Patent Publication Number: US-2023152417-A1

Title: Method for locating a vehicle

Description:
The invention relates to a method and a system for locating a vehicle. 
     It is known, in addition to the measurements of an inertial measurement unit, for measurements to be used of the distance between a mobile transceiver fixed to the vehicle and a fixed transceiver located along the path of the vehicle. This improves the accuracy of locating the vehicle. Such a location method is described, for example, in the following articles:
     V. Di Pietra et al.: “ Loosely Coupled GNSS and UWB with INS Integration for Indoor/Outdoor Pedestrian Navigation ”, Sensors, 5 Nov. 2020; and   Monica N. et al.: “ Hybrid GNSS/INS/UWB Positioning forLive Demonstration Assisted Driving ”, 2019 IEEE Intelligent Transportation Systems Conference (ITSC), Auckland, NZ, Oct. 27-30, 2019;   Navarro Monica et al.: “ Hybrid GNSS/INS/UWB Positioning for Live Demonstration Assisted Driving ”, 2019 IEEE Intelligent Transportation Systems Conference, 27 Oct. 2019, pg. 3294-3301.   

     More specifically, in these known methods, the location of the vehicle is corrected as a function of a difference between:
         a distance between the fixed and mobile transceivers measured from the transmission or reception instants of radio signals exchanged between the fixed and mobile transceivers; and   an estimate of this distance that is constructed from the estimated position of the vehicle at an instant t m  and from the known position of the fixed transceiver.       

     The prior art is also known from the following documents:
     CN 112349143 A;   Sirorenko Juri et al.: “ Error corrections for Ultra - wide band ranging ”, IEEE Transaction on instrumentation and measurement, vol. 69, No. 11, 21 May 2019, pg. 9037-9047;   CN 109946730 A;   GB 2551861 A;   WO 2020/063979 A1.   

     The invention aims to propose such a method for locating a vehicle, in which the location of the vehicle is more accurate. 
     Therefore, an aim of the invention is such a method for locating a vehicle. 
     A further aim of the invention is an information storage medium that comprises non-transitory instructions, executable by an electronic computer, for executing the aforementioned method for locating a vehicle. 
     Finally, the invention also relates to a system for locating a vehicle. 
    
    
     
       The invention will be better understood upon reading the following description, which is provided solely by way of a non-limiting example and with reference to the drawings, in which: 
         FIG.  1    is a schematic illustration of a system for locating a vehicle; 
         FIG.  2    is a schematic illustration of various software modules implemented in the system of  FIG.  1   ; 
         FIG.  3    is a flow chart of a method for locating a vehicle using the system of  FIG.  1   ; 
         FIG.  4    is a timing chart showing the instants at which different events occur on different time axes. 
     
    
    
     Throughout these figures, the same reference signs are used to denote the same elements. 
     Throughout the remainder of this description, the features and functions that are well known to a person skilled in the art are not described in detail. In particular, for the general knowledge of a person skilled in the art relating to systems for locating a vehicle using an inertial navigation unit, reference is made, for example, to the following thesis: S. Godha, “ Performance Evaluation of Low Cost MEMS - Based IMU Integrated With GPS for Land Vehicle Navigation Application ”, PhD report, 2006. Hereafter, this thesis is referred to as “Godha2006”. 
     In this description, a detailed example of an embodiment is first described in Chapter I with reference to the figures. Then, in the next chapter II, variants of this embodiment are presented. Finally, the advantages of the various embodiments are presented in chapter Ill. 
     Chapter I: Example of an Embodiment 
       FIG.  1    shows a vehicle  2  capable of moving along a path. For example, in this example, the vehicle  2  is a motor vehicle travelling along a road. The vehicle  2  in this case is equipped with propulsion means  34 , such as an engine that drives the wheels of the vehicle  2 . 
     The vehicle  2  is equipped with a system  30  for locating this vehicle. This system  30  is capable of determining the position, the orientation and the velocity of the vehicle  2  in a terrestrial coordinate system R T . In this case, the terrestrial coordinate system R T  is fixed without any degree of freedom relative to the earth. The coordinate system R T  comprises three axes, which are typically orthogonal to each other. For example, in this case, the coordinate system R T  is the coordinate system known as the ECEF (“Earth Centred, Earth Fixed”) coordinate system. 
     A movable coordinate system R b  is also fixed without any degree of freedom relative to the vehicle  2 . This coordinate system R b  comprises three axes that are orthogonal to each other, denoted x b , y b  and z b , respectively. Conventionally, when the vehicle  2  moves horizontally, the x b  and y b  axes are in a horizontal plane and the z b  axis is vertical. In this case, the x b  axis is oriented and pointed in the direction in which the vehicle is moving when it is moving forwards. 
     In this case, the position of the vehicle  2  in the coordinate system R T  is expressed by coordinates of the origin of the coordinate system R b  in the coordinate system R T . 
     The orientation of the vehicle  2  is expressed by the yaw angle ψ, the pitch angle θ and the roll angle φ of the coordinate system R b  defined relative to a coordinate system called “navigation” coordinate system. In practice, the orientation of the vehicle is usually in the form of an orientation matrix, from which the yaw angle, the pitch angle and the roll angle of the vehicle can be derived. The orientation of the vehicle also can be in the form of a vector directly comprising the yaw angle, the pitch angle and the roll angle of the vehicle. Hereafter, these two cases are considered to be equivalent and therefore that the orientation of the vehicle comprises the yaw angle, the pitch angle and the roll angle of the vehicle as soon as these three angles can be directly derived from a matrix or a vector. 
     The position, the orientation and the velocity determined by the system  6  are delivered to an output  37 . Hereafter, the position, the orientation and the velocity delivered to the output  37  by the system  30  for an instant t k  are denoted P(k), O(k) and V(k), respectively. 
     Typically, the vehicle  2  comprises a cockpit  38  for guiding or assisting the guiding of the vehicle  2  to a predefined destination. The cockpit  38  is connected to the output  37 . The cockpit  38  can be a manual and/or automatic cockpit. In the case of a manual cockpit, the determined position, orientation and velocity are transmitted to a human-machine interface to help a human being to steer the propulsion means  34 . In the case of an automatic cockpit, the determined position, orientation and velocity are automatically converted into commands for driving the propulsion means  34 , then are automatically transmitted to these propulsion means  34 . 
     The system  30  comprises a satellite geolocation unit  40  and an inertial measurement unit  42 . 
     The unit  40  is known using the acronym GNSS (Global Navigation Satellite System). Based on the satellite signals that it receives, the unit  40  generates signals representing the position and the velocity of the vehicle in the coordinate system R T . The unit  40  updates its measurements at a frequency F 40 . Conventionally, the frequency F 40  ranges between 0.1 Hz and 20 Hz. 
     The unit  42  is known using the acronym IMU (“Inertial Measurement Unit”). In particular, the unit  42  comprises a triaxial accelerometer  44  and a triaxial gyroscope  46 . By virtue of these sensors, the unit  42  is capable of measuring the variation of the orientation, the position and the velocity of the vehicle  2 . In this case, the measurement axes of the accelerometer  44  and the gyroscope  46  are coincident with the x b , y b  and z b  axes of the coordinate system R b , respectively. Furthermore, the accelerometer  44  is arranged such that a positive measurement of the acceleration of the vehicle  2  along the x b  axis means that the vehicle  2  is accelerating while moving forward. 
     The unit  42  updates the acceleration and angular velocity measurements at a high frequency F 42 . Conventionally, the frequency F 42  ranges between 20 Hz and 2,000 Hz. For example, in this case the frequency F 42  is equal to 200 Hz. 
     In order to accurately locate the vehicle  2  along its path, the system  30  also comprises a radio transceiver  20  on board this vehicle. One or more fixed transceiver(s) located along the path of the vehicle  2  is/are also provided. For example, the fixed transceivers are arranged at regular intervals along the path of the vehicle  2 .  FIG.  1    shows a single fixed transceiver  22 . 
     The description provided hereafter in the particular case of this transceiver  22  similarly applies to all the other fixed transceivers disposed along the path of the vehicle  2 . 
     The transceiver  22  is stationary and its position in the terrestrial coordinate system R T  is known in advance and does not change. When the vehicle  2  is located on a segment of its path in the vicinity of the transceiver  22 , irrespective of the position of the vehicle  2  on this segment, the transceivers  20 ,  22  are capable of exchanging frames of information with each other, allowing the distance separating them to be measured. 
     The transceiver  20  exchanges frames of information with the transceiver  22  by means of a wireless radio link  48 . These frames of information are particularly exchanged in order to measure the distance that separates these transceivers  20 ,  22  based on the flight times of these frames of information. To this end, in this case the transceivers  20 ,  22  are Ultra-Wide Band (UWB) transceivers. The term “ultra-wide band transceiver” or “UWB transceiver” in this case denotes a transceiver that uses a wide frequency band to send and receive the frames of information. A “wide” frequency band is a frequency band with a width that is greater than 0.2 f c , where f c  is the median frequency of this frequency band. Typically, a wide frequency band is greater than 250 MHz or even greater than 400 MHz. 
     Each measurement of a distance between the transceivers  20 ,  22  requires exchanging several frames of information between these transceivers  20 ,  22  and measuring the transmission and reception instants of these frames of information. This exchange of frames of information is repeated at a frequency F 20  in order to update the distance measurement at this frequency. The frequency F 20  is smaller than the frequency F 42 . Typically, the frequency F 20  is ten or fifty times smaller than the frequency F 42 . Conventionally, the frequency F 20  ranges between 0.1 Hz and 20 Hz. In this case, the transmission and reception instants of the frames of information are obtained by the transceiver  20  housed in the vehicle  2 . 
     In order to determine the position, the orientation and the velocity of the vehicle  2  from the measurements of the units  40  and  42  and the transmission and reception instants obtained by the transceiver  20 , the system  30  comprises a programmable electronic computer  50 . This computer  50  is capable of acquiring the measurements of the units  40  and  42  and the transmission and reception instants obtained by the transceiver  20 . Then, from these measurements, the computer  50  determines the position, the orientation and the velocity of the vehicle  2  in the coordinate system R T . The computer  50  comprises a microprocessor  52  and a memory  54  comprising the instructions and the data needed to implement the method described with reference to  FIG.  3   . 
     More specifically, the memory  54  comprises the instructions of a software module  56  capable of determining the position, the orientation and the velocity of the vehicle  2  from the measurements acquired when it is executed by the microprocessor  52 . In this case, the module  56  particularly implements a merge algorithm that establishes a new estimate of the position, the orientation and the velocity of the vehicle  2  from a previous estimate of the position, the orientation and the velocity of the vehicle  2  and from new measurements acquired since this previous estimate. Typically, the merge algorithm also establishes margins of error on each new estimate. 
     The general principles of merge algorithms are well known to a person skilled in the art. For example, an interested reader can once again refer to the aforementioned Godha2006 thesis. Typically, this merge algorithm implements one or more Kalman filter(s). In this case, the module  56  implements an architecture known as a “closed loop integration scheme” or “closed loop approach”. 
       FIG.  3    shows the architecture of the module  56  in more detail. The module  56  comprises:
         a sub-module  60  for integrating an inertial measurement;   a sub-module  61  for computing a corrected distance between the transceivers  20 ,  22  from the transmission and reception instants obtained by the transceiver  20 ; and   a correction sub-module  62 .       

     The general operating principles of the sub-modules  60  and  62  are known. For example, for a detailed description of these general principles, the reader can consult Chapter 4 of the Godha2006 thesis. Thus, hereafter, only the details specific to the invention are described in detail. 
     The sub-module  60  is known as “Mechanization”. For each instant t k , the sub-module  60  constructs a rough estimate of a position P e (k), an orientation O e (k) and a velocity V e (k) of the vehicle  2 . Throughout this document, the “k” symbol is the sequence number of the instant t k  in the temporally ordered sequence {0, t 1 , t 2 , . . . , t k−1 , t k , . . . } of the instants t k . Let k−1 be the sequence number of the instant t k−1  immediately preceding the instant t k . The position P e (k), the orientation O e (k) and the velocity V e (k) of the vehicle  2  are each a vector comprising three coordinates. The coordinates of the position P e (k) in the coordinate system R T  are denoted x e (k), y e (k) and z e (k). The coordinates of the orientation O e (k) are denoted ψ e (k), θ e (k) and φ e (k) and the coordinates of the velocity V e (k) are denoted Vx e (k), Vy e (k) and Vz e (k). 
     The frequency of the instants t k  is less than or equal to the frequency F 42 . In this case, the frequency of the instants t k  is equal to the frequency F 42 . 
     The sub-module  60  constructs the position P e (k), the orientation O e (k) and the velocity V e (k) from:
         the previous position P(k−1), the previous orientation O(k−1) and the previous velocity V(k−1) determined for the vehicle  2  at the instant t k−1  by the system  30  and delivered to the output  37 ; and   the measurements of the accelerometer  44  and of the gyroscope  46  acquired by the sub-module  60  at the instant t k .       

     The combination of the sub-module  60  and of the unit  42  forms an Inertial Navigation System, which is known using the acronym INS. 
     The sub-module  61  acquires the transmission and reception instants obtained by the transceiver  20  and the last position of the vehicle  2  estimated by the sub-module  60 . Then, the sub-module  61  delivers a corrected distance to the sub-module  62  that is computed from the acquired transmission and reception instants and from the last acquired position of the vehicle  2 . The detailed operation of this sub-module  61  is described with reference to  FIG.  3   . 
     At particular instants t k , the sub-module  62  corrects the position P e (k), the orientation O e (k) and the velocity V e (k) constructed by the sub-module  60  for this instant t k  in order to obtain a corrected position P c (k), a corrected orientation O c (k) and a corrected velocity V c (k) for this instant t k . Hereafter, these particular instants t k  are called “instants t m ”. The “m” symbol is equal to the sequence number of a particular instant t k  in the sequence {0, t 1 , t 2 , . . . , t k−1 , t k , . . . }. Each sequence number m is therefore equal to a respective sequence number k. Thus, the position P e (m), the orientation O e (m) and the velocity V e (m) are equal to the position P e (k), the orientation O e (k) and the velocity V e (k), respectively, constructed for the instant t k  equal to the instant t m . The sequence {0, t 1 , t 2 , . . . , t m-1 , t m , . . . } of the instants t m  is a sub-set of the sequence {0, t 1 , t 2 , . . . , t k−1 , t k , . . . }. Thus, the correction by the sub-module  62  is not carried out for each instant t k  but only for some of them. At each instant t m , the sub-module  62  combines the position P e (m), the orientation O e (m) and the velocity V e (m) with respective correction coefficients in order to obtain the corrected position P c (m), the corrected orientation O c (m) and the corrected velocity V c (m). At the instants t m , the corrected position P c (m), the corrected orientation O c (m) and the corrected velocity V c (m) are delivered to the output  37  and not the position P e (m), the orientation O e (m) and the velocity V e (m). The correction coefficients are updated as a function of the measurements of the unit  40  and of the corrected distance determined by the sub-module  61 . The correction coefficients are therefore updated at a frequency that is less than the frequency F 42 . 
     The sub-module  62  acquires the measurements of the unit  40  at a frequency that is less than or equal to the frequency F 42 . In this case, the acquisition frequency of the measurements of the unit  40  is equal to the frequency F 40 . Hereafter, tg i  denotes the acquisition instants of a new measurement of the unit  40 . These instants tg i  form a temporally ordered sequence {0, tg 1 , tg 2 , . . . , tg i-1 , tg i , . . . } of instants tg i . The “i” symbol denotes the sequence number of the instant tg i  in this sequence. The sub-module  62  updates the correction coefficients each time a new measurement of the unit  40  is acquired and therefore for each instant tg i . The instants tg i  are less frequent than the instants t k . 
     The sub-module  62  also acquires the corrected distance, delivered by the sub-module  61 , at a frequency that is less than or equal to the frequency F 42 . In this case, the acquisition frequency of the corrected distance is equal to the frequency F 20 . Hereafter, to j  denotes the acquisition instants of each new corrected distance. Also, dc j  denotes the corrected distance acquired at the instant to j . The “j” symbol is the sequence number of the instant to j  in the temporally ordered sequence {0, to 1 , to 2 , . . . , to j−1 , to j , . . . } of the instants to j . The sub-module  62  also updates the correction coefficients each time a new corrected distance dc is acquired and therefore for each instant to j . Since the frequency F 20  is lower than the frequency F 42 , several instants t k  systematically exist between the instants to j−1  and to j . 
     Hereafter, the sequences {0, tg 1 , tg 2 , . . . , tg i-1 , tg i , . . . } and {0, to 1 , to 2 , . . . , to j−1 , to 1 , . . . } are both considered to be sub-sets of the sequence {0, t 1 , t 2 , . . . , t k−1 , t k , . . . }. Thus, each instant tg i  and to j  corresponds to a respective instant t k  of the sequence {0, t 1 , t 2 , . . . , t k−1 , t k , . . . }. Furthermore, in this embodiment, the instants tg i  and to j  are separate. In other words, at an instant tg i  where the measurement of the unit  40  is acquired, no new corrected distance is acquired, and vice versa. Finally, throughout this document, the instants t m  are equal to the instants at which the sub-module  62  acquires either a measurement of the unit  40  or a new corrected distance. 
     In order to update the correction coefficients as a function of the measurements of the unit  40  and of the corrected distance, the sub-module  62  comprises a Kalman filter  64 . In order to combine the correction coefficients with the rough estimates delivered by the sub-module  60 , the sub-module  62  also comprises an adder  66 . 
     Herein, the filter  64  is known using the acronym ESKF (Error State Kalman Filter) since it estimates corrections to be made to the position, the orientation and the velocity estimated by the sub-module  60 . More specifically, the filter  64  provides a state vector X m|m  for each instant t m . In particular, the state vector X m|m  contains the correction coefficients to be used to correct the position P e (m), the orientation O e (m) and the velocity V e (m). For each instant t m , the adder  66  combines the correction coefficients provided by the filter  64  with the position P e (m), the orientation O e (m) and the velocity V e (m) in order to obtain the corrected position P c (m), the corrected orientation O c (m) and the corrected velocity V c (m). For each instant t k  after the instant t m  and before the instant t m +1, no correction is made to the estimates constructed by the sub-module  60 . 
     For example, in this case, the state vector X m|m  contains correction coefficients δ x (m), δ y (m) and δ z (m) of the coordinates x e (m), y e (m) and z e (m), respectively, of the position P e (m). The adder  66  adds these coefficients δx(m), δy(m) and δz(m), respectively, to the coordinates x e (m), y e (m) and z e (m) in order to obtain the coordinates x c (m), y c (m) and z c (m), respectively, of the corrected position P c (m). 
     The state vector X m|m  also comprises correction coefficients δ ψ (m), δ θ (m) and δ φ (m) of the coordinates ψ e (m), θ e (m) and φ e (m), respectively, of the orientation O e (m). The adder  66  adds these coefficients δ ψ (m), δ θ (m) and δ φ (m), respectively, to the coordinates ψ e (m), θ e (m) and φ e (m) in order to obtain the corrected coordinates ψ c (m), θ c (m) and φ c (m), respectively, of the orientation O c (m). 
     Similarly, the state vector X m|m  also comprises three correction coefficients δv x (m), δv y (m) and δv z (m) used to respectively correct the coordinates Vx e (m), Vy e (m) and Vz e (m) of the velocity V e (m). 
     Conventionally, the state vector X m|m  also comprises correction coefficients for correcting other parameters, such as measurement biases of the accelerometer  44  and of the gyroscope  46  or the like. In this embodiment, the state vector X m|m  also contains:
         three correction coefficients δba x (m), δba y (m) and δba z (m) for correcting the measurement biases of the accelerometer  44  in directions x b , y b  and z b , respectively;   three correction coefficients δbg x (m), δbg y (m) and δbg z (m) for correcting the measurement biases of the gyroscope  46  around the axes parallel to the x b , y b  and z b , respectively.       

     In this embodiment, the state vector X m|m  is therefore the following vector with fifteen coordinates: [δ ψ (m), δ θ (m), δ φ (m), δv x (m), δv y (m), δv z (m), δ x (m), δ y (m), δ z (m), δba x (m), δba y (m), δba z (m), δbg x (m), δbg y (m), δbg z (m)] T , where the “ T ” symbol is the symbol of the transposed operation. 
     The filter  64  is a recursive algorithm, which, for each instant t m , provides the adder  66  with a new state vector X m|m  computed from:
         the previous state vector X m-1|m-1 ;   the measurement of the unit  40  or of the new corrected distance acquired at the instant t m ; and   the position P e (m), the orientation O e (m) and the velocity V e (m) constructed by the sub-module  60  for the instant t m .       

     Conventionally, the filter  64  comprises a prediction block  68  computing a first state vector X m|m-1  from the vector X m-1|m-1 , followed by an update block  70  computing the vector X m|m  from the predicted vector X m|m-1 . These blocks are executed one after the other for each vector X m|m . 
     More specifically, the block  68  constructs a prediction X m|m-1  of the state vector from the previous state vector X m-1|m-1 . 
     In this case, an embodiment of the blocks  68  and  70  is described in the particular case where the filter  64  is an Extended Kalman Filter (EKF). 
     The propagation or state prediction equation of the filter  64  implemented by the block  68  is defined by the following relation (1): 
         X   m|m-1   =A   m-1   X   m-1|m-1 , 
     where:
         X m-1|m-1  is the estimate of the state vector at the instant t m-1  obtained by taking into account all the measurements up to the instant t m-1 ;   X m|m-1  is the prediction of the state vector at the instant t m  obtained by taking into account all the measurements up to the instant t m-1  and without taking into account the measurements acquired at the instant t m :   A m-1  is the state transition matrix at the instant t m-1 .       

     In the particular case described herein whereby the filter  64  is an Error State Kalman Filter, the vector X m-1|m-1  is always zero since it is assumed that the error was corrected beforehand. In other words, relation (1) is reduced to the following relation: 
         X   m|m-1 =0. 
     The propagation or prediction equation of the error covariance matrix implemented by the block  68  is defined by the following relation (2): 
         P   m|m-1   =A   m-1   P   m-1|m-1   A   m-1   T   +Q   m-1 , 
     where:
         P m-1|m-1  is the estimate of the covariance matrix of the error at the instant t m-1  obtained by taking into account all the measurements acquired up to the instant t m-1      P m|m-1  is the prediction of the covariance matrix P m  at the instant t m  obtained by only taking into account the measurements acquired up to the instant t m-1 ;   Q m-1  is the covariance matrix of the process noise v.       

     Block  70  corrects the prediction X m|m-1  of the state vector in order to obtain the state vector X m|m . The corrected vector X m|m  is constructed as a function of a difference Y m  between:
         an estimate {circumflex over (z)} m  of a physical quantity at the instant t m ; and   the measurement z m  of this same physical quantity at the instant t m .       

     The difference Y m  is known as “innovation”. In this case, the measured physical quantities are the position and the velocity measured by the unit  40  and, alternately, the corrected distance delivered by the sub-module  61 . Thus, for each instant tg i , the block  70  corrects the prediction X m|m-1  solely from the measurement of the unit  40  acquired at this instant tg i . Conversely, for each instant to 1 , the block  70  corrects the prediction X m|m-1  solely from the corrected distance acquired at this instant to 1 . The correction of the prediction X m|m-1 , at the instants tg i , as a function of the differences in position and in velocity, is carried out, for example, as described in Godha2006. Thus, this functionality of the block  70  is not described in further detail. Only the correction of the prediction X m|m-1 , at the instants to 1 , as a function of the corrected distance, is described hereafter. 
     In this embodiment, the physical quantity is the corrected distance dc m . The estimate {circumflex over (z)} m  of the corrected distance dc m  is constructed using the following relation (3): 
         {circumflex over (z)}   m =√{square root over (( x   e ( m )− B   x ) 2 +( y   e ( m )− B   y ) 2 +( z   e ( m )− B   z ) 2 )}
 
     where:
         m is the sequence number of an instant t m  of the sequence {0, t 1 , t 2 , . . . , t m-1 , t m , . . . } where a new corrected distance is acquired;   x e (m), y e (m) and z e (m) are the coordinates of the position P e (m) estimated by the sub-module  60  and expressed in the coordinate system R T ;   B x , B y , B z  are the coordinates of the position of the transceiver  22  in the coordinate system R T .       

     The coordinates B x , B y , B z  are constant and are pre-stored in the memory  54 . 
     The innovation Y m  is obtained using the following relation (4): Y m =dc m −{circumflex over (z)} m . 
     Typically, the block  70  corrects the prediction X m|m-1  by adding the innovation Y m  multiplied by the Kalman gain K m . The gain K m  is computed using the following relation (5): 
         K   m   =P   m|m-1   H   m   T ( H   m   P   m|m-1   H   m   T   +R   m ) −1 , where:         the matrix R m  is the covariance matrix of the noise over the corrected distance; and   H m  is an observation matrix.       
     The observation matrix H m  is a function of the partial drift of the relation (3) relative to the various parameters of the state vector X m|m . The matrix R m  is, for example, constant and is initialised using data relating to the covariance of the noise on the measurements of the transmission and reception instants obtained by the transceiver  20 . 
     Then, the state vector X m|m  is obtained using the following relation (6): X m|m =X m|m-1 +K m Y m . 
     The updated covariance matrix of the error at the instant t m  is computed using the following relation (7): P m|m =(I−K m H m )P m|m-1 , where I is the identity matrix. 
     The matrix P m|m  contains the margins of error on the estimates of the correction coefficients. 
     In this particular embodiment, the adder  66  is a simple adder that adds the corresponding correction coefficients that are contained in the state vector X m|m  to the position P e (k), to the orientation O e (k) and to the velocity V e (k). Then, the adder  66  delivers the corrected position P c (k), orientation O c (k) and velocity V c (k) obtained thus to the output  37 . 
     The operation of the system  30  will now be described with reference to the method in  FIG.  3    and using the timing chart in  FIG.  4   . 
     The use of the system  30  for locating the vehicle  2  starts with a phase  120  of initializing the system  30 . This phase  120  starts immediately after the system  30  is activated, i.e., typically immediately after it has been powered up. During this phase  120 , the various variables and parameters needed to execute the module  56  are initialized. For example, the initial values of the position, the velocity and the orientation of the vehicle  2  and the correction coefficients are initialized. Numerous algorithms exist for quickly obtaining these initial values. 
     Once the initialization phase  120  is complete, a phase  130  of executing the module  56  begins. 
     During a step  136 , each time new measurements of the unit  42  are acquired by the computer  50 , the module  56  determines and updates the position, the orientation and the velocity of the vehicle  2 . Thus, this updating is carried out for each instant t k . 
     More specifically, step  136  comprises an operation  138 , during which the accelerometer  44  and the gyroscope  46  respectively measure the acceleration and the angular velocity of the vehicle  2  and these new measurements are acquired by the computer  50  at the instant t k . 
     Then, during an operation  140 , the sub-module  60  constructs the rough estimates P e (k), O e (k) and V e (k) from:
         the previous position P(k−1), the previous orientation O(k−1) and the previous velocity V(k−1); and   the measurements of the accelerometer  44  and the gyroscope  46  acquired at the instant t k .       

     The lower portion of  FIG.  4    comprises a time axis  142 , along which the instants t k  to t k+10  are shown at which the unit  42  measures the acceleration and the angular velocity. The time axis  144  shows the times at which the sub-module  60  acquires the acceleration and the angular velocity measured by the unit  42 . A dashed arrow connects each instant t k  at which a measurement is carried out by the unit  42  to the instant at which the sub-module  60  acquires this measurement. The time axis  146  shows the instants at which the sub-module  60  delivers the estimates P e (k), O e (k) and V e (k). A dashed arrow connects each instant at which a measurement is acquired by the sub-module  60  to the instant at which the sub-module  60  delivers the estimates P e (k), O e (k) and V e (k) obtained from this acquired measurement. 
     At the same time as step  136 , during a step  148 , the transceivers  20  and  22  exchange frames of information in order to allow a rough distance to be measured between these transceivers  20 ,  22  from the transmission and reception instants of these frames of information. Each exchange of frames of information allows enough transmission and reception instants to be acquired to compute a rough distance between these transceivers  20  and  22 . In this case, these exchanges are triggered periodically at the frequency F 20 . Each exchange therefore occurs over a respective period T 20,j  equal to 1/F 20 . Each of the periods T 20,j  starts at a respective instant tu j  of a temporally ordered sequence {0, tu 1 , tu 2 , . . . , tu j−1 , tu j , . . . } of the instants tu j . The difference between the instants tu j +1 and tu j  is equal to the duration of the period T 20,j . 
     In this embodiment, the method for measuring round-trip distance is implemented. This distance measurement method is better known as “two-way ranging”. According to this method, each exchange comprises:
         the transceiver  20  transmitting a first frame of information; then   in response to the transceiver  22  receiving this first frame of information, the transceiver  22  transmitting a second frame of information.       

     The first frame of information is transmitted at an instant M 1,j  and is received by the transceiver  22  at an instant M 2,j . The second frame of information is transmitted at an instant M 3,j  and is received by the transceiver  20  at an instant M 4,j . The instant M 1,j  is not necessarily coincident with the instant tu j . The duration between the instants tu j  and M 1,j  is referred to herein as the duration DT1. The instant M 3,j  necessarily occurs after the start of the period T 20,j . The duration between the instants tu j  and M 3,j  is referred to herein as the duration DT2. These durations DT1 and DT2 can be computed from the instant tu j  and the measurements of the instants M 1,j  and M 3,j . 
     The instants M 1,j  and M 4,j  are measured by the transceiver  20 . The instants M 2,j  and M 3,j  are measured by the transceiver  22 . 
     In the upper part of  FIG.  4   , a time axis  150  shows the instants M 1,j  and M 4,j  measured by the transceiver  20 . A time axis  152  shows the instants M 2,j  and M 3,j  measured by the transceiver  22 . An arrow connects the transmission and reception instants M 1,j  and M 2,j , respectively, of the first frame of information. Another arrow connects the transmission and reception instants M 3,j  and M 4,j , respectively, of the second frame of information. The durations DT1 and DT2 are shown in  FIG.  4    for the period T 20,j . Finally, a time axis  154  shows the instants to 1  at which the distances dc j  are delivered by the sub-module  61 , then acquired by the sub-module  62 . In  FIG.  4   , the periods T 20j−1  to T 20,j+1 , as well as the start and end instants tu j−1  to tu j+2  of each of these periods, are shown. 
     Since the instant M 3,j  is measured by the transceiver  22 , it cannot be transmitted to the transceiver  20  in the second frame of information transmitted at this instant. In this case, the instants M 2,j  and M 3,j  measured by the transceiver  22  are transmitted to the transceiver  20  in the second frame of information transmitted during the next period T 20,j+1 . Accordingly, the instant to j  at which the sub-module  61  delivers the distance dc does not occur in the period T 20,j , but in the next period T 20,j+1 . A delay of several tens of milliseconds therefore exists between the instants M 1,j , M 2,j , M 3,j  and M 4,j  used to compute the distance dc j  and the instant at which this distance dc j  is available for processing by the sub-module  62 . However, at an instant t m , the sub-module  62  computes the innovation Y m  from the difference between the last acquired distance dc m  and an estimate {circumflex over (z)} m  of this distance constructed from the last estimated position P e (m). Assuming that the instant t m  is equal to the instant t k+9  in  FIG.  4   , then the last distance dc m  is equal to the distance dc j . The last acquired position is the position P e (k+9). As illustrated in  FIG.  4    by dashed arrows that point toward the sub-module  62 , this distance dc j  and this position P e (k+9) are transmitted to the sub-module  62  so that it computes the new state vector X m|m  from these measurements. If no correction is made, the innovation Y m  computed by the sub-module  62  is equal to the difference between the measured distance dc and the estimated distance {circumflex over (z)} k+9 . The distance dc j  corresponds to the distance between the transceivers  20 ,  22  as it was during the period T 20,j , while the estimated distance {circumflex over (z)} k+9  corresponds to the distance between the transceivers  20 ,  22  as it was at the instant t k+9 , i.e., during the period T 20,j+1 . In other words, the innovation compares a distance as it was during the period T 20,j  with an estimate of the distance as it is in the next period T 20,j+1 . However, when the vehicle  2  moves quickly, the distance between the transceivers  20 ,  22  varies by several tens of centimetres between the period T 20,j  and the period T 20,j+1 . Thus, this introduces an error into the computation of the innovation Y m  that degrades the accuracy of the location of the vehicle. Hereafter, this error is called “measurement delay” since it originates from the fact that the distance measurement occurs over a fairly long duration. As described in detail hereafter, in this method the distance dc is corrected in order to compensate for this measurement delay. 
     At the same time as step  148 , during a step  160 , during each period T 20,j , the sub-module  61  acquires a position P j  and a velocity V j  representing the position and the velocity of the vehicle  2  during this period T 20,j . This position P j  and this velocity V j  are temporarily stored in order to be used during the next period T 20,j+1 . For example, in this case, at the beginning of each period T 20,j , the sub-module  61  acquires the position P e (k) and the velocity V e (k) delivered by the sub-module  60  at the instant t k  immediately after the instant tu j . This position P e (k) and this velocity V e (k) are then stored as a position P j  and a velocity V j , respectively. 
     When the transceiver  20  has measured the instants M 1,j  and M 4,j  and has received the measurements M 2,j  and M 3,j , during a step  162 , the transceiver  20  transmits these measurements to the sub-module  61 . 
     In response, during a step  164 , the sub-module  61  computes a rough distance db j  solely from the transmission and reception instants measured during the period T 20,j . 
     In this case, the distance db j  is computed using the following relation (8): 
     
       
         
           
             
               db 
               j 
             
             = 
             
               c 
               . 
               
                 
                   
                     ( 
                     
                       
                         M 
                         
                           4 
                           , 
                           j 
                         
                       
                       - 
                       
                         M 
                         
                           3 
                           , 
                           j 
                         
                       
                     
                     ) 
                   
                   + 
                   
                     ( 
                     
                       
                         M 
                         
                           2 
                           , 
                           j 
                         
                       
                       - 
                       
                         M 
                         
                           1 
                           , 
                           j 
                         
                       
                     
                     ) 
                   
                 
                 2 
               
             
           
         
       
     
     where the “c” symbol denotes the speed of light. Hereafter, unless otherwise stated, the “.” symbol in a mathematical relation denotes the arithmetic operation of multiplication. 
     During a step  166 , the sub-module  61  corrects the rough distance db j  in order to obtain a corrected distance dc j . In this embodiment, step  166  comprises:
         an operation  168  for correcting the movement of the vehicle  2  during the durations DT1 and DT2 in order to obtain a measurement of the distance at the instant tu j , and   an operation  170  for correcting the measurement delay.       

     During operation  168 , the sub-module  61  corrects the distance db j  in order to take into account the fact that the vehicle  2  moves between the instants tu j  and M 4,j  and to thus obtain a more accurate distance dp j  between the transceivers  20 ,  22  at the instant tu j . To this end, in this embodiment, the movement velocity of the vehicle  2  is considered to be constant over the entire period T 20,j . Under these conditions, the distance dp j  is computed using the following relation: dp j =db j +δd 1 , where δd 1 =−v a1 .(DT2+DT1)/2, where v a1  is the apparent movement velocity of the vehicle  2  towards the transceiver  22 . The amplitude of the velocity v a1  is equal to the norm of the orthogonal projection of a velocity v j1  of the vehicle  2  onto the axis that passes through the geometric centre of the antennae of the transceivers  20 ,  22 . The velocity v j1  is a velocity that represents the velocity of the vehicle  2  during the interval [tu j ; M 4,j ]. In this case, the velocity v j1  is selected as equal to the velocity v j  stored during step  160 . The velocity v a1  is a number that is positive when the vehicle  2  approaches the transceiver  22  and is negative when it moves away from this transceiver  22 . 
     In this case, the velocity v a1  is computed using the following relation: v a1 =−V j .u bv , where:
         the “.” symbol denotes the scalar product operation;   V j  is the velocity stored for the period T 20,j  during step  160 ; and   u bv  is a direction vector that points from the geometric centre of the transceiver antenna  22  toward the geometric centre of the transceiver antenna  20 .       

     The coordinates of this vector u bv  are provided by the following relation: 
     
       
         
           
             	 
             
               ? 
             
           
         
       
       
         
           
             
               ? 
             
             indicates text missing or illegible when filed 
           
         
       
     
     where:
         x j , y j  and z j  are the coordinates of the position P j  of the vehicle stored during the period T 20,j  during step  160 ; and   B x , B y , B z  are the coordinates of the position of the transceiver  22 .       

     During operation  170 , the sub-module  61  corrects the distance dp j  so that it is as close as possible to the distance between the transceivers  20 ,  22  at the instant t m . Thus, using the example of  FIG.  4    again, the sub-module corrects the distance dp j  so that it is close to the distance between the transceivers  20 ,  22  at the instant t k+9 . To this end, the sub-module  61  adds a corrective term δd 0  to the distance dp j  that corresponds to the distance the vehicle  2  has travelled towards the transceiver  22  during the time interval [tu j , t j ]. Thus, the corrected distance is computed using the following relation: dc j =dp j −δd 0 . The term δd 0  is computed using the following relation: δd 0 =v a0 ·DT0, where:
         DT0 is equal to the elapsed time between the instants tu j  and t m ;   v a0  is an apparent movement velocity of the vehicle  2  towards the transceiver  22 .       

     The velocity v a0  is defined as the velocity v a1 , i.e., its amplitude is equal to the norm of the orthogonal projection of a velocity V j0  of the vehicle  2  onto the axis that passes through the geometric centre of the antennae of the transceivers  20 ,  22 . The velocity V j0  is a velocity representing the velocity of the vehicle  2  during the interval [tu j ; t m ]. The velocity v a0  is a number that is positive when the vehicle  2  approaches the transceiver  22  and is negative when it moves away from this transceiver  22 . In this case, in order to simplify the computations, the velocity v a0  is considered to be equal to the velocity v a1 . 
     In this case, the duration DT0 is a constant pre-stored in the memory  54  or computed from the instants tu j  and t m . Indeed, in this case, the clocks triggering the instants t k  and tu j  are synchronised. For example, to this end, the system  30  uses the same clock to generate the instants t k  and tu j . 
     It is this distance dc j  that is acquired by the sub-module  62  at the instant to j . 
     Then, only if the instant t k  is also an instant tg i  at which a measurement of the unit  40  is acquired, after step  136 , the computer  50  executes a step  170  of updating the correction coefficients as a function of the new measurement of the unit  40 . During this step  170 , the correction coefficients are updated without using the transmission and reception instants obtained by the transceiver  20 . 
     Only if the instant t k  is an instant to j  at which a corrected distance dc j  is acquired, after step  136 , the computer  50  executes a step  180  of updating the correction coefficients as a function of the new corrected distance dc j . During this step  180 , the correction coefficients are updated without using the measurement of the unit  40 . 
     If the instant t k  corresponds neither to an instant tg i  nor to an instant to j , then the position P e (k), the orientation O e (k) and the velocity V e (k) estimated by the sub-module  60  and not corrected by the sub-module  62  are delivered to the output  37 . Thus, at the instants t k  between the instants t m , the position P e (k), the orientation O e (k) and the velocity V e (k) are delivered to the output  37 . Furthermore, the method returns to step  136  without executing either step  170  or step  180 . In this case, the previous position, the previous orientation and the previous velocity used during the next iteration of step  136  are equal to the position P e (k), the orientation O e (k) and the velocity V e (k), respectively. 
     During step  180 , the sub-module  62  begins by acquiring, during an operation  201 , the new corrected distance dc j . 
     Then, during an operation  202 , the block  68  is executed by the computer  50  in order to obtain the predicted state vector X m|m-1  from the previous estimate X m-1|m-1  of this state vector. The previous estimate X m-1|m-1  is the one obtained at the previous instant t m-1 . The previous instant t m-1  corresponds either to an instant tg i  or to the instant to j−1 . Therefore, the previous estimate X m-1|m-1  is the one that was constructed either during the previous execution of step  170  or during the previous execution of step  180 . 
     The prediction X m|m-1  of the state vector is constructed by implementing relation (1). In this particular case whereby the filter  64  is an error-state Kalman filter, the prediction X m|m-1  is systematically zero. 
     During operation  202 , the block  68  also constructs the prediction P m|m-1  of the covariance matrix P m  at the instant t m  by implementing relation (2). 
     During an operation  206 , the block  70  constructs the estimate {circumflex over (z)} m  of the distance between the transceivers  20 ,  22  by implementing the relation (3). In this embodiment, during operation  206 , the block  70  also computes the observation matrix H m . The matrix H m  is, for example, computed by deriving the relation (3) relative to each of the various parameters of the state vector X m|m . 
     During the next operation  208 , the block  70  updates the correction coefficients. To this end, it corrects the prediction X m|m-1  as a function of the difference Y m  between the corrected distance dc j  and its estimate z m . To this end, the block  70  computes the difference Y m  according to relation (4). Then, the gain K m  is computed using relation (5). The corrected state vector X m|m  is then obtained by implementing relation (6). 
     During operation  208 , the block  70  also obtains the updated covariance matrix P m|m  using relation (7). 
     On completion of steps  170  and  180 , during a step  210 , the sub-module  62  corrects the position P e (m), the orientation O e (m) and the velocity V e (m) in order to obtain the corrected position P c (m), the corrected orientation O c (m) and the corrected velocity V c (m). 
     To this end, the adder  66  adds the correction coefficients contained in the vector X m|m  to the corresponding coordinates of the position P e (m), the orientation O e (m) and the velocity V e (m), constructed during the last execution of operation  136 , in order to obtain the position P c (m), the orientation O c (m) and the velocity V c (m). Thus, the position P c (m), the orientation O c (m) and the velocity V c (m) are delivered to the output  37  only at the instants t m  and not the position P e (m), the orientation O e (m) and the velocity V e (m). Furthermore, during step  210 , the position P(k), the orientation O(k) and the velocity V(k) are transmitted to the sub-module  60  and are used by the sub-module  60  as the previous position, the previous orientation and the previous velocity of the vehicle  2  during the next iteration of step  136 . 
     After step  210 , the method returns to step  136 . 
     Chapter II: Variants 
     Variants of Determining Distance: 
     Other methods for measuring the rough distance db j  from the transmission and reception instants of frames of information between the transceivers  20  and  22  can be implemented. For example, as a variant, the method for measuring the round-trip distance is replaced by a method for measuring distance with two outbound and one return trip, known as “three-way ranging”. In this “three-way ranging” method, each exchange of frames of information between the transceivers  20  and  22  comprises, in addition to the transmission of the first and second frames of information, the transceiver  20  transmitting, in response to the reception of the second frame of information, a third frame of information at an instant M 5,j  and the transceiver  22  receiving this third frame of information at an instant M 6,j . In this case, the rough distance db j  is computed using the following relation: 
     
       
         
           
             
               db 
               j 
             
             = 
             
               
                 c 
                 . 
                 
                   1 
                   
                     2 
                     + 
                     
                       ε 
                       AB 
                     
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     ( 
                     
                       
                         M 
                         
                           3 
                           , 
                           j 
                         
                       
                       - 
                       
                         M 
                         
                           2 
                           , 
                           j 
                         
                       
                     
                     ) 
                   
                   + 
                   
                     
                       ( 
                       
                         1 
                         + 
                         
                           ε 
                           AB 
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           M 
                           
                             4 
                             , 
                             j 
                           
                         
                         - 
                         
                           M 
                           
                             1 
                             , 
                             j 
                           
                         
                       
                       ) 
                     
                   
                 
                 ) 
               
             
           
         
       
     
     where ε AB  is defined by the following relation: 
     
       
         
           
             
               ε 
               AB 
             
             = 
             
               
                 
                   ( 
                   
                     
                       M 
                       
                         6 
                         , 
                         j 
                       
                     
                     - 
                     
                       M 
                       
                         2 
                         , 
                         j 
                       
                     
                   
                   ) 
                 
                 
                   Δ 
                   ⁢ 
                   T 
                 
               
               - 
               1 
             
           
         
       
     
     where ΔT is equal to M 5,j −M 1,j . 
     As a variant, computing the rough distance db j  takes into account the drift of the clock located in the transceiver  20  relative to the clock located in the transceiver  22 . These clocks are used to measure the transmission and reception instants of the frames of information. To this end, for example, the rough distance db j  is computed using the following relation: 
     
       
         
           
             
               db 
               j 
             
             = 
             
               c 
               . 
               
                 
                   
                     ( 
                     
                       
                         M 
                         
                           4 
                           , 
                           j 
                         
                       
                       - 
                       
                         M 
                         
                           1 
                           , 
                           j 
                         
                       
                     
                     ) 
                   
                   - 
                   
                     
                       ( 
                       
                         
                           M 
                           
                             3 
                             , 
                             j 
                           
                         
                         - 
                         
                           M 
                           
                             2 
                             , 
                             j 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         1 
                         + 
                         
                           ε 
                           
                             drift 
                             , 
                             j 
                           
                         
                       
                       ) 
                     
                   
                 
                 2 
               
             
           
         
       
     
     where ε drift,j  is defined by the following relation: 
     
       
         
           
             
               ε 
               
                 drift 
                 , 
                 j 
               
             
             = 
             
               
                 
                   Δ 
                   ⁢ 
                   
                     T 
                     
                       remote 
                       , 
                       j 
                     
                   
                 
                 - 
                 
                   Δ 
                   ⁢ 
                   
                     T 
                     
                       local 
                       , 
                       j 
                     
                   
                 
               
               
                 Δ 
                 ⁢ 
                 
                   T 
                   
                     remote 
                     , 
                     j 
                   
                 
               
             
           
         
       
     
     where ΔT remote,j =M 2,j −M 2,j−1  and ΔT local,j =M 1,j −M 1,j−1 . 
     The measurements of the instants M 2,j  and M 3,j  can be transmitted to the transceiver  20  by means other than the second frame of information transmitted during the period T 20,j+1 . For example, these instants M 2,j  and M 3,j  are transmitted to the transceiver  20  by means of an additional frame of information, the transmission and reception instants of which are not used for computing the distance db j . For example, this additional frame of information is transmitted at an instant M 5,j  and is received by the transceiver  20  at an instant M 6,j . The instants M 5,j  and M 6,j  are then typically included between the instants M 4,j  and tu j+1 . In this case, the instant to j  is closer to the instant tu j  than in the previous embodiments. For example, the instant to j  is then located towards the end of the period T 20,j . However, even in this case, a measurement delay exists that is worthwhile correcting. In another embodiment, this additional frame is transmitted by means of an information transmission link established using transceivers independent of the transceivers  20  and  22 . 
     As a variant, the transceivers  20  and  22  are capable of carrying out a rough measurement and a precise measurement of the reception instants. In this case, this possibility can be taken advantage of, for example, in accordance with the following scheme. UWB technology uses an indicator known using the acronym FPI (“First Path Index”). This indicator is constructed by the transceivers  20 ,  22 . This indicator normally must be between high L H  and low L B  limits. When this indicator is between the high L H  and low L B  limits, the precise measurement is used. Conversely, if this indicator is not between the high L H  and low L B  limits, the rough value is used. 
     The roles of the transceivers  20  and  22  can be reversed. In this case, it is the transceiver  22  that transmits the first frame of information at the instant M 1,j  and, in response to receiving this first frame of information, the transceiver  20  transmits the second frame of information at the instant M 3,j . In this embodiment, the instants M 2,j  and M 3,j  are measured by the transceiver  20  and the instants M 1,j  and M 4,j  are measured by the transceiver  22 . The transceiver  22  transmits the measured instants M 1,j  and M 4,j  to the transceiver  20 , for example, in the first frame of information transmitted at the instant M 1,j+1 . 
     As a variant, the coordinates B x , B y  and B z  of the position of the fixed transceiver  22  are contained in a frame of information, for example, the second frame of information, transmitted from the transceiver  22  to the transceiver  20 . In this case, these coordinates do not need to be previously stored in the memory  54 . 
     Other methods for computing the apparent velocity v a0  are possible. For example, as a variant, the velocity V j0  used to compute the velocity v a0  is equal to the average of the velocities V e (k) measured by the sub-module  61  during the entire period T 20,j . To this end, for example, during step  160 , the sub-module  61  records each of the velocities V e (k) throughout the period T 20,j , then computes an average velocity from these velocities V e (k). The stored velocity Vj0 is equal to this average velocity. Similarly, the position Pj can be taken as an average of the positions P e (k) recorded during the period T 20,j . In another embodiment, the velocity V j0  is considered to be equal to the velocity V e (k) recorded at the instant t k  closest to the middle of the period T 20,j . 
     The variants of the previous paragraph can be adapted to the computation of the velocity v a1 . In this case, the average velocity is preferably computed by taking into account only the velocities V e (k) recorded during the interval [tu j , M 4,j ]. Similarly, the average position taken into account for computing the velocity v a1  is an average position over the interval [tu j , M 4,j ]. This example also shows that the apparent velocities v a0  and v a1  do not need to be identical. 
     In a simplified embodiment, the operation  168  of correcting the movement of the vehicle  2  during the durations DT1 and DT2 is omitted. This is particularly the case when the durations DT1 and DT2 are very small. 
     In another embodiment, the corrective term δd 1  is subtracted from the distance db j  and is not added. In this case, the distance dp j  that is obtained corresponds to the distance between the transceivers  20 ,  22  at the instant M 4,j  and not at the instant tu j . Therefore, during operation  170 , the duration DT0 is considered to be equal to the duration of the interval [M 4,j ; t m ]. This variant is functionally identical to the description provided in Chapter I, since the sum δd 1 +δd 0  of the corrective terms computed according to this variant is equal to the sum of the corrective terms computed according to the method described in Chapter I. 
     Variants of the Kalman Filter: 
     Numerous other embodiments of the filter  64  are possible. For example, the filter  64  can be a linear Kalman filter, an Extended Kalman Filter (EKF), an Unscented Kalman Filter (UKF) or even an adaptive Kalman filter. 
     Numerous variants of the relations implemented in the Kalman filter exist. Indeed, these relations depend on the coordinate system in which the position, the orientation and the velocity of the vehicle are expressed. However, other coordinate systems can be used instead of the coordinate system R T . For example, the ECI (Earth Centred Inertial) coordinate system can be cited. The ECI coordinate system is not fixed relative to the surface of the earth since the earth rotates in this frame. The coordinate system R T  also can be a coordinate system that is fixed relative to the stars. When another coordinate system is used, it is possible, simply by changing the coordinate system, to return to the situation described herein. 
     The Kalman filter relations can also contain an additional rotation matrix for taking into account the fact that the measurement axes of the unit  42  are not aligned on the axes of the coordinate system R b . 
     Similarly, numerous variants of the state vector X m|m  are possible. For example, the state vector X m|m  also may not comprise a correction coefficient for the biases of the accelerometer  44  and of the gyroscope  46 . The state vector X m|m  can also comprise additional state variables. 
     In another embodiment, the corrected distance is added to the state vector of the Kalman filter and the state and observation matrices are modified accordingly. However, such an embodiment then requires executing the Kalman filter at each instant t k , which is not always desirable. 
     The previous teaching for the particular case whereby the correction sub-module  62  uses one or more Kalman filter(s) also applies to correction sub-modules that construct the correction coefficients using estimators other than Kalman filters. In general, the description provided herein applies to any correction sub-module configured to update the correction coefficients using a difference between:
         a measurement of a physical quantity constructed from the corrected distance dc j ; and   an estimate of this physical quantity constructed from measurements of the unit  42  or of another sensor separate from the transceiver  20 .       

     Other embodiments of the sub-module  62  are possible. For example, as a variant, the sub-module  62  is arranged as described in the architecture known as “tight coupling”. This architecture is described in more detail in chapter 4.1.2 of the Godha2006 thesis. 
     Variants of the Method: 
     The position of the vehicle  2  can be determined from measurements of one or more measurement unit(s) other than the inertial measurement unit  42 . For example, these measurement units are selected from the group made up of:
         the satellite geolocation unit  40 ;   the inertial measurement unit  42 ;   an odometer;   a magnetometer associated with a map of the magnetic fields of the earth.       

     For example, in one embodiment, the unit  42  is replaced by the satellite geolocation unit  40 . The position P e (k) and the velocity V e (k) are then the measurements of the position and of the velocity of the vehicle  2  delivered by this unit  40  at the instants tg i . In such an embodiment, the correction sub-module  62  corrects the position P e (k) and the velocity V e (k) solely from the distance dc j  delivered by the sub-module  61 . The duration DT0 is then considered to be equal to the duration of the interval between the instant tu j  and the last instant tg i  at which the unit  40  delivered an estimate of the position and of the velocity of the vehicle. In another embodiment, a combination of several sensors delivers, at each instant t k , the position P e (k) and the velocity V e (k). For example, this combination of sensors comprises an odometer that allows the velocity of the vehicle  2  to be estimated and a triaxial magnetometer that allows the orientation of the vehicle  2  to be estimated. It is also possible to deliver a position P e (k) and a velocity P e (k) from these two sensors. Other combinations of sensors are possible. Thus, the description that has been provided also can be implemented in a location system in which the units  40  and  42  are replaced by one or more other sensor(s) from which the position and the velocity of the vehicle  2  can be determined. 
     As a variant, the system  30  is equipped with additional sensors, such as, for example, a magnetometer, a barometer, an altimeter or an odometer. In this case, the correction sub-module  62  is modified in order to take into account the measurements of these additional sensors for correcting the rough estimates delivered by the integration sub-module  60 . 
     In another embodiment, the satellite geolocation unit  40  is omitted. In this case, for example, the correction coefficients are only updated from the corrected distances dc j . 
     If the movement of the vehicle  2  is limited, then certain measurements along certain measurement axes may be omitted. For example, if the vehicle  2  is limited to moving in a horizontal plane, the measurements along the Z T  axis can be omitted. 
     Variants of the Locating System: 
     As a variant, the transceivers  20 ,  22  are not UWB transceivers. For example, the transceivers  20 ,  22  are replaced by radio transceivers that use a much narrower frequency spectrum for exchanging frames of information. 
     As a variant, the system for locating the vehicle  2  comprises a single fixed transceiver or, alternatively, several fixed transceivers. In the case whereby the system comprises several fixed transceivers, these are preferably distributed at regular intervals along the path or along a portion of this path. In this latter case, if the mobile transceiver  20  can simultaneously communicate with several fixed transceivers, then, instead of providing a single corrected distance at an instant to 1 , the sub-module  61  simultaneously provides several corrected distances, with each of these distances corresponding to a distance between the transceiver  20  and a respective fixed transceiver. Subsequently, the sub-module  62  corrects the estimate of the position by taking into account these different distances and the known positions of the various fixed transceivers. In this case, advantageously, the first frame of information transmitted by the transceiver  20  is common to all the fixed transceivers. 
     As a variant, the electronic computer  50  is not housed inside the vehicle  2  but elsewhere. For example, the electronic computer  50  is housed inside a fixed terminal that already contains the transceiver  22 . 
     Temporal synchronisation between the instants tu j  and t k  can be obtained by other means. For example, as a variant, a common trigger signal is sent to the transceiver  20  and to the unit  42  in order to trigger the completion of the measurements at the same time. 
     Other Variants: 
     The vehicle  2  is not necessarily a motor vehicle. The description that has been provided applies to any vehicle capable of moving along a path equipped with fixed transceivers. For example, the vehicle  2  also can be a railway vehicle or a boat. 
     As a variant, the vehicle  2  does not comprise propulsion means  34  on board the vehicle  2 . This is the case, for example, when the vehicle  2  is a cable-car towed by a cable. 
     Similarly, the cockpit  38  can be remote and located outside the vehicle  2 . This is the case when the vehicle  2  is a remotely controlled vehicle or a cable-car. 
     In a simplified embodiment, the system  30  does not deliver the position or the velocity or the orientation of the vehicle  2  to the output  37 . For example, in a highly simplified embodiment, only the distance dc j  that separates the vehicle  2  from the transceiver  22  is delivered to the output  37 . However, even in such a simplified embodiment, the position and the velocity of the vehicle  2  are determined in order to make the various corrections described above. 
     Chapter III: Advantages of the Described Embodiments 
     Adding the corrective term δd 0  to the rough distance db 1  allows a corrected distance dc j  to be obtained that takes into account the fact that the vehicle  2  has moved between the instants tu j  and t m . Thus, the distance dc j  reduces the amplitude of the measurement delay. The computed innovation Y m  is then more accurate, which allows more precise location of the vehicle to be obtained. 
     Adding the corrective term δd 1  to the rough distance db j  allows a corrected distance dc j  to be obtained that also compensates for the fact that the vehicle  2  has moved between the instants tu j  and M 4,j . This allows more precise location of the vehicle to be obtained. 
     The use of UWB transceivers allows more precise location of the vehicle  2  to be obtained.