensor 110 should be carried by the person or object 220 so that the horizontal plane HOZ is substantially perpendicular to the gravity direction G3. It is understood that substantially perpendicular means that a deviation of a few degrees from perfect perpendicular does not affect the determination of the direction of motion DOM. Whereas the two coordinate acceleration sensor 110 must be oriented so that the horizontal plane HOZ is spanned by the two sensor-directions Al-Al, the horizontal plane HOZ of a three coordinate sensor 110 may also be defined by two sensor-directions out of the three sensor-directions A1-A3, when the three coordinate sensor is oriented so that two sensor directions A1-A2 spans a horizontal plane HOZ perpendicular to the gravity direction G3. Clearly, this also applies to sensors 110 with more than three sensor directions.

By obtaining two or more samples 203 of two- or three coordinate accelerations from an acceleration sensor 110 having two or three sensor-directions Al -A3 it is possible to determine the average vector or direction of movement DOM by utilizing that the sum or average value of lateral displacements LAT determined from the samples of acceleration measurements equals or approximates zero. Methods for determining the direction of movement is explained in the following.

An output from the acceleration sensor 110 can be described as a vector acceleration measurement vA, vA = (Al,A2,A3) for a three coordinate sensor, whereas the vector acceleration measurement vA for a two coordinate sensor is vA = (A\,A2) . The prefix "v" in the term vA indicates that vA is a vector, and this notation applies to other similar vector definitions in the description. One vector acceleration measurement vA represents a single sample at a given time of an output signal from the acceleration sensor.

Thus, a value of lateral displacement LAT may be equated as a displacement of the acceleration sensor 110 from one or more vector acceleration measurements vA. That is, having a single acceleration measurement vA, an acceleration component in the direction of lateral directions vLAT can be determined by projection of vA onto the lateral direction. From the acceleration component in the lateral direction vLAT, a lateral displacement LAT over a given period of time ΔTarb can be determined using well-known physical equations for calculating distance from acceleration. The period of time ΔTarb may be the period of time ΔTs between samples of acceleration measurements vA or any other arbitrary period of time.

Assuming now that the acceleration sensor is a three coordinate sensor, the earth-gravity acceleration g can be determined or approximated as the average vector acceleration vAs obtained by averaging at least two vector acceleration measurements vA, vAs = vA(i) , where vA{ϊ) is interpreted as the average of a number of samples at i, and where the bar symbolizes any method for averaging. Instead of averaging a number of samples at i, the average vector acceleration vAs may be obtained as a time average vA{t) of the analogue vector acceleration measurement signal from the acceleration sensor 110. The time average vA{t) may also be obtained by low-pass filtering vA(t) . The time window, number of samples, or time-constant of the filter should be so large that the inertial accelerations of the moving object 220 averages to zero or approximately zero, so the average vector acceleration vAs equals or approximates the static acceleration of the object 220 and, thereby, the Earth-gravity vector. The coordinates of the averaged vector acceleration are: vAs = vA(J) = [A\ ⁽ J), Al(J), A3(i)] = [Ah, AIs, i = 1,2,3... n

When the third axis A3 of the acceleration sensor is parallel with the gravity, the averaged acceleration vector becomes vAs = (0,0, g) , where g is the gravity acceleration. However, in general all three components of vAs are non-zero.

By calculating the difference between the average vector acceleration vAs and the at least two vector accelerations vA(i), a number of inertial vector accelerations vAI are obtained: v AI (J) = v A(J) - v As = [AU (i), AlI(J), i = 1,2,3...n

The index i, e.g. in vAI(i) indicates a vector vAI at a sampling moment i. For convenience, the index i will be omitted and, therefore, vAI (or similar terms) should be understood as a sequence equivalent Iy to vAI(i).

The inertial vector accelerations express the time- varying acceleration of the object 220 induced by movement.

In order to determine the direction of movement DOM of the object 220, the inertial vector accelerations need to be separated into vertical inertial vector components vAI V parallel with the average vector acceleration vAs or gravity vector, and horizontal inertial vector components vAI H component laying in a horizontal plane HOZ (not shown) perpendicular to the average vector acceleration vAs. The horizontal plane HOZ of the three- coordinate sensor corresponds to the horizontal plane HOZ of the two-coordinate sensor. The vertical vector components vAI V may be determined by projecting the inertial vector accelerations vAI onto the average vector acceleration vAs as follows:

The horizontal vector components vAI H are determined using the obtained vertical vector components vAI V as follows: vAI _H = vAI -vAI _V eq. 2

The inertial vector accelerations vAI, the vertical inertial vector components vAI V and the horizontal inertial vector components vAI H are all inertial acceleration components. For convenience these inertial components may equally be referred to as vector accelerations vAI, vertical vector components vAI V and horizontal vector components vAI H without indicating that they are inertial vectors.

Fig. 3 illustrates the geometry of vectors of an acceleration measurement vA, an average acceleration vAs, inertial accelerations vAI, vertical components vAI V of the inertial accelerations vAI and horizontal components vAI H of the inertial accelerations vAI. Thus, the horizontal components vAI H of the inertial accelerations vAI lie in the horizontal plane HOZ perpendicular to the average vector acceleration vAs. The horizontal plane HOZ is at least approximately parallel within the horizontal G1-G2 plane of the Earth coordinate system 190, i.e. the G1-G2 plane being perpendicular to the gravity vector.

Since the acceleration sensor 110 generally is arbitrary oriented with respect to the forward or anterior-posterior direction of object 220, the direction of movement DOM of the object 220 cannot be determined directly from the horizontal vector components vAI H. In some applications of the processing device 100, the acceleration sensor may be loosely attached to a person 220 so that the orientation of the sensor-coordinate-system 111 relative to the person 220 changes over time, for example if the acceleration sensor 110 is loosely attached with a strap to the person's belt.

However, for a moving object 220, it is practically the case that the object does not change moving direction within a sufficiently small time interval, or at least the change will be negligible. Thus, in this time interval the accumulated lateral displacement LAT of the object 220 in the lateral direction vLAT orthogonal to the moving direction DOM equals zero or at least approximates zero. By using this physical observation, the average vector of movement DOM can be determined under the constraint of minimizing the accumulated lateral displacement LAT or average value of lateral displacements LAT. Since the direction of lateral displacements vLAT until now is undefined, the lateral direction vLAT is constrained to be perpendicular to the direction of movement DOM. The direction of movement DOM and the lateral direction vLAT are determined from the horizontal vector components vAI H and, therefore, lie in the horizontal plane HOZ being perpendicular to the average vector acceleration vAs and at least substantially perpendicular to an earth-gravity.

Fig. 4 illustrates the geometry of the vectors of the direction of movement DOM, and the lateral direction vLAT of the lateral displacement LAT obtained by projection of the horizontal component vAI H onto the unit vectors s and f, where s points in the direction of the lateral direction vLAT and f points in the direction of movement DOM.

It is understood that the direction of movement of an object 220 is described equivalently by the DOM- vector and the f- vector, the only difference being the magnitude of the vectors.

Thus, the projections of vAI H onto the f and s vectors give:

DOM = (vAI H * f) f

^~ eq. 3 vLAT = (vAI_H » s) s

The f vector and equivalently the direction of movement DOM can be derived from a set of constraints as follows:

When a three coordinate acceleration sensor 110 is used, equation 4 has six equations and six unknown parameters (three in vector f and three in vector s) and, therefore, equation 4 is solvable. However, when a two coordinate acceleration sensor 110 is used, equation 4 only has four equations and four unknown parameters since the horizontal plane HOZ is defined by the A1-A2 axes and, therefore, only the last four equations eq. 4.3 - 4.6 need to be solved. All vectors in equation 4, including f and s, are expressed in the sensor coordinate system 111 that is continuously moving relative to the Earth-coordinate system 190 since the object 220 moves. Therefore, these vectors are time- varying even though some of them may remain unchanged relative to the Earth. Since f and s are assumed to be constant in equation 4 within the time interval ΔT (otherwise eq. 4 will be unsolvable), the solutions will satisfy equation 4 in a least-mean-square (LMS) sense, that is, they will make the equations hold on average over ΔT. For instance, known from real life experiences, ΔT should be in the range of a few seconds for a walking or running person. For example, when the processing device 100 is used for determining the direction of movement DOM of a walking person, the sampling frequency 1/ΔTs may be chosen to be at least 4 Hz in order to correctly sample a typical 2 Hz lateral motion pattern of a walking person.

The physical implication of each expression in equation 6 is as follows: eq. 4.1 : f is perpendicular to vAs, eq. 4.2: s is perpendicular to vAs, eq. 4.3: f and s are mutually perpendicular, eq. 4.4: f has a unit length, eq. 4.5: s has a unit length, and eq. 4.6: The net lateral displacement LAT along s, or perpendicular to the moving direction DOM, is zero.

Equation 4 gives the solution to the direction of movement DOM, for analogue or time-continuous signals outputted by the acceleration sensor 110. When the acceleration sensor 110 outputs digital signals or when the analogue signal from the acceleration sensor 110 is converted by an analogue-to-digital converter comprised by the processing device 110, the solution to the direction of movement DOM is given by a discrete-time equivalent to equation 4:

/ • 5 = 0 eq. 5

= 1 = 1 where n and k represent sample times 203 and Δt is the sampling period which corresponds to the sampling period ΔTs. Equation 5 can be solved by minimizing the cost function J obtained from eq. 5 : J(f,s) vAs) ₁₁

In equation 5, W ₁ (I = I,- - - ,6) are tuneable weighting factors that adjust the importance of each item in cost function J .

Minimizing eq. 6 gives solutions of / and s for every time interval of AT .

This process involves solving nonlinear equations, which can be circumvented by an iterative gradient descent algorithm. In the iterative gradient descent algorithm, a new target function

J is defined where the integrations over AT are replaced by the instantaneous values:

J(I _k A) + -w ₂ [{s • vAs) _k ] ²

4w ₃ [(/.4] ² 4w ₄ [| _Λ |-i] ² ₊ Iw ₅ [| _?i |-i] eq. 7

And the rules for updating / and s are described as

where \i _f and \i _s are positive factors controlling the update rate. Equations 7 and 8 update f and s at every sampling moment k based on their values at the previous moment and the newly received acceleration samples vA. Compared to minimizing eq. 6, this algorithm provides somehow more noisy instantaneous values of f and s , but avoids solving nonlinear equations and therefore lowers the computational complexity.

Accordingly, the direction of movement DOM may be determined using other methods than suggested by any of the above equations 4-7. However, in general the methods for determining the direction of movement DOM involves minimizing a sum or average value of lateral displacements LAT determined from the vector acceleration measurements vA for example by minimizing lateral displacements LAT expressed by the term (vAI H • s ) _n At which is contained in any of the above equations 4-7. Strictly speaking, the term (vAI H • s ) _n At gives the variation of the lateral moving speed from one sample i to the next sample i+1, but can indicate the lateral displacement when the initial lateral moving speed for each AT period is zero. The other constraints of equations 4-7, such as the constraints of equations 4.1-4.5 may be formulated differently.

Even though the term (vAI H • s ) _n At merely gives the variation of the lateral moving speed, it is understood that minimizing a sum or average value of lateral displacements (LAT) also comprises minimizing terms, which due to mathematical reductions, represents other quantities, such as the variation of the lateral moving speed, {vAI H ^ s ) _n At .

Fig. 5 illustrates a possible implementation of the processing device 100 and a method for performing method step for determining the direction of movement DOM or f.

As a first step, at least two vector acceleration measurements vA are provided from the acceleration sensor 110 where the measurements are separated in time. The first step may be implanted by supplying the at least two vector acceleration measurements vA to an input 520 of a first processing device 501.

As a second step, the average vector acceleration vAs may be determined from the at least two acceleration measurements vA. The second step may be implemented by supplying the at least two acceleration measurements vA to the first processing device 501 which is configured for determining and outputting the average vector acceleration vAs.

As a third step, at least two inertial vector accelerations vAI may be determined by comparing the average vector acceleration vAs with the at least two vector acceleration measurements vA, for example by summing or calculating the difference of the average vector acceleration vAs and vector acceleration measurements vA. The third step may be implemented with a summation unit 504 which determines the sum or difference of the inputted average vector acceleration vAs and the at least two vector acceleration measurements vA.

As a fourth step, at least two horizontal vector accelerations vAI H may be determined from the inertial vector accelerations vAI, so that the horizontal vectors vAI H lie in the horizontal plane HOZ perpendicular to the average vector acceleration vAs. This may be performed by use of equations 1 and 2. The fourth step may be implemented by the second processing unit 502 which is configured to determine horizontal vector accelerations vAI H, for example on bases of equations 1 and 2. The second processing unit may additionally output vertical vector accelerations vAI V, for example determined by equation 1.

As a fifth step, the direction of movement DOM may be determined as suggested above using for example equation 7 or other equivalent methods. It is understood that the direction of movement DOM may equivalently be expressed in terms of the DOM- vector or the unit-vector f. The fifth step, may be implemented by the third processing unit 503 configured for determining the direction of movement DOM, for example on the basis of equation 7.

When the acceleration sensor 110 is a two-coordinate sensor having only first and second sensor-directions Al and A2, the second to fourth steps are not performed since the sensor only provides acceleration vectors in the A1-A2 plane or the horizontal plane HOZ which preferably should be parallel with or approximately parallel with the horizontal plane G1-G2 of the Earth coordinate system 190. Furthermore, when the acceleration sensor 110 is a two-coordinate sensor, any of the equation systems eq. 4-7 only comprises the last four equations since the horizontal plane of the two-coordinate system is already parallel or approximately parallel with the horizontal plane G1-G2 of the Earth coordinate system 190.

One or more of the first, second and third processing devices 501-503 and the summation unit 504 may be comprised by the processing device 100. Similarly one or more first, second and third processing devices 501-503 and the summation unit 504 may be integrated into one or more processing units comprised by the processing device 100.

Fig. 6 illustrates in detail a possible method and implementation of the method for determining the direction of movement DOM under the constraint of minimising a sum or average value of lateral displacements LAT according to equation 7. The scheme in Fig. 6 shows that the vectors of the horizontal vector accelerations vAI H and the average vector acceleration vAs (or the static sensor-direction AS in case of two-coordinate acceleration sensor taking a value of zero) is supplied to the algorithm. In Fig. 6 symbols 601 illustrate inner product, symbols 602 illustrate calculating the length of a vector, symbol 603 illustrates the gradient descent algorithm for minimizing J{f _k ,s _k ) , symbols 604 illustrates summation units, symbols 605 illustrates the different terms of equation 7.

When the direction of movement DOM has been determined, it is possible to determine the velocity (VDOM, not illustrated) of the object 220 in the direction of movement DOM. This may be achieved by projecting a vector of acceleration measurements vA, inertial vector accelerations vAI or horizontal vector accelerations vAI H onto the vector of the direction of movement DOM or the unit-vector f and integrating over a time period ΔTarb. The time period ΔTarb may be the time between succeeding samples of acceleration measurements vA or any other arbitrary period of time.

The direction of movement DOM,f does not directly provide the direction of movement of the object 220 relative to the Earth-coordinate system 190, since the acceleration sensor 110 is generally oriented arbitrarily with respect to the Earth-coordinate system 190. However, there are different possibilities for synchronizing the orientation of the coordinate system 111 of the acceleration sensor 110 with the Earth-coordinate system 190 so as to obtain an absolute direction of motion DOM relative to the Earth-coordinate system 190.

In general, an absolute direction of movement DOM relative to the Earth coordinate system 190 may be achieved by comparing the direction of movement DOM with a reference of the Earth coordinate system. The reference of the Earth coordinate system may be provided by a compass, a GPS or other auxiliary direction sensors comprised by the processing device 100. Accordingly, if the absolute North direction is known relative to the coordinate system 111 of the acceleration sensor 110 then the absolute direction of movement DOM can be determined.

Thus, if a reference of the Earth coordinate system is determined, for example at the beginning of using the processing device 100, then a first direction of movement DOM can be compared with the reference direction, for example by subtraction of the vectors, to get a difference vector. Subsequently calculated directions of movement DOM can be added to this difference vector or directly compared to a newly determined reference direction, to determine a new absolute direction of movement. Thus, in principle it is sufficient to determine a single reference direction of the Earth coordinate system in order to translate the relative direction of movement DOM to an absolute direction of movement.

Although the present invention has been described in connection with the specified embodiments, it is not intended to be limited to the specific form set forth herein. Rather, the scope of the present invention is limited only by the accompanying claims. In the claims, the term "comprising" does not exclude the presence of other elements or steps. Additionally, although individual features may be included in different claims, these may possibly be advantageously combined, and the inclusion in different claims does not imply that a combination of features is not feasible and/or advantageous. In addition, singular references do not exclude a plurality. Thus, references to "a", "an", "first", "second" etc. do not preclude a plurality. Furthermore, reference signs in the claims shall not be construed as limiting the scope.