GB2583914A

GB2583914A - Accelerometer calibration

Info

Publication number: GB2583914A
Application number: GB1906403.9A
Authority: GB
Inventors: Welsh Callum; Kendall Philip
Original assignee: Intercept Ip Ltd
Current assignee: Intercept Ip Ltd
Priority date: 2019-05-07
Filing date: 2019-05-07
Publication date: 2020-11-18
Also published as: GB201906403D0

Abstract

A method for calibrating a vehicle-mounted accelerometer having an unknown orientation comprising the steps of: defining a time period equal to a length of a journey of the vehicle; obtaining a set of acceleration vectors from the accelerometer during the time period, said acceleration vectors comprising x, y and z scalar components; rotating the z-axis of the accelerometer by a polar angle, such that the z-axis is aligned parallel to the direction of gravitational force; and rotating the x-y plane of the accelerometer by an azimuthal angle. This results in the x and y axes of the accelerometer being aligned with the x and y axes of the vehicle. The x-axis may correspond to the vehicle’s forwards/backwards motion, and the y-axis to lateral, sideways motion. The step of rotating the z-axis may comprise rotating each acceleration vector to produce a set of transformed acceleration vectors, such that a z scalar component of a mean acceleration vector is equal to a gravitational acceleration value, said mean acceleration vector calculated from the set of transformed acceleration vectors. The step of rotating each acceleration vector may comprise applying a 3D rotation matrix to the vector.

Description

ACCELEROMETER CALIBRATION

Field of Invention

The current invention relates to a method for calibrating accelerometers for use in vehicles. In particular, a method for calibrating a vehicle-mounted accelerometer having an unknown orientation is described.

Background of the Invention

Telematics insurance (also known as black box insurance) is when one or more devices are fitted inside of a vehicle to monitor how, when and where the vehicle is driven, helping to reduce the cost of insurance. These devices are either typically fitted inside the car itself when the car is purchased, or are provided by the insurance companies to be fitted inside the vehicle.

One such device is a 3-axis accelerometer, which can give information about how the driver accelerates from rest, how harshly they brake and how they take corners. Accelerometers can also be used to detect accidents, with some systems providing automated alerts if such an event is detected However, in order to effectively use the accelerometer for this purpose, the axes of the accelerometer must be aligned with the axes of the vehicle. On installation, it is unlikely that this will be achieved, especially if the device is intended to be installed by the customer themselves. Thus, the device must be calibrated upon installation for it to function properly.

In the past, this meant that such telematics devices have used heuristic algorithms to determine their calibration, which have been subject to errors In addition, such calibration algorithms may require maintaining a larger amount of data than it is possible to store on the device, and so may also be computationally intensive requiring a large amount of processing power for the device, increasing cost.

The present invention aims to at least ameliorate the aforementioned disadvantages by providing a more efficient method for calibrating the accelerometer axes with that of the vehicle, requiring only a small amount of memory and power.

Summary of the Invention

According to a first aspect of the present invention there is provided a method for calibrating a vehicle-mounted accelerometer having an unknown orientation, said method comprising the steps of: defining a time period equal to a length of a journey of the vehicle; obtaining a set of acceleration vectors from the accelerometer during the time period, said acceleration vectors comprising x, y and z scalar components; rotating the z-axis of the accelerometer by a polar angle, such that the z-axis is aligned parallel to the direction of gravitational force; and rotating the x-y plane of the accelerometer by an azimuthal angle, such that the x and y axes of the accelerometer are aligned with the x and y axes of the vehicle.

Aspects of the present disclosure describe a method which, after observing accelerometer data over a given time period, will align the axis of an accelerometer to the axis of the vehicle on which it is installed. In particular, the accelerometer can be installed in any position on the car and can be facing any direction, yet the method can rotate these accelerometer values onto the axis of the vehicle This aspect allows the orientation of the accelerometer with respect to gravity to be determined. In particular, one of the axis are aligned with gravity, and this axis is then assigned and defined to be the z-axis of the accelerometer. Once the z-axis is defined and aligned, the x-y plane can be rotated to align with the x and y axes of the vehicle. This method allows the accelerometer to be calibrated independently from the installation site or angle or position. By undertaking an initial calibration in the manner described, the accelerometer is able to be calibrated without external input and without the need to undertake repeated heuristic algorithmic steps.

In an embodiment, the x axis of the vehicle may correspond to the forwards and backwards motion of the vehicle, and/or the y-axis may correspond to the sideways motion of the vehicle. This can allow the degree of rotation about the x-y plane to align with the x and y axes of the vehicle to be determined.

In an embodiment, the step of rotating the z-axis may comprise the step of rotating each acceleration vector to produce a set of transformed acceleration vectors, such that a z scalar component of a mean acceleration vector is equal to a gravitational acceleration value. As noted above, this allows the z-axis of the accelerometer to be calibrated. The mean acceleration vector may be calculated from the set of transformed acceleration vectors.

In such embodiments, the step of rotating each acceleration vector may comprise the step of applying a 3-d rotation matrix on each acceleration vector. This allows the axes of the accelerometer to be aligned with the axes of the vehicle.

In one embodiment, the step of defining a time period may further comprise the steps of: defining a time slot, said time slot being a subset of the time period of the journey of the vehicle. Defining a subset of the time period of the journey allows the effect of acceleration to be compensated for.

In said embodiments, the step of rotating the x-y plane may further comprise the steps of defining a score value, said score value initialised to null. Next a step of applying a 2-d rotation matrix on each transformed acceleration vector within the timeslot produces a set of rotated acceleration vectors. This set of rotated acceleration vectors may then be used to calculate a sum of squares for each set of x and for each set of y scalar components of the rotated acceleration vectors within the timeslot. These sums of squares are then compared to a condition, which is an inequality checking whether there is a high variation in the x direction and low variation in the y direction for a given angle. If the condition is satisfied, then the method increments the score value by unity.

The method then can seek to define a new timeslot, adjacent to the previously defined timeslot to be the current timeslot. The steps noted above may then be repeated for this new current timeslot until a maximum value for the score value is reached. This maximum score value corresponds to the rotation values for the x-y plane which corresponds to the azimuthal angle needed for rotation to improve alignment of the accelerometer, by producing a first set of acceleration vectors. It can be appreciated that this set of acceleration vectors may be misaligned by multiples of 90 degrees or 7[/2 rad. If the condition is not satisfied, then the accelerometer x and y axes are either already aligned with that of the vehicle, or are misaligned by multiples of 90 degrees or 7c/2 rad.

However, computing the score value in this way for every timeslot is very computationally taxing, demanding a high amount of power and memory from the device. For the same reasons, existing algorithms cannot be used because they require maintaining a larger amount of data than it is possible to store on the telematics device. Therefore, the method of the present disclosure is additionally memory and time efficient in order to be useable directly on the accelerometer itself, which removes the need for external calibration and ensures the accelerometer can be set-up and calibrated without utilising external bandwidth.

Thus, in an alternative embodiment, to allow for a more efficient calibration of the x and y axes, the step of rotating the x-y plane may comprise the steps of defining a time slot, said time slot being a subset of the time period of the journey of the vehicle. Then sum of squares for each set of x and for each set of y scalar components and the sum of cross product between x and y scalar components are calculated for each time slot. These values are then used to identify if a particular condition (a mathematical inequality) is satisfied. If the condition is satisfied, then the x and y axes of the accelerometer are rotated anti-clockwise by an angle given by the inequality/condition. Subsequently, the method seeks to define a new timeslot, adjacent to the previously defined timeslot to be the current timeslot. The steps noted above are then repeated until the condition is no longer stratified, to produce a first set of acceleration vectors. If and when the condition is no longer satisfied, it implies that the accelerometer x and y axes are now either aligned with that of the vehicle, or are misaligned by multiples of 90 degees or z/2 rad.

In the above method, the method or algorithm only calculates the sum of squares of x and y scalar components, and the sum of products of x and y scalar components for each timeslot. This eliminates the need to apply a 2-d rotation matrix on the set of x and y scalar components for each timeslot The method defined above may further comprise the step of identifying timeslots where the ranges of x and y scalar components for the first set of acceleration vectors are at a value of zero or close to zero. It can be appreciated that these timeslots can correspond to instances when the vehicle is at rest. Once said timeslots are identified, the method may further comprise the step of identifying a first series of timeslots for when the vehicle is moving, said series of timeslots defined after the timeslots for when the vehicle is at rest Once the timeslots defining the moving vehicle are known, the method may calculate a range for the x and y scalar components for each timeslot for when the vehicle is moving.

Furthermore, the method may define a second score value, said second score value again initialised to null as defined above. A second score value may be increased by unity if the range of y is greater than x for a particular timeslot, otherwise the second score value may be decreased by unity. Again, the process may be repeated for all timeslots within the series.

Finally, if the second score value is greater than zero, the method may comprise the step of rotating the x-y plane of the accelerometer anti-clockwise by 90 degrees, such that a second set of acceleration vectors are produced Alternatively, the method defines the first set of acceleration vectors to be the second set.

As noted above, the method may identify a timeslot where both the ranges of x and y scalar components for the first set of acceleration vectors are at a value of zero or close to zero.

This timeslot is then used to correspond to when the vehicle is at rest. The method then identifies a second series of timeslots for when the vehicle is moving, said series of timeslots defined after the timeslot for when the vehicle is at rest.

The method may then determine if the x scalar components for each timeslot are increasing or decreasing. This allows the direction that the accelerometer is facing to be determined and a forward direction assigned accordingly.

In a further embodiment, the method may define a third score value, said third score value initialised to null. This third score function may be increased by unity if the x scalar components are decreasing, otherwise it may be decreased by unity. As noted above, this may be repeated for all timeslots within the series. Accordingly, if the third score value is more than zero, the method rotates the x-y plane of the accelerometer by 180 degrees anticlockwise, such that a third set of acceleration vectors are produced. Othenvise the method defines the second set of acceleration vectors to be the third set Once this condition is met then the accelerometer axes now correspond to the axes of the vehicle.

The present invention seeks to utilise an initial calibration journey to determine initially a z-axis by determining the relative orientation of the accelerometer with respect to gravity.

Once determined, the method then seeks to align the x-y plane about this defined z-axis. As noted above, this can involve analysing time portions of the calibration journey to determine the probable alignment of the accelerometer in both the x and y axes. Once determined, the accelerometer axes (i.e. the relative accelerometer vector values) are then aligned to the axes of the vehicle.

Finally, it can be appreciated that the method may be repeated at periodic points in the lifetime of the accelerometer, for example at the beginning of a journey, if the accelerometer determines movement indicative of replacement or a fall from its installed location, or if the accelerometer determines a likely misalignment from its calibrated position (for example if the z-axis no longer equals a negative unity value). Alternatively, or additionally, a user may be prompted to recalibrate the accelerometer if the installed location is altered.

According to a second aspect of the present invention, there is provided a 3-axis accelerometer for mounting to a vehicle, said accelerometer comprising: mounting means for mounting the accelerometer to the vehicle; and a processor for carrying out the method of any embodiment of the first aspect.

It can also be appreciated that the accelerometer may comprise a series of accelerometers, one for each axis. The accelerometer may also comprise ancillary components, such as a housing, further elements of the mounting means, power components, and the like. Typically the accelerometer comprises a battery to power the components.

There may be provided a computer program, which when run on the processor, causes the processor to configure the accelerometer, including any aspect of the accelerometer such as a circuit, controller, sensor, filter, or device disclosed herein to perform any method disclosed herein The computer program may be a software implementation, and the computer may be considered as any appropriate hardware, including a digital signal processor, a microcontroller, and an implementation in read only memory (ROM), erasable programmable read only memory (EPROM) or electronically erasable programmable read only memory (EEPRONI), flash memory, or a chip as non-limiting examples. The software implementation may be an assembly program The computer program may be provided on a computer readable medium, which may be a physical computer readable medium, such as a disc or a memory device, or may be embodied as a transient signal. Such a transient signal may be a network download, including an internet download.

These and other aspects of the invention will be apparent from, and elucidated with reference to, the embodiments described hereinafter.

Brief description of drawings

Embodiments will be described, by way of example only, with reference to the drawings, in 15 which figure la shows a vehicle having an accelerometer according to the present invention, both of which axes are misaligned; figure lb shows the vehicle of figure la, when the vehicle z axis and the accelerometer z axis are aligned, but their x and y axes are misaligned; figures 2a-2c shows an schematic of x and y axes of figure lb, when the x and y axes of the vehicle and accelerometer are offset by; it/2; it; or 37c/2 figure 3 shows a plot of a score value for three journeys obtained sing a calibrated accelerometer as a function of misaligned azimuthal angle; and figures 4a to 4c show plots of the acceleration vectors for raw ideally model ca brined accelerometer values; accelerometer values from an uncalibrated accelerometer attained hy artificial rotation of calibrated accelerometer and the re-aligned accelerometer axes attained by applying the calibration algorithm, such that it substantially matches figure 4a.

Detailed description of the invention

Throughout a journey, three time series, each corresponding to a accelerometer axis 102, is generated by an accelerometer. Coordinates xi, yi and zi (measured in g's, where is g is the gravitational acceleration value) are generated as the accelerometer moves through space. Let 37 and be the mean for each of these series. If the accelerometer is aligned perfectly with the axis of the vehicle, then the mean acceleration vector (1,7, f = (0, 0, -1). From the start of a journey to finish, the vehicle (on average) will accelerate the same number of times as it will decelerate, and that the number of right turns will typically be equal to the left turns. This results in the integral of the 1, 7 traces over the journey time being zero The mean z axis is expected to have a negative unit value due to the effects of gravity.

However, when the accelerometer is initially mounted into a vehicle 104, this will not be the case. Figure la shows that the accelerometer axes 102 are misaligned with respect to the vehicle axes 100. For this reason, the first stage of the algorithm is to rotate our accelerometer readings such that 0, 7, = (0, 0, -1). Note that here the gravitational acceleration value g is set to unity. Also note, it is assumed that modulus of the mean acceleration vector is unity i.e. Ilk, 7, 41= 1; if this is not true rescale to ensure that (X:, 7, f) is a unit vector.

Note that, for a 3-D unit vector u = (us., uy, us), one can define: R(u, 0) = [cos0 + uR1-cos0) uyu,(1-case) + uzsin0 uzu,(1-cos0) -uysin0 (1) ux u (1 -cos0) -uzsin0 usu,(1 -cast) + uysinG y uyuz(1 -case) -ussine COSA u(1 -COSO) cos61 + uz2(1 -cose) U U (1 -COSO) UxSi2261 z y where Nit, 0) is the (3-D) rotation matrix for an anticlockwise rotation of with axis u, and 9 is the polar angle (see figure la). Moreover, to wish to rotate (±, 7, 2) onto (0, 0, -1) then the axis of rotation will be: Z) x (0, 0, -1) = 0) (2) and the angle of rotation 0 will satisfy: (.27.,37,Z). (0, 0, -1) = cos0 = arccos(-I) (3) Thus, the rotation matrix becomes: M R ((\lx2 +y2 g2 +y2, 0) , arccos(-2)) (4) The Al will rotate (X:, y, Z) onto (0, 0, -1). Therefore, each accelerometer vector (xi, yi, zi) is rotated by computing: (x;., yi, )T = M (xi, yi, ZDT (5) where superscript T denotes the transpose of the vector. This therefore yields three rotated time series (4, yi, 4), where the z-component (4) will be corrected for gravity.

This is shown in figure lb, where the z-axis 102 of the accelerometer is parallel to the z-axis 100 of the vehicle. However, there is still the problem of orientating the x-y plane of the accelerometer to coincide with the vehicle's x-y plane, which may differ by an azimuthal angle 0, as shown in figure lb. Therefore, one embodiment seeks to find the value of co e [0, 271-,i such that when the x-y plane of the accelerometer anticlockwise by 0 it coincides with that of the vehicle. In the present invention, this is done by producing a score for each (1), say 1,(0), representing the likelihood of the angle being correct.

First, L(P) is set to zero. Then, the journey is divided into finite time periods (e.g. measured in seconds). For example, if this finite time period is set to 1 second, then 100 acceleration vectors (xi, yi, zi) will be produced in that time period using a 100 Hz accelerometer. Then for every x and y component, one can define the following: 4(0) = 4cos(0) -yisin(0) (6a) y;(0) = 4sin(0) + y;cos(0) (6b) Equation 6 is a (2-D) rotation matrix and (4(0), 4(0)) are the accelerometer traces for when the x-y plane is rotated anticlockwise by J. Note that in equation 6, the rotated acceleration components (4, y;) are used. From this, one can calculate the sum of squares of S: NH 4 la in the following manner: S(a, b) = Eil°?(ai -a) (b1-b) (7) And compute S(x'(0), x1(0)) and S(.)/ (0). 3?(0)). Then, L(0) is incremented by one if the following condition is satisfied: 16 (8) S (y' (0), yr (0)) < 1100 Intuitively, equation 8 is met when there is high activity in the x-direction and low activity in the y-direction, which is expected when a vehicle is accelerating forwards or is braking. This process is then repeated using the rotated acceleration components (4, )4) from subsequent time periods, until a maximum value of L(0) is reached. When rotated by 0 corresponding to the maximum value of L(0), the x-y plane of the accelerometer then should either coincide with the x-y plane of the vehicle, or will be misaligned by multiples of 90 degrees or R/2 rad.

However, note that computing L(15) in this way for a large number of different angles will end up being very computationally taxing However, equation 8 can be simplified significantly by first noting that: S (x' (0), x' (0)) = S(x', xr)cos2 0 + S(y', y') sin2 -S(x' y')sin 20 (9a) S (y' (0), y' (0)) = S(x' , x')sin2 + S(y' , y') cos20 + S(x' , ypsin 20 (9b) Equations 8a and 8b can be simplified even further by noting that: S (x' (0), x' (0)) = S(x/ x' )cos2 0 + S (y1, y') sin2 -S(x/ y')sin 20 = S(xcx')[1 + cos20] + , y')[1 -cos20] -S(x' y')sin 20 = S(x',x')+25(y',y') C(x',x')-2S(yi,y1 COS20 -S(X1, y')sin 20 = Rsin(20 -a) + C, if S(x', y') > 0 (10) Rsin(20 -a) + C, if S(x', y') < Where R = \IS (x', y')2 + (S(x', x') -S(y1, y9)2 oc = arctane(x' 'x') s(111.3?)) and 4 2S(x11) c _ s(xr,x')+ S(y1*3?) Similarly: Rsin(20 -a) + C, if S(x',y') > 0 S(Yi (0),31(0)) = t-Rsin(20 -a) + C, if S(x' y') < 0 (11) Now, equations 1 and 10 can be used to re-write the condition of equation 8 For the case where S(x1,y1) > 0: -Rsin(20 -a) + C > and Rsin(20 -a) + C < 0 4 sin(20 -a) < R-1 min (C - 1 -----c) 16'100 (12a) And in the case where S(x', y') < 0: sin(20 -a) > R-1 max (I--C C- 1 (12b) 16 100) 16 ' where Mill 'max(a, b) denotes taking the minimum/maximum of values a and b. Thus, for each finite time period of the journey one only needs to calculate S(x',x'),S(y1, ypand S(x', y'). Once these are found R, a, and C can be calculated, and subsequently which angle 0 (if any) to increment.

It is clear that 40) is period of it, that is, L(0) = L(0 + IC) V P. Figures 2a, 2b and 2c show three different orientations of the x-y plane 100 of the accelerometer relative to vehicle plane 102. These correspond to an offset of m/2, n. or 3r t/2, respectively, of the accelerometer plane with respect to the vehicle plane. Typically two of these orientations will produce a peak value for 40). Thus, additional checks are required to ensure that maximum value of L(0) corresponds to when 0 -0 (i.e. when the two planes are perfectly aligned).

Figure 3 shows a series of plots L(0) with 0 El [0, for three different journeys (106, 108, 110) obtained using a calibrated accelerometer which was initially calibrated (i.e. 0 -0). For each of the three journeys peaks at around 0 -0, a./2 and 71 can be seen. The peaks at x/2 and it correspond when to when there is an offset of fri2 and If between the two planes. This is shown in figures 2a and 2b, respectively.

The first thing to check is if the forwards and sideways directions have been interchanged, orrespoud to an offset of 0 -it/2 or 37t./2 between the two planes, as shown in figures 2a and 2c, respectively. To do this, the total journey time is again led into finite time periods (e.g. l second). This time, the range(x) and range(y) is calculated for all the acceleration vectors belonging to each time period, and the time period where both of these values are below 0.01g is identified. This period corresponds to when the vehicle is very likely to be at rest. The next step is to identify a subsequent time period where the vehicle is not at rest, and calculate range(x) and range(y) for that period. This process is repeated several times throughout the journey. If, throughout the journey, there are more instances/periods where the range(y) > range(x), then the x-y plane of the accelerometer is rotated anti-clockwise by it/2, otherwise nothing is done. Intuitively, this works because there will be more activity in the x-direction when the vehicle sets off from rest.

After doing the above correction, the x-y plane of the accelerometer will either be rotated correctly, or will be offset by 0 = 7C, as shown in figure 2b. In other words, the backwards and forwards may still be interchanged. To correct this, the total journey time is again divided it Ito finite time periods and a period where both the range(x) and range(y)are below 0.018 is identified (vehicle at rest). Then, a subsequent time period where the vehicle is not at rest is identified, to see whether the x acceleration has increased or decreased. This process is repeated several times throughout the journey. If, throughout the journey, there are more instances where the x acceleration has increased then the accelerometer axis is likely to be perfectly aligned with the vehicle. However, if there are more instances where the x acceleration has decreased, then the accelerometer x-y plane is rotated by 71 to bring it into likely alignment with the vehicle.

A 3-axis accelerometer measures acceleration in 3 orthogonal directions simultaneously (see Fig 1) These 3-axis accelerometers may be useful in telematics devices, since they give information about how the driver of a vehicle accelerates from rest, how harshly they brake and how they take corners. However, as noted above, to use the accelerometer for this purpose, it is essential that the axis of the accelerometer is aligned to the axis of the vehicle (i.e. the x axis of the accelerometer is aligned with the forwards/backwards direction of travel, y axis aligned to side to side, z axis vertically upwards). In the past, this meant that telematics devices would have to be installed very precisely, so that they were perfectly flat and faced directly forwards.

The accompanying figures show an example of running the method or algorithm on a journey. Fig.4a shows raw x, y and z accelerometer readings for the start of a journey, where the accelerometer is aligned perfectly to the axis of the vehicle Figure 4b show data from a misaligned (raw) accelerometer. The accelerometer vectors in this figure being artificially rotated to simulate the accelerometer being installed in a nonstandard position on the vehicle (shown in Fig.4b). By applying the algorithm to these rotated accelerometer vector values the original accelerometer traces can be recreated (see figure 4c).

Comparing Figures 4a and 4c, shows that the accelerometer axes are successfully aligned with the axes of the vehicle by the algorithm From reading the present disclosure, other variations and modifications will be apparent to the skilled person. Such variations and modifications may involve equivalent and other 20 features which are already known in the art of accelerometer calibration and which may be used instead of, or in addition to, features already described herein.

Although the appended claims are directed to particular combinations of features, it should be understood that the scope of the disclosure of the present invention also includes any novel feature or any novel combination of features disclosed herein either explicitly or implicitly or any generalisation thereof, whether or not it relates to the same invention as presently claimed in any claim and whether or not it mitigates any or all of the same technical problems as does the present invention Features which are described in the context of separate embodiments may also be provided in combination in a single embodiment. Conversely, various features which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable sub-combination. The applicant hereby gives notice that new claims may be formulated to such features and/or combinations of such features during the prosecution of the present application or of any further application derived therefrom.

For the sake of completeness it is also stated that the term "comprising" does not exclude other elements or steps, the term "a" or "an" does not exclude a plurality, and reference signs in the claims shall not be construed as limiting the scope of the claims.

Claims

Claims 1 A method for calibrating a vehicle-mounted accelerometer having an unknown orientation, said method comprising the steps of: a) defining a time period equal to a length of a journey of the vehicle; b) obtaining a set of acceleration vectors from the accelerometer during the time period, said acceleration vectors comprising x, y and z scalar components; c) rotating the z-axis of the accelerometer by a polar angle, such that the z-axis is aligned parallel to the direction of gravitational force; and d) rotating the x-y plane of the accelerometer by an azimuthal angle, such that the x and y axes of the accelerometer are aligned with the x and y axes of the vehicle.
2 The method of claim 1, wherein the x axis of the vehicle corresponds to the forwards and backwards motion of the vehicle, and/or the y-axis corresponds to the sideways motion of the vehicle.
3 The method of claim 2, wherein the step of rotating the z-axis comprises rotating each acceleration vector to produce a set of transformed acceleration vectors, such that a z scalar component of a mean acceleration vector is equal to a gravitational acceleration value, said mean acceleration vector calculated from the set of transformed acceleration vectors.
4. The method of claim 3, wherein the step of rotating each acceleration vector comprises applying a 3-d rotation matrix on each acceleration vector.
The method of claim any one of claims 1 to 4, wherein step a) further comprises the steps of: defining a time slot, said time slot being a subset of the time period of the journey of the vehicle; and where step d) further comprises the step of i) defining a score value, said score value initialised to null; ii) applying a 2-d rotation matrix on each transformed acceleration vector within the timeslot to produce a set of rotated acceleration vectors; Hi) calculating a sum of squares for each set of x and for each set of y scalar components of the rotated acceleration vectors for the timeslot; incrementing the score value by unity if the sum of squares satisfy a particular condition; v) defining new timeslot adjacent to the previously defined timeslot to be the timeslot; and vi) repeating steps ii) to v) until a maximum value for the score value is reached corresponding to the azimuthal angle, to produce a first set of acceleration vectors.
6 The method of any one of claims 1 to 4, wherein step a) further comprises the step of defining a time slot, said time slot being a subset of the time period of the journey of the vehicle; and where step d) further comprises the step of: i) calculating the sum of squares for each set of x and for each set of y scalar components and the sum of cross product between the sets x and y scalar components for the time slot; using the sum of squares for each set of x and y scalar components and sum of cross product between x and y scalar components for each timeslot to identify if a particular condition is satisfied; calculating angle of rotation for the x and y axes of the accelerometer, and rotating the x and v axes of the accelerometer anti-clockwise by the said calculated angle, iv) defining new timeslot adjacent to the previously defined timeslot to be the timeslot; repeating steps i) to iv) until the condition is no longer satisfied, to produce a first set of acceleration vectors 7 The method of claim 5 or claim 6, further comprising the steps of i) identifying timeslots where both the ranges of x and y scalar components for the first set of acceleration vectors are at a value of zero or close to zero, said timeslots correspond to when the vehicle is at rest; ii) identifying a first series of timeslots for when the vehicle is moving, said series of timeslots defined after the timeslots for when the vehicle is at rest; calculating ranges of x and y scalar components for each timeslot for when the vehicle is moving; iv) defining a second score value, said second score value initialised to null, v) increasing the score value by unity if the range of y is greater than x for a particular timeslot, otherwise decrease it by unity; repeating step v) for all timeslots within the series; and if the second score value is greater than zero, rotating the x-y plane of the accelerometer anti-clockwise by 90 degrees, such that a second set of acceleration vectors are produced, otherwise defining the first set of acceleration vectors to be the second set.8 The method of claim 7, further comprising the steps of: i) identifying timeslots where both the ranges of x and y scalar components for the second set of acceleration vectors are at a value of zero or close to zero, said timeslots correspond to when the vehicle is at rest; identifying a second series of timeslots for when the vehicle is moving, said series of timeslots defined after the timeslots for when the vehicle is at rest; iii) determining if the x scalar components for each timeslot are decreasing or increasing; iv) defining a third score value, said third score value initialised to null; v) increasing the score value by unity if the x scalar components are decreasing, otherwise decrease it by unity; vi) repeating step v) for all timeslots within the series; and vii) if the third score value is more than zero, rotating the x-y plane of the accelerometer by 180 degrees anti-clockwise, such that a third set of acceleration vectors are produced, otherwise defining the second set of acceleration vectors to be the third set, such that the accelerometer axes are aligned with the vehicle axes.A 3-axis accelerometer for mounting to a vehicle, said accelerometer comprising: mounting means for mounting the accelerometer to the vehicle; and a processor for carrying out the method of any preceding claim.