Patent Publication Number: US-2023152414-A1

Title: Method for determining a corrected distance

Description:
The invention relates to a method for determining a corrected distance between a mobile transceiver fastened to a vehicle and a fixed transceiver. 
     The invention also relates to:
         a method for locating a vehicle implementing the method for determining a corrected distance, and   a system for determining a corrected distance.       

     Such distance-determining methods are for example implemented in methods for locating a vehicle. Such a locating method is for example described in the following article: V. Di Pietra et al.: “ Loosely Coupled GNSS and UWB with INS Integration for Indoor/Outdoor Pedestrian Navigation ”, Sensors, May 11, 2020. 
     More precisely, in such locating methods, the distance between the fixed and mobile transceivers is used to correct a position of the vehicle estimated using other sensors. Thus, the more accurate the distance, the more accurate the position of the vehicle. [0°  5 ] The distance between the fixed and mobile transceivers is obtained from the transmission and reception times of radio signals exchanged between these transceivers. These radio signals are electromagnetic waves that propagate at the speed of light. Thus, even a very small error in the measurement of these transmission and reception times results in an error of several tens of centimetres in the determined distance. 
     To overcome this problem, it has been proposed to correct a raw distance, computed solely from the measured transmission and reception times, by adding a correction coefficient thereto. The difficulty is then that the value of this correction coefficient depends on a plurality of parameters, notably including:
         the relative orientation of the antenna of the mobile transceiver with respect to the antenna of the fixed transceiver,   the presence on the path of the exchanged radio signals of any elements, notably metal elements, able to perturb propagation of the signal, and   the power of the radio signals received by the fixed and mobile transceivers.       

     A variation in the power of the radio signals received by the fixed and mobile transceivers generally induces a variation in time lags in the mechanism for detecting arrival time within the receiver. 
     It is therefore difficult to construct a correction function that returns the value of such a correction coefficient given the current position and orientation of the vehicle with respect to the fixed transceiver. As a result, there are mainly two possible strategies. The first strategy consists in using a correction function that is complex and accurate but that is difficult to implement and time-consuming to execute. In particular, such a correction function is difficult to implement because it has very many parameters and because it is difficult to accurately adjust each of these parameters. The second strategy consists, conversely, in using a correction function that is simple to implement and rapid to execute. However, simplification of the implementation of the correction function comes at the price of a lower accuracy. 
     Prior art relative to these issues may be found in the following documents:
     Whenda ZHAO et al.: “Learning-based Bias Correction for Time Difference of Arrival Ultra-wideband Localization of Resource constrained Mobile Robots”, Cornell University Library, Feb. 3, 2021,   WO2021143920A1, and   US2003216865A1.   

     The invention aims to overcome this contradiction by providing a method for determining the distance between fixed and mobile transceivers, in which the correction function may be implemented both simply and rapidly without however requiring the accuracy of the determined distance to be decreased. 
     One subject thereof is therefore such a method for determining a distance. 
     Another subject of the invention is a method for locating a vehicle implementing the above method for determining a distance. 
     Lastly, another subject of the invention is a system for determining a distance. 
    
    
     
       The invention will be better understood on reading the following description, which is given solely by way of non-limiting example, with reference to the drawings, in which: 
         FIG.  1    is a schematic illustration of a vehicle constrained to move along a path, 
         FIG.  2    is a schematic illustration of a system for locating the vehicle of  FIG.  1   ; 
         FIG.  3    is a schematic illustration of various software modules implemented in the system of  FIG.  2   ; 
         FIG.  4    is a flowchart of a method for locating the vehicle of  FIG.  1    using the system of  FIG.  2   . 
     
    
    
     In these figures, the same references have been used to designate elements that are the same. 
     In the remainder of this description, features and functions well known to those skilled in the art are not described in detail. In particular, with respect to the general knowledge of those skilled in the art of devices for locating a vehicle using an inertial navigation system, the reader is referred, 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. Below, this thesis is designated by the expression “Godha2006”. 
     In this description, a detailed example of embodiment is first described in Section I with reference to the figures. Next, in the following section, Section II, variants of this embodiment are presented. Lastly, the advantages of the various embodiments are presented in Section III. 
     Section I: Example of Embodiment 
       FIG.  1    shows a vehicle  2  capable of moving along each of the path segments of a predetermined set of a plurality of path segments. Each segment starts at a point, called the “start point” below, and ends at a point, called the “end point” below. The length of path that connects the start and end points of the segment is known in advance and set. The vehicle  2  is constrained, by mechanical or electronic means, to move solely along segments of this group. 
     For example, in this example of embodiment, the vehicle  2  is a gondola lift suspended from a cable  4 . In  FIG.  1   , lengths of the cable have been drawn with dashed lines to indicate that only one portion of the cable  4  has been shown. The cable  4  forms a loop that extends between a start station  6  and an end station  8 . The cable  4  is driven to rotate by a motor in the direction indicated by the arrow  10 . The rotation of the cable  4  causes the vehicle  2  to move between the stations  6  and  8  along a loop-shaped path defined by the cable  4 . In this context, the path of the vehicle  2  is considered to coincide with the path of the cable  4 . 
     The path of the vehicle  2  here comprises an upward stretch  12  from the station  6  to the station  8 , and a downward stretch  14  from the station  8  to the station  6 . Here, these upward and downward stretches  12 ,  14  do not coincide. 
     With a view to accurately locating the vehicle  2  along its path, the vehicle  2  comprises a radio transceiver  20  located on-board this vehicle. One or more fixed transceivers are also provided, these being located along the path of the vehicle  2 . For example, the fixed transceivers are placed at regular intervals along the upward stretch  12 . In  FIG.  1   , a single fixed transceiver  22  has been shown. 
     The description given below in the particular case of this transceiver  22  applies identically to all the other fixed transceivers placed along the path of the vehicle  2 . 
     The transceiver  22  is immobile and its position in a terrestrial frame of reference R T  is known in advance and does not change. Here, the terrestrial frame of reference R T  is fixed without any degree of freedom to the Earth. The frame of reference R T  comprises three axes, which are typically orthogonal to one another. For example, here, the frame of reference R T  is the ECEF frame of reference (ECEF standing for “Earth Centred, Earth fixed”). 
     In  FIG.  1   , only four path segments S 1 , S 2 , S 3  and S 4  have been shown. The segments S 1  and S 2  belong to the upward stretch  12  of the path whereas the segments S 3  and S 4  belong to the downward stretch  14  of the path. Segment S 1  extends from a start point A to an end point B. Segment S 2  extends from the point B to an end point C. 
     Segment S 3  extends from a start point D to an end point E. Segment S 4  extends from the point E to an end point F. In this embodiment, the end and start point of segments S 1  and S 2  are coincident. Likewise, the end and start point of segments S 3  and S 4  are coincident. 
     Here, the points B and E are the points, of the upward and downward stretches  12 ,  14  respectively, closest to the transceiver  22 . 
     Whatever the position of the vehicle on any one of the segments S 1  to S 4 , the fixed and mobile transceivers are capable of exchanging data frames allowing the distance that separates them to be measured. As a result, below, segments S 1  to S 4  are said to be “associated” with the fixed transceiver  22 . 
     Typically, the movement of the vehicle  2  is controlled from a control post  38 . Here, this post  38  is located in the start station  6 . 
       FIG.  2    shows in more detail the vehicle  2  and notably a system  30  for locating the vehicle  2  located on-board this vehicle. 
     The system  30  is able to determine the position, orientation and speed of the vehicle  2  in the terrestrial frame of reference R T . To this end, a mobile frame of reference R b  that is fixed with no degree of freedom to the body of the vehicle  2  is defined. This frame of reference R b  comprises three axes that are orthogonal to one another, denoted x b , y b  and z b , respectively. Conventionally, when the vehicle  2  moves horizontally, the axes x b  and y b  are in a horizontal plane and the axis z b  is vertical. Here the axis x b  is oriented and points in the direction in which the vehicle moves when it moves forward. 
     Here, the position of the vehicle  2  in the frame of reference R T  is expressed by coordinates of the origin of the frame of reference R b  in the frame of reference 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 frame of reference R b  with respect to a frame of reference referred to as the “navigation” frame of reference. In practice, most often, the orientation of the vehicle takes the form of an orientation matrix from which it is possible to deduce the yaw angle, the pitch angle and the roll angle of the vehicle. The orientation of the vehicle may also take the form of a vector directly comprising the yaw angle, the pitch angle and the roll angle of the vehicle. Below, these two particular cases will be considered to be equivalent and hence the orientation of the vehicle will be considered to comprise the yaw angle, the pitch angle and the roll angle of the vehicle if these three angles can be deduced directly from a matrix or a vector. 
     The position, orientation and speed determined by the system  30  are delivered to an output  37 . Below, the position, orientation and speed delivered to the output  37  by the system  30  for a time t k  are denoted P(k), O(k) and V(k), respectively. 
     The output  37  is for example connected to a human-machine interface  34  that is housed in the vehicle  2  and that displays the position, orientation and speed determined by the system  30 . The output  37  may also be connected to the control post  38  via a wireless or wired link. In the latter case, the position, orientation and speed determined by the system  30  are automatically converted into commands for controlling the motor used to drive the cable  4 . 
     The system  30  comprises a satellite geolocation unit  40 , an inertial measurement unit  42  and the transceiver  20 . 
     The unit  40  is a GNSS unit (GNSS being the acronym of Global Navigation Satellite System). From the satellite signals that it receives, the unit  40  generates signals representative of the position and speed of the vehicle in the frame of reference R T . The unit  40  updates its measurements at a frequency F 40 . Conventionally, the frequency F 40  is comprised between 0.1 Hz and 20 Hz. 
     The unit  42  is an IMU (acronym of Inertial Measurement Unit). The unit  42  notably comprises a triaxial accelerometer  44  and a triaxial gyrometer  46 . By virtue of these sensors, the unit  42  is capable of measuring the variation in the orientation, position and speed of the vehicle  2 . Here, the measurement axes of the accelerometer  44  and of the gyrometer  46  are coincident with the axes x b , y b  and z b  of the frame of reference R b , respectively. In addition, the accelerometer  44  is arranged so that a positive measurement of the acceleration of the vehicle  2  along the axis x b  means that the vehicle  2  accelerates by moving forward. 
     The unit  42  updates the measurements of acceleration and speed at a high frequency F 42 . Conventionally, the frequency F 42  is comprised between 20 Hz and 2000 Hz. For example, here, the frequency F 42  is equal to 200 Hz. 
     The transceiver  20  exchanges data frames with the transceiver  22  via a wireless radio link  48 . These data frames are notably exchanged with a view to measuring, based on the times of flight of these data frames, the distance that separates these transceivers  20 ,  22 . To this end, here, the transceivers  20 ,  22  are ultra-wideband (UWB) transceivers. The term “ultra-wideband transceiver” or “UWB transceiver” here designates a transceiver that uses a wide frequency band to send and receive the data frames. A “wide” frequency band is a frequency band the width of which is larger than 0.2f c , where f c  is the central frequency of this frequency band. Typically, a wide frequency band has a width larger than 250 MHz or even larger than 400 MHz. 
     Measurement of a distance between the transceivers  20 ,  22  requires the exchange of a plurality of data frames between these transceivers  20 ,  22  and measurement of the times of transmission and reception of these data frames. This exchange of data frames is repeated at a frequency F 20 , in order to update at this frequency the distance measurement. The frequency F 20  is lower than the frequency F 42 . Typically, the frequency F 20  is ten or fifty times lower than the frequency F 42 . Conventionally, the frequency F 20  is comprised between 0.1 Hz and 20 Hz. Here, the times of transmission and reception of the data frames are obtained by the transceiver  20  housed in the vehicle  2 . 
     To determine the position, orientation and speed of the vehicle  2  from the measurements of the units  40  and  42  and from the transmission and reception times obtained by the transceiver  20 , the system  30  comprises a programmable electronic computer  50 . This computer  50  is able to acquire the measurements of the units  40  and  42  and the transmission and reception times obtained by the transceiver  20 . Next, from these measurements, the computer  50  determines the position, orientation and speed of the vehicle  2  in the frame of reference R T . The computer  50  comprises a microprocessor  52  and a memory  54  comprising the instructions and data required to implement the method described with reference to  FIG.  4   . 
     More precisely, the memory  54  comprises the instructions of a software module  56  able to determine the position, orientation and speed of the vehicle  2  from the acquired measurements when it is executed by the microprocessor  52 . Here, the module  56  notably implements a fusing algorithm that establishes, from a preceding estimation of the position, orientation and speed of the vehicle  2  and from new measurements acquired since this preceding estimation, a new estimation of the position, orientation and speed of the vehicle  2 . Typically, the fusing algorithm also establishes margins of error in each new estimation. 
     The general principles of fusing algorithms are well known to those skilled in the art. For example, the interested reader may once again refer to the thesis Godha2006 cited above. Typically, this fusing algorithm implements one or more Kalman filters. Here, the module  56  employs an architecture known as a “closed loop integration scheme” or “closed loop approach”. 
     Here, the memory  54  also comprises a table  58  that with each segment Sn associates one respective correction function f sn (d), where the index Sn is the identifier of one segment among the segments S 1  to S 4 . 
       FIG.  3    shows in more detail the architecture of the module  56 . The module  56  comprises:
         a sub-module  60  for inertial measurement integration,   a sub-module  61  for computing a corrected distance between the transceivers  20 ,  22  from the transmission and reception times obtained by the transceiver  20 , and   a correcting 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 may consult chapter 4 of the thesis Godha2006. Thus, below, only details specific to the invention are described in detail. 
     The sub-module  60  is also known as the “mechanization”. For each time t k , the sub-module  60  constructs a raw estimation of a position P e (k), orientation O e (k) and speed V e (k) of the vehicle  2 . In this text, the symbol “k” is the order number of the time t k  in the time-ordered sequence {0, t 1 , t 2 , . . . , t k-1 , t k , . . . } of times t k . The order number of the time t k-1  that immediately precedes the time t k  is denoted k−1. The position P e (k), orientation O e (k) and speed V e (k) of the vehicle  2  are each a vector containing three coordinates. The coordinates of the position P e (k) in the frame of reference 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 speed V e (k) are denoted Vx e (k), Vy e (k) and Vz e (k). 
     The frequency of the times t k  is lower than or equal to the frequency F 42 . Here, the frequency of the times t k  is equal to the frequency F 42 . 
     The sub-module  60  constructs the position P e (k), orientation O e (k) and speed V e (k) from:
         the preceding position P(k−1), the preceding orientation O(k−1) and the preceding speed V(k−1), i.e. the position, orientation and speed determined for the vehicle  2  at the time t k-1  by the system  30  and delivered to the output  37 , and   measurements of the accelerometer  44  and of the gyrometer  46  acquired by the sub-module  60  at the time t k .       

     The combination of the sub-module  60  and of the unit  42  forms what is known as an INS (acronym of Inertial Navigation System). 
     The sub-module  61  acquires the transmission and reception times obtained by the transceiver  20  and the last position of the vehicle  2  estimated by the sub-module  60 . Next, the sub-module  61  delivers, to the sub-module  62 , a corrected distance computed from the acquired transmission and reception times and from the last acquired position of the vehicle  2 . The operation of this sub-module  61  is described in more detail with reference to  FIG.  4   . 
     At certain particular times t k , the sub-module  62  corrects the position P e (k), orientation O e (k) and speed V e (k) constructed by the sub-module  60  for this time t k , in order to obtain a corrected position P c (k), a corrected orientation O c (k) and a corrected speed V c (k) for this time t k . Below, these particular times t k  are called “times t m ”. The symbol “m” is equal to the order number of a particular time t k  in the sequence {0, t 1 , t 2 , . . . , t k , . . . }. Each order number m is therefore equal to one respective order number k. Thus, the position P e (m), orientation O e (m) and speed V e (m) are equal to the position P e (k), orientation O e (k) and speed V e (k) constructed for the time t k  equal to the time t m , respectively. The sequence {0, t 1 , t 2 , . . . , t m−1 , t m , . . . } of times t m  is a sub-set of the sequence {0, t 1 , t 2 , . . . , t k , . . . }. Thus, the sub-module  62  does not make the correction for each time t k , but only for some thereof. At each time t m , the sub-module  62  combines the position P e (m), orientation O e (m) and speed V e (m) with respective correction coefficients to obtain the corrected position P c (m), the corrected orientation O c (m) and the corrected speed V c (m). At the times t m , it is the corrected position P c (m), the corrected orientation O c (m) and the corrected speed V c (m) that are delivered to the output  37 , and not the position P e (m), orientation O e (m) and speed V e (m). The correction coefficients are updated depending on the measurements of the unit  40  and on the corrected distance determined by the sub-module  61 . The correction coefficients are therefore updated at a frequency lower than the frequency F 42 . 
     The sub-module  62  acquires the measurements of the unit  40  at a frequency lower than or equal to the frequency F 42 . Here, the frequency of acquisition of the measurements of unit  40  is equal to the frequency Foo. Below, the acquisition times of a new measurement of the unit  40  are denoted tg i . These times tg i  form a time-ordered sequence {0, tg 1 , tg 2 , . . . , tg i , . . . } of times tg i . The symbol “i” designates the order number of the time 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 time tg i . The times tg i  are less frequent than the times t k . 
     The sub-module  62  also acquires the corrected distance, delivered by the sub-module  61 , at a frequency lower than or equal to the frequency F 42 . Here, the frequency of acquisition of the corrected distance is equal to the frequency F 20 . Below, the acquisition times of each new corrected distance are denoted to j . The corrected distance acquired at the time to j  is further denoted dc j . The symbol “j” is the order number of the time to j  in the time-ordered sequence {0, to 1 , to 2 , . . . , to j-1 , to j , . . . } of times to j . The sub-module  62  also updates the correction coefficients each time a new corrected distance dc j  is acquired and therefore for each time to j . Since the frequency F 20  is lower than the frequency F 42 , there are systematically a plurality of times t k  between the times to j-1  and to j . 
     Below, 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 sub-sets of the sequence {0, t 1 , t 2 , . . . , t k-1 , t k , . . . }. Thus, each time tg i  and to j  corresponds to one respective time t k  of the sequence {0, t 1 , t 2 , . . . , t k-1 , t k , . . . }. In addition, in this embodiment, the times tg i  and to j  are different. In other words, at a time tg i  when the measurement of the unit  40  is acquired, no new corrected distance is acquired and vice-versa. Lastly, in this text, the times t m  are equal to the times at which the sub-module  62  acquires either a measurement of the unit  40  or a new corrected distance. 
     To update the correction coefficients depending on the measurements of the unit  40  and on the corrected distance, the sub-module  62  comprises a Kalman filter  64 . To combine the correction coefficients with the raw estimations delivered by the sub-module  60 , the sub-module  62  also comprises an adder  66 . 
     Here, the filter  64  is an error-state Kalman filter (ESKF) because it estimates corrections to be made to the position, orientation and speed estimated by the sub-module  60 . More precisely, the filter  64  delivers, for each time t m , a state vector X m|m . The state vector X m|m  notably contains the correction coefficients to be used to correct the position P e (m), orientation O e (m) and speed V e (m). For each time t m , the adder  66  combines the correction coefficients delivered by the filter  64  with the position P e (m), orientation O e (m) and speed V e (m) to obtain the corrected position P c (m), the corrected orientation O c (m) and the corrected speed V c (m). For each time t k  subsequent to the time t m  and prior to the time t m+1 , no correction is made to the estimations constructed by the sub-module  60 . 
     For example, here, the state vector X m|m  contains correction coefficients δ x (m), δ y (m) and δ z (m) for the coordinates x e (m), y e (m) and z e (m) of the position P e (m), respectively. The adder  66  adds these coefficients δ x (m), δ y (m) and δ z (m) to the coordinates x e (m), y e (m) and z e (m) to obtain the coordinates x c (m), y c (m) and z c (m) of the corrected position P c (m), respectively. 
     The state vector X m|m  also contains correction coefficients δ ψ (m), δ θ (m) and δ φ (m) for the coordinates ψ e (m), θ e (m) and φ e (m) of the orientation O e (m), respectively. The adder  66  adds these coefficients ψ e (m), θ e (m) and φ e (m) to the coordinates ψ e (m), θ e (m) and φ e (m) to obtain the corrected coordinates ψ c (m), θ c (m) and φ c (m) of the orientation O c (m), respectively. 
     Similarly, the state vector X m|m  also contains three correction coefficients δv x (m), δv y (m) and δv z (m) used to correct the coordinates Vx e (m), Vy e (m) and Vz e (m) of the speed V e (m), respectively. 
     Conventionally, the state vector X m|m  also contains correction coefficients for correcting other parameters, such as measurement biases of the accelerometer  44  and of the gyrometer  46 , inter alia. In this embodiment, the state vector X m|m  in addition contains:
         three correction coefficients δba x (m), δba y (m) and δba z (m) for correcting the measurement biases of the accelerometer  44  in the 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 gyrometer  46  around axes parallel to the directions x b , y b  and z b , respectively.       

     In this embodiment, the state vector X m|m  is therefore the following vector of fifteen coordinates: [δ ψ (m), δ e (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 2 (m)] T , where the symbol “T” symbolizes the transpose operation. 
     The filter  64  is a recursive algorithm that, for each time t m , delivers to the adder  66  a new state vector X m|m  computed from:
         the preceding state vector X m−1|m-1 ,   the measurement of the unit  40  or the new corrected distance acquired at the time t m , and   the position P e (m), orientation O e (m) and speed V e (m) constructed by the sub-module  60  for the time t m .       

     Conventionally, the filter  64  comprises a predicting block  68  for computing a first state vector X m|m-1  from the vector X m|m-1 , followed by an updating block  70  that computes 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-1 . 
     More precisely, the block  68  constructs a prediction X m|m-1  of the state vector from the preceding state vector X m|m-1 . 
     Here, an example of embodiment of the blocks  68  and  70  is described in the particular case where the filter  64  is an extended Kalman filter (EKF). 
     The equation used by the block  68  to propagate or predict the state of the filter  64  is defined by the following relationship, relationship (1): 
     
       
      
       X 
       m|m-1 
       =A 
       m−1 
       X 
       m−1|m-1  
      
     
     where:
         X m|m-1  is the estimation of the state vector at the time t m−1 , said estimation being obtained taking into account all the measurements up to the time t m−1 ,   X m|m-1  is the prediction of the state vector at the time t m , said prediction being obtained taking into account all the measurements up to the time t m−1  but not taking into account the measurements acquired at the time t m ,   A m−1  is the state transition matrix at the time t m−1 .       

     In the particular case described here where the filter  64  is an error-state Kalman filter, the vector X m−1|m-1  is always zero because it is assumed that the error was corrected previously. In other words, relationship (1) simplifies to the following relationship: X m|m-1 =0. 
     The equation used by the block  68  to propagate or predict the error covariance matrix is defined by the following relationship, relationship (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 estimation of the error covariance matrix at the time t m−1 , said estimation being obtained taking into account all the measurements acquired up to the time t m−1 ,   P m|m-1  is the prediction of the covariance matrix P m  at the time t m , said prediction being obtained solely taking into account the measurements acquired up to the time t m−1 ,   Q m−1  is the covariance matrix of the process noise v.       

     The block  70  corrects the prediction X m|m-1  of the state vector so as to obtain the state vector X m|m . The corrected vector X m|m  is constructed depending on a difference Y m  between:
         an estimation {circumflex over (z)} m  of a physical quantity at the time t m , and   the measurement z m  of the same physical quantity at the time t m .       

     The difference Y m  is known as “innovation”. Here, the measured physical quantities are the position and speed measured by the unit  40  and, alternately, the corrected distance delivered by the sub-module  61 . Thus, for each time tg i , the block  70  corrects the prediction X m|m-1  solely on the basis of the measurement of the unit  40  acquired at this time tg i . Reciprocally, for each time to j , the block  70  corrects the prediction X m|m-1  solely on the basis of the corrected distance acquired at this time to j . At the times tg i , the prediction X m|m-1  is corrected depending on differences in position and speed, for example as described in Godha2006. Thus, this functionality of the block  70  is not described in more detail. Only correction of the prediction X m|m-1 , at the times to j  depending on the corrected distance, is described below. 
     In this example of embodiment, the physical quantity is the corrected distance dc m . The estimation {circumflex over (z)} m  of the corrected distance dc m  is constructed using the following relationship, relationship (3): 
     where: 
         {circumflex over (z)} =√{square root over (( x   e ( m )− B   x ) 2 +( y   e ( m )− B   y ) 2 +( z   e ( m )− B   z ) 2 )}
         m is the order number of a time t m  of the sequence {0, t 1 , t 2 , . . . , t m−1 , t m , . . . } when 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 , said coordinates being expressed in the frame of reference R T ,   B x , B y , B z  are the coordinates of the position of the transceiver  22  in the frame of reference R T .       

     The coordinates B x , B y , B z  are constants and stored beforehand in the memory  54 . 
     The innovation Y m  is obtained using the following relationship, relationship (4): Y m =dC m −{circumflex over (z)} m . 
     Typically, the block  70  corrects the prediction X m|m-1  by adding thereto the innovation Y m  multiplied by the Kalman gain Km. The gain K m  is computed using the following relationship, relationship (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 in the corrected distance, and   H m  is an observation matrix.       

     The observation matrix H m  is dependent on the partial derivative of relationship (3) with respect to the various parameters of the state vector X m|m . The matrix R m  is for example constant and initialized using data on the covariance of the noise in the measurements of the transmission and reception times obtained by the transceiver  20 . 
     Next, the state vector X m|m  is obtained using the following relationship, relationship (6): X m|m =+K m Y m . 
     The updated error covariance matrix at the time t m  is computed using the following relationship, relationship (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 in the estimations of the correction coefficients. 
     In this particular embodiment, the adder  66  is a simple adder that adds, to the position P e (k), orientation O e (k) and speed V e (k), the corresponding correction coefficients contained in the state vector X m|m . Next, the adder  66  delivers, to the output  37 , the corrected position P c (k), orientation O c (k) and speed V c (k) thus obtained. 
     The operation of the system  30  will now be described with reference to the method of  FIG.  4   . 
     The method starts with a calibrating phase  100 . In this phase  100  the correction functions f Sn  associated with each of the segments S 1  to S 4  are determined. 
     To do this, in a step  102 , the vehicle  2  is made to travel the entirety of the segment S 1 , starting from point A and ending at point B. 
     In parallel to step  102 , in a step  104 , the transceivers  20  and  22  exchange data frames in order to allow a raw distance between these transceivers  20 ,  22  to be measured from the transmission and reception times of these data frames. Each exchange of data frames allows a sufficient number of transmission and reception times to be acquired to compute a raw distance between these transceivers  20  and  22 . For example, here, these exchanges are triggered periodically at the frequency F 20 . Each exchange therefore occurs over the course of one respective period T 20,j . 
     In this example of embodiment, the two-way ranging method is employed. In this method, each exchange comprises:
         transmission by the transceiver  20  of a first data frame, then   in response to reception of this first data frame by the transceiver  22 , transmission by the transceiver  22  of a second data frame.       

     The first data frame is transmitted at a time M 1,j  and received by the transceiver  22  at a time M 2,j . The second data frame is transmitted at a time M 3,j  and received by the transceiver  20  at a time M 4,j . 
     The times M 1,j  and M 4,j  are measured by the transceiver  20 . The times M 2,j  and M 3,j  are measured by the transceiver  22 . Since the time M 3,j  is measured by the transceiver  22 , it cannot be transmitted to the transceiver  20  in the second data frame transmitted at this time. Here, the times M 2,j  and M 3,j  measured by the transceiver  22  are transmitted to the transceiver  20  in the second data frame sent in the course of the following period T 20,j+1 . Because of this delay, the time to j  at which the sub-module  62  acquires the distance dc j  is well after the end of the period T 20,j . 
     When the transceiver  20  has measured the times M 1,j  and M 4,j  and received the measurements M 2,j  and M 3,j , in a step  106 , the transceiver  20  transmits these measurements to the sub-module  61 . 
     In response, in a step  108 , the sub-module  61  computes a raw distance db j  only from the transmission and reception times measured during the period T 20,j . Here, the distance db j  is computed using the following relationship, relationship (8): 
     
       
         
           
             
               db 
               j 
             
             = 
             
               c 
               · 
               
                 
                   
                     ( 
                     
                       
                         M 
                         
                           4 
                           , 
                           j 
                         
                       
                       - 
                       
                         M 
                         
                           3 
                           , 
                           j 
                         
                       
                     
                     ) 
                   
                   + 
                   
                     ( 
                     
                       
                         M 
                         
                           2 
                           , 
                           j 
                         
                       
                       - 
                       
                         M 
                         
                           1 
                           , 
                           j 
                         
                       
                     
                     ) 
                   
                 
                 2 
               
             
           
         
       
     
     where the symbol “c” designates the speed of light. Below, unless otherwise indicated, the symbol “.” in a mathematical relationship designates the arithmetical operation of multiplication. 
     In parallel to steps  104  to  108 , in a step  110 , and in each period T 20,j , a precise distance dp j  is measured without using the transmission and reception times of the data frames. To do this, measurements are taken by another sensor independent of the transceivers  20  and  22 . Typically, this other sensor is used only during the calibrating phase  100 . This sensor must have a better accuracy, and typically an accuracy two or ten times better, than the accuracy of the measurement of the raw distance db j . For example, this other sensor is an optical range-finder temporarily installed along the segments S 1  to S 4 . 
     In a step  112 , once the distances db j  and dp j  have been obtained for a multitude of different positions of the vehicle  2  along the segment S 1 , a correction function f s1  that returns the correction coefficient allowing the distance db j  to be corrected is determined. To do this, for each pair of distances db j  and dp j , an error ed j  between these distances db j  and dp j  is computed. The function f s1  is parametrized by the value of a physical quantity chosen from the group consisting:
         of the distance d between the transceivers  20  and  22 , and   of a physical quantity representative of the power of the received radio signals.       

     In this example of embodiment, the function f s1  is parametrized by the distance d and therefore denoted f s1  (d). 
     Here, the function f s1  (d) is defined by the following relationship, relationship (9): 
     
       
         
           
             
               
                 f 
                 
                   s 
                   ⁢ 
                   1 
                 
               
               ( 
               d 
               ) 
             
             = 
             
               
                 
                   a 
                   
                     s 
                     ⁢ 
                     1 
                   
                 
                 · 
                 
                   d 
                   
                     
                       
                         d 
                         
                           0 
                           , 
                           
                             s 
                             ⁢ 
                             1 
                           
                         
                         2 
                       
                       + 
                       
                         d 
                         2 
                       
                     
                   
                 
               
               + 
               
                 b 
                 
                   s 
                   ⁢ 
                   1 
                 
               
             
           
         
       
     
     where a s1 , b s1  and d 0,s1  are constants. This function f s1  (d) is entirely defined once the values of the constants a s1 , b s1  and d 0,s1  are known. Here, to determine the function f s1  (d), the values of the constants a s1 , b s1  and d 0,s1  that minimize the following difference for all the measured distances dp j  are computed: |f s1 (dp j )−ed j |. For example, to do this, a numerical solver is used. 
     Once the function f s1  (d) has been determined, it is associated with the segment S 1  in the table  58 . For example, to do this, the values of the constants a s1 , b s1  and d 0,s1  are associated with the segment S 1  by the table  58 . 
     The preceding steps, which have been described in the particular case of the segment S 1 , are reiterated for each of the segments and hence, at the end of the phase  100 , the table  58  contains one correction function associated with each of the segments S 1  to S 4 . Most often, the correction functions thus determined are all different from one another. 
     After the calibrating phase  100 , the system  30  is used to determine a corrected distance dc j  between the transceivers  20  and  22  and to locate the vehicle  2 . 
     Use of the system  30  to locate the vehicle  2  starts with a phase  120  of initializing the system  30 . This phase  120  starts immediately after activation of the system  30 , i.e. typically just after it has been turned on. In this phase  120 , the various variables and parameters required by the execution of the module  56  are initialized. For example, the values of the position, speed and orientation of the vehicle  2  and of the correction coefficients are initialized to initial values. There are many algorithms that allow these initial values to be rapidly obtained. 
     Once the initializing phase  120  has ended, a phase  130  of executing the module  56  begins. 
     In 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, orientation and speed of the vehicle  2 . Thus, for each time t k , the position, orientation and speed of the vehicle  2  are updated. 
     More precisely, step  136  comprises an operation  138  in which the accelerometer  44  and gyrometer  46  measure the acceleration and angular velocity of the vehicle  2 , respectively, and these new measurements are acquired by the computer  50  at the time t k . 
     Next, in an operation  140 , the sub-module  60  constructs the raw estimations P e (k), O e (k) and V e (k) from:
         the preceding position P(k−1), the preceding orientation O(k−1) and the preceding speed V(k−1), and   the measurements of the accelerometer  44  and of the gyrometer  46  acquired at the time t k .       

     In parallel to step  136 , a step  150  of determining the distance between the transceivers  20 ,  22  is executed. This step  150  is reiterated at the frequency F 20  in order to provide, to the sub-module  62 , a new corrected distance dc j  at each time to j . 
     Step  150  comprises the following operations in succession:
         an operation  152  of exchanging data frames between the transceivers  20 ,  22 ,   an operation  154  of transmission of the times M 1,j , M 2,j , M 3,j  and M 4,j  to the computer  50  and of acquisition of these times by the sub-module  61 ,   an operation  156  of computation of the raw distance db j ,   an operation  158  of identification among the segments S 1  to S 4  of the segment on which the vehicle  2  is found,   an operation  160  of selection of the correction function associated with the identified segment,   an operation  162  of execution of the selected correction function, then   an operation  164  of correction of the raw distance db j  to obtain the corrected distance dc j .       

     Operations  152 ,  154  and  156  are identical to steps  104 ,  106  and  108 , respectively. 
     In the operation  158 , to identify the segment on which the vehicle  2  is currently found, the sub-module  61  uses the last position of the vehicle  2  estimated by the sub-module  60 . In contrast, in this example of embodiment, the coordinates of the segments S 1  to S 4  are not used. To perform said identification, direction vectors u v  and u b  are associated with the transceivers  20  and  22 , respectively. The vector u v  is fixed with respect to the body of the vehicle  2 . Thus, this vector u v  changes only if the orientation of the vehicle changes. The vector u b  is fixed with respect to the transceiver  22 . Since the transceiver  22  is immobile, the vector u b  does not change. The directions in which the vectors u v  and u b  point may be chosen arbitrarily. Specifically, these vectors u v  and u b  are simply used to express the relative orientation of the transceivers  20 ,  22 . 
     In this example of embodiment, to simplify the computations, the vectors u v  and u b  are horizontal. Again to simplify the computations, the vector u v  is chosen to lie parallel to the direction x b  of the frame of reference R b  and to be of opposite sign to the direction x b . Here, the vector u b  is chosen to lie parallel to and to be of same sign as the vector u v , when the vehicle is on the segment S 1 . 
     Under these conditions, the coordinates of the vector u v  are given by the following relationship: 
         u   v =[cos(ψ v )sin(ψ v )0] T  
 
     where the angle ψ v  is the yaw angle of the vehicle  2 , which is obtained from the last orientation O e (k) estimated by the sub-module  60 . 
     For its part, the vector u b  is defined by the following relationship: 
         u   b =[cos(ψ b )sin(ψ b )0] T  
 
     where the angle ψ b  is the yaw angle of the transceiver  22 . The angle ψ b  is a constant because the transceiver  22  is fixed. 
     In the operation  158 , the sub-module  61  computes the coordinates of a direction vector u bv  that points from the geometric centre of the antenna of the transceiver  22  to the geometric centre of the antenna of the transceiver  20 . The coordinates of this vector u bv  are given by the following relationship: 
     
       
         
           
             
               u 
               bv 
             
             = 
             
               
                 
                   [ 
                   
                     
                       
                         x 
                         e 
                       
                       ( 
                       k 
                       ) 
                     
                     - 
                     
                       
                         B 
                         x 
                       
                       ⁢ 
                          
                       
                         
                           y 
                           e 
                         
                         ( 
                         k 
                         ) 
                       
                     
                     - 
                     
                       
                         B 
                         y 
                       
                       ⁢ 
                           
                       
                         
                           z 
                           e 
                         
                         ( 
                         k 
                         ) 
                       
                     
                     - 
                     
                       B 
                       z 
                     
                   
                   ] 
                 
                 T 
               
               
                  
                 
                   [ 
                   
                     
                       
                         x 
                         e 
                       
                       ( 
                       k 
                       ) 
                     
                     - 
                     
                       
                         B 
                         x 
                       
                       ⁢ 
                          
                       
                         
                           y 
                           e 
                         
                         ( 
                         k 
                         ) 
                       
                     
                     - 
                     
                       
                         B 
                         y 
                       
                       ⁢ 
                           
                       
                         
                           z 
                           e 
                         
                         ( 
                         k 
                         ) 
                       
                     
                     - 
                     
                       B 
                       z 
                     
                   
                   ] 
                 
                  
               
             
           
         
       
     
     where:
         x e (k), y e (k) and z e (k) are the coordinates of the current position P e (k) of the vehicle  2 , and   B x , B y , B z  are the coordinates of the position of the transceiver  22 .       

     Next, the sub-module  61  computes the cosine of an end angle α v  and of a start angle α b  using the following relationships: 
     and 
       cos(α v )=− u   bv   T   ·u   v  
 
       cos(α b )= u   bv   T   ·u   b  
 
     Finally, the sub-module  61  identifies the segment on which the vehicle  2  is found from the signs of the cosines of the angles α v  and α b  using a pre-stored table such as the following table: 
     
       
         
           
               
               
               
             
               
                   
               
               
                 Sign of cos 
                 Sign of cos 
                 Corresponding  
               
               
                 (α v ) 
                 (α b ) 
                 segment 
               
               
                   
               
             
            
               
                 − 
                 + 
                 S1 
               
               
                 + 
                 − 
                 S2 
               
               
                 − 
                 − 
                 S3 
               
               
                 + 
                 + 
                 S4 
               
               
                   
               
            
           
         
       
     
     This table allows the identified segment to be obtained from the signs of the computed cos(α v ) and cos(α b ). The signs in the columns of this table result from arbitrary choices made when defining the direction vectors u v  and u b . This table must therefore be modified depending on these choices. The only really important thing is to keep the same conventions between the time when this table is constructed and the times when this table is used. 
     In the operation  160 , the sub-module  61  selects the correction function associated by the table  58  with the segment identified in the operation  158 . 
     In the operation  162 , the sub-module  61  executes the selected correction function. To do this, for example, it computes a distance d between the transceivers  20 ,  22  on the basis of the last position P e (k) estimated for the vehicle  2  and of the coordinates of the transceiver  22 . Next, it executes the selected correction function parametrized by the value of this distance d. The sub-module  61  thus obtains a correction coefficient Cd. 
     Lastly, in the operation  164 , the sub-module  61  computes the corrected distance dc j  using the following relationship: dc j =db j −Cd. It is this distance dc j  that is acquired by the sub-module  62  at the time to j . 
     Next, only if the time t k  is in addition a time tg i  when a measurement of the unit  40  is acquired, after step  136 , the computer  50  executes a step  170  of updating the correction coefficients depending on the new measurement of the unit  40 . In this step  170  the correction coefficients are updated without using the transmission and reception times obtained by the transceiver  20 . 
     Only if the time t k  is a time to j  when a corrected distance dc j  is acquired, after step  136 , the computer  50  executes a step  180  of updating the correction coefficients depending on the new corrected distance dc j . In this step  180  the correction coefficients are updated without using the measurement of the unit  40 . 
     If the time t k  corresponds neither to a time tg i  nor to a time to j , then the position P e (k), orientation O e (k) and speed V e (k) as estimated by the sub-module  60  and not corrected by the sub-module  62  are delivered to the output  37 . Thus at times t k  located between the times t m , it is the position P e (k), orientation O e (k) and speed V e (k) that are delivered to the output  37 . In addition, the method returns to step  136  without executing either step  170  or step  180 . In this case, the preceding position, the preceding orientation and the preceding speed used in the next iteration of step  136  are also the position P e (k), orientation O e (k) and speed V e (k), respectively. 
     In step  180 , the sub-module  62  begins by acquiring, in an operation  201 , the new corrected distance dc j . 
     Next, in an operation  202 , the block  68  is executed by the computer  50  to obtain the predicted state vector X m|m  from the preceding estimation X m−1|m-1  of this state vector. The preceding estimation is the estimation obtained at the preceding time t m−1 . The preceding time t m−1  corresponds either to a time tg i  or to the time to j-1 . Thus, the preceding estimation is the estimation that was constructed either in the preceding execution of step  170  or in the preceding execution of step  180 . The prediction X m|m-1  of the state vector is constructed by implementing relationship (1). In this particular case where the filter  64  is an error-state Kalman filter, the prediction X m|m-1  is systematically zero. 
     In the operation  202 , the block  68  also constructs the prediction P m|m-1  of the covariance matrix P m  at the time t m  by implementing relationship (2). 
     In an operation  206 , the block  70  constructs the estimation {circumflex over (z)} m  of the distance between the transceivers  20 ,  22  by implementing relationship (3). In this embodiment, in the operation  206 , the block  70  also computes the observation matrix H m . The matrix H m  is, for example, computed by taking the derivative of relationship (3) with respect to each of the various parameters of the state vector X m|m . 
     In the following operation, operation  208 , the block  70  updates the correction coefficients. To do this, it corrects the prediction X m|m-1  depending on the innovation Y m  between the corrected distance dc j  and its estimation {circumflex over (z)} m . To this end, the block  70  computes the innovation Y m  using relationship (4). Next, the gain K m  is computed using relationship (5). The corrected state vector X m|m  is then obtained by implementing relationship (6). 
     In the operation  208 , the block  70  also obtains the covariance matrix P m|m  updated using relationship (7). 
     At the end of steps  170  and  180 , in a step  210 , the sub-module  62  corrects the position P e (m), orientation O e (m) and speed V e (m) to obtain the corrected position P c (m), the corrected orientation O c (m) and the corrected speed V c (m). 
     To do this, the adder  66  adds the correction coefficients contained in the vector X m|m  to the corresponding coordinates of the position P e (m), orientation O e (m) and speed V e (m) constructed in the last execution of the operation  136 , to obtain the position P c (m), orientation O c (m) and speed V c (m). Thus, only at the times t m , it is the position P c (m), orientation O c (m) and speed V c (m) that are delivered to the output  37 , and not the position P e (m), orientation O e (m) and speed V e (m). In addition, in step  210 , the position P(k), orientation O(k) and speed V(k) are transmitted to the sub-module  60  and used by the sub-module  60  as preceding position, preceding orientation and preceding speed of the vehicle  2  in the next iteration of step  136 . 
     After step  210 , the method returns to step  136 . 
     Section II: Variants 
     Variants of the Determination of Distance: 
     Other methods for measuring the raw distance db j  from the times of transmission and reception of data frames between the transceivers  20  and  22  may be implemented. For example, as a variant, the two-way ranging method is replaced by a three-way ranging method. In this three-way ranging method, each exchange of data frames between the transceivers  20  and  22  comprises, in addition to the transmission of first and second data frames, the transmission by the transceiver  20 , in response to reception of the second data frame, of a third data frame at a time M 5,j  and reception of this third data frame by the transceiver  22  at a time M 6,j . In this case, the raw distance db j  is computed using the following relationship: 
     
       
         
           
             
               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 relationship:
 
where ΔT is equal to M 5,j −M 1,j .
 
     
       
         
           
             
               ε 
               AB 
             
             = 
             
               
                 
                   ( 
                   
                     
                       M 
                       
                         6 
                         , 
                         j 
                       
                     
                     - 
                     
                       M 
                       
                         2 
                         , 
                         j 
                       
                     
                   
                   ) 
                 
                 
                   Δ 
                   ⁢ 
                   T 
                 
               
               - 
               1 
             
           
         
       
     
     The measurements of the times M 2,j  and M 3,j  may be transmitted to the transceiver  20  by other means than the second data frame emitted in the course of the period T 20,j+1 . For example, these times M 2,j  and M 3,j  are transmitted to the transceiver  20  via an additional data frame the transmission and reception times of which are not used to compute the distance db j . In another embodiment, this additional frame is transmitted via a data-transmission link set up using transceivers independent of the transceivers  20  and  22 . 
     As a variant, the transceivers  20  and  22  are capable of taking an approximate measurement and a precise measurement of the reception times. In this case, advantage may be taken of this capability, for example in the following way. UWB technology uses an indicator known by the acronym FPI (standing for First Path Index). This indicator is constructed by the transceivers  20 ,  22 . This indicator must normally be comprised between an upper limit L H  and a lower limit L B . When this indicator is between the limits L H  and L B , it is precise measurement that is used. In contrast, if this indicator is not comprised between these limits L H  and L B , it is the approximate measurement that is used. 
     As a variant, the computation of the raw distance db j  allows for drift in the clock located in the transceiver  20  with respect to the clock located in the transceiver  22 . 
     These clocks are used to measure the transmission and reception times of the data frames. To do this, for example, the raw distance db j  is computed using the following relationship: 
     
       
         
           
             
               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 relationship: 
     
       
         
           
             
               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 roles of the transceivers  20  and  22  may be reversed. In this case, it is the transceiver  22  that transmits the first data frame at the time M 1,j  and, in response to reception of this first data frame, the transceiver  20  transmits the second data frame at the time M 3,j . In this embodiment, the times M 2,j  and M 3,j  are measured by the transceiver  20  and the times M 1,j  and M 4,j  are measured by the transceiver  22 . The transceiver  22  transmits the measured times M 1,j  and M 4,j  to the transceiver  20 , for example in the first data frame transmitted at the time 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 data frame, for example the second data frame transmitted from the transceiver  22  to the transceiver  20 . In this case, these coordinates do not need to be stored in the memory  54  beforehand. 
     Other embodiments of the correction functions are possible. In particular, forms other than the one given in relationship (9) are possible for each correction function. For example, the correction function may be entirely defined by the values of four constants instead of three. For example, the correction function may be a polynomial of third or second degree, or a quotient of two polynomials of first degree. In particular, it is possible to use correction functions that are entirely defined by less than three constants. For example, in this case, the correction function is a polynomial of first degree or a constant. In the latter case, the correction coefficient is constant and independent of the distance d. 
     In the operation  162 , the value of the distance d used to execute the selected correction function may be obtained differently. For example, the distance d is set equal to the distance db j  computed in operation  156 . 
     As a variant, the correction function is parametrized by the value of a physical quantity representative of the power of the radio signal received by the transceivers  20 ,  22 . This physical quantity may be directly the power of the received radio signal or another physical quantity that represents this power. For example, by way of illustration, this physical quantity may also be the signal-to-noise ratio, a gain, a number of pilot symbols used, inter alia. In the case where the correction function is parametrized by a physical quantity representative of the power of the received radio signal, in the calibrating phase  100  this physical quantity is measured for each position where the distance dp j  is measured. Next, these measurements of this physical quantity are used to determine the various constants that define the correction function. 
     In another variant, the correction function is parametrized both by the distance d and by the physical quantity representative of the power of the received radio signals. 
     Although the commonest case is for all the determined correction functions to be different from one another, the correction functions associated with two or more segments may potentially be identical. 
     Other methods for identifying the segment on which the vehicle  2  is found are possible. For example, as a variant, the segment on which the vehicle  2  is found is identified by comparing the current position P e (k) of the vehicle  2  with the coordinates of the various segments S 1  to S 4 . For example, in the case where the segments S 1  to S 4  are straight line segments, the sub-module  61  verifies that the position P e (k) belongs to one of these straight line segments. To do this, for example, the equations defining each of these straight line segments are used. In the latter case, the orientation O e (k) of the vehicle  2  is not required to identify the segment on which the vehicle  2  is current found. In another variant, the current position P e (k) allows the curvilinear abscissa of the vehicle  2  with respect to a reference point to be determined. This curvilinear abscissa then allows the segment on which the vehicle  2  is found to be identified by comparing it to the curvilinear abscissae of the start and end points of each segment. 
     The number of predetermined segments may be different from four. For example, in one simplified embodiment, it is equal to two. Such a case is obtained if the segments S 1  and S 2  are replaced by a single segment that extends from point A to point C and if the segments S 3  and S 4  are replaced by a single segment that extends from point D to point F. In another variant, the number of predetermined segments associated with the transceiver  22  is higher than four. 
     Variants of the Kalman Filter: 
     Many other embodiments of the filter  64  are possible. For example, the filter  64  may be a linear Kalman filter, an extended Kalman filter (EKF), an unscented Kalman filter (UKF) or even an adaptive Kalman filter. 
     There are many variants of the relationships implemented in the Kalman filter. Specifically, these relationships depend on the frame of reference in which the position, orientation and speed of the vehicle are expressed. However, other frames of reference are usable instead of the frame of reference R T . For example, mention may be made of the ECI frame (ECI standing for Earth Centred Inertial). The ECI frame is not stationary with respect to the Earth&#39;s surface since the Earth rotates in this frame of reference. The frame of reference R T  may also be a frame of reference that is fixed with respect to the stars. When another frame of reference is used, it is possible, via a simple change of coordinate system, to return to the situation described here. 
     The relationships of the Kalman filter may also contain an additional rotation matrix in order to take into account the fact that the measurement axes of the unit  42  are not aligned with the axes of the frame of reference R b . 
     Likewise, many variants of the state vector X m|m  are possible. For example, the state vector X m|m  may also not contain a correction coefficient for the biases of the accelerometer  44  and of the gyrometer  46 . The state vector X m|m  may also contain additional state variables. 
     What was taught above in the particular case where the correcting sub-module  62  uses one or more Kalman filters also applies to correcting sub-modules that construct the correction coefficients using estimators other than Kalman filters. Generally, what has been taught here applies to any correcting sub-module configured to update the correction coefficients using an innovation between:
         a measurement of a physical quantity constructed using the corrected distance dc j , and   an estimation of this physical quantity constructed using measurements of the unit  42 .       

     Other embodiments of the sub-module  62  are possible. For example, as a variant, the sub-module  62  has a tight-coupling architecture. This architecture is described in more detail in chapter 4.1.2 of the thesis Godha2006. 
     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 to exchange the data frames. 
     As a variant, the system  30  is equipped with additional sensors, such as for example a magnetometer, a barometer or an odometer. In this case, the correcting sub-module  62  is modified to take into account the measurements of these additional sensors to correct the raw estimations delivered by the integrating sub-module  60 . 
     In another embodiment, the satellite geolocation unit  40  is omitted. In this case, for example, the correction coefficients are updated solely using the corrected distances dc j . 
     As a variant, the system for locating the vehicle  2  comprises a single fixed transceiver or, in contrast, a plurality of fixed transceivers. In the case where the system comprises a plurality of fixed transceivers, the latter are preferably distributed at regular intervals along the path or along one length of this path. In the latter case, if the mobile transceiver  20  is able to simultaneously communicate with a plurality of fixed transceivers, then, instead of delivering at a time to j  a single corrected distance, the sub-module  61  simultaneously delivers a plurality of corrected distances, each of these distances corresponding to a distance between the transceiver  20  and one respective fixed transceiver. Next, the sub-module  62  corrects the estimation of the position by taking into account these various distances and the known positions of the various 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 anchor that already contains the transceiver  22 . 
     Variants of the Method: 
     The method described here for determining the corrected distance dc j  may be used in methods other than methods for locating a vehicle. In particular, the corrected distance dc j  may be used for purposes other than the purpose consisting in correcting an estimation of the position of the vehicle. For example, the method for determining the corrected distance dc j  is implemented only in the case where only the distance between the transceivers  20 ,  22  must be determined. In such a case, the position of the vehicle is determined by any means such as, for example, solely using the satellite geolocation unit  40  or any other sensor capable of determining the position of the vehicle  2  independently of the measurements of the times of transmission and reception of data frames exchanged between the transceivers  20 ,  22 . 
     The position, orientation and speed of the vehicle  2  may be determined by methods other than those implementing a fusing algorithm such as described above. In this case, the fusing algorithm is replaced by another algorithm that performs the same function and that allows the position of the vehicle  2  to be determined. Thus, in simplified variants, only the position of the vehicle  2  is estimated. 
     The position of the vehicle  2  may be determined from measurements of one or more other measurement units. For example, these measurement units are chosen from the group consisting of:
         the satellite geolocation unit  40 ;   the inertial measurement unit  42 ,   an odometer,   a magnetometer associated with a map of terrestrial magnetic fields.       

     Thus, what has been described may also be implemented in a locating system in which the units  40  and  42  are replaced by one or more other sensors whereby the position of the vehicle  2  may be determined. 
     As a variant, it is possible for, at a given time t m , a new measurement of the unit  40  and a new corrected distance to be acquired. In other words, as a variant, the times tg i  and to j  may be concomitant. In this case, the computer  50  updates the correction coefficients depending both on the new measurements of the unit  40  and on the new corrected distance. For example, to do this, the computer  50  computes a new gain K m  depending on an observation matrix formed by concatenation of the matrix H m  and of the observation matrix used to update the correction coefficients depending on the measurement of the unit  40 . 
     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 the Kalman filter to be executed at each time t k , this not always being desirable. 
     Other Variants: 
     The vehicle  2  is not necessarily a gondola lift. What has been described applies to any vehicle constrained to move over a countable number of predetermined segments. For example, the system  30  may be applied to the case where the vehicle is a motor vehicle. In this case, each segment corresponds to one traffic lane. If the road comprises more than two traffic lanes then, preferably, more than two predetermined segments are used in order for each segment to correspond to one respective lane. The system  30  may also be applied to a rail vehicle. In the latter case, the lanes are tracks of a railway. 
     As a variant, the various predetermined segments associated with the same fixed transceiver are not parallel to one another. Such a situation may arise when the segments correspond to segments of railway tracks or of traffic lanes that cross in proximity to a given fixed transceiver. 
     As a variant, when the vehicle  2  is travelling a path segment, it may diverge slightly from the reference path travelled by this vehicle in the calibrating phase  100  without this decreasing the accuracy of the corrected distance dc j . Here, a difference between the current path of the vehicle  2  and the reference path is considered to be slight if, at any point A of the current path, the difference |θ v −θ ref | remains smaller than 10° or 5°, where:
         θ v  is the angle between the direction vectors u v  and u b  that were defined above when the vehicle is located at point A of the current path, and   θ ref  is the angle between the direction vectors u v  and u b  when the vehicle is located on the point of the reference path closest to the current point A.       

     As a variant, the control post  38  is located inside the vehicle  2 . This is notably the case when the vehicle  2  is, for example, a motor vehicle or a rail vehicle. 
     In one simplified embodiment, the system  30  does not determine the speed of the vehicle  2 . In this case, the module  56  may be simplified. 
     Section III: Advantages of the Described Embodiments 
     The fact of using a plurality of correction functions each associated with one respective segment of the path makes it possible to determine, on each of these segments, a correction function that is both simple and rapid to execute while remaining accurate. In addition, these correction functions are simpler to establish. Specifically, the number of values that each of these correction functions must approximate as accurately as possible is much lower than the total number of values to be approximated along the complete path of the vehicle  2 . The fact that the number of values to be approximated is much lower makes it possible to use, at equal accuracy, a correction function that is simpler to implement and more rapid to execute. Thus, by associating with each of the segments one respective correction function, it is possible to simplify the implementation of the method without decreasing accuracy, or indeed even increasing it. In addition, the number of segments remains low since the vehicle is constrained to move along a limited number of segments. 
     In the context where the corrected distance dc j  is used to locate a vehicle, simplifying the implementation of the determination of this corrected distance without decreasing the accuracy thereof also makes it possible not to decrease the accuracy of the position determined for the vehicle. 
     Parametrizing the correction function with the distanced between the transceivers  20  and  22  or depending on a physical quantity representative of the power of the received radio signals improves the accuracy of the corrected distance dc j . 
     The fact that the correction function is parametrized by the distance d rather than a physical quantity representative of the power of the received radio signals also makes it possible to further increase the accuracy of the distance dc j . 
     The fact that the correction function is entirely defined by at most three constants simplifies the determination of this correction function in the calibrating phase  100 . In addition, such a calibration function is then simple to implement, without however decreasing the accuracy of the corrected distance dc j .