A method of broadcasting precise time signals using a network of beacons with imprecise positions.

Abstract

The invention relates to a method for transferring time to a receiver linked via radio frequency to at least three synchronized terrestrial time-transfer beacons, each transmitting a time message. The described method comprises: a step (201) for determining a pseudo-distance measurement Pdi associated with each time-transfer beacon; a step (202) for determining an initial position and an initial time offset of said receiver from the pseudo-distance measurements; and a step (203) for calculating a fine time offset of the receiver by a solution algorithm optimizing a maximum likelihood criterion that jointly solves for the positions of the terrestrial time-transfer beacons, the position, and the time offset of the receiver. The invention also relates to radiocommunication equipment implementing the method, as well as a computer program and a computer medium containing said program. Figure for the abstract: Fig. 2.

Description

Title of the invention: Method for broadcasting precise time by a network of imprecise position beacons Technical field

[0001] The invention relates to the field of transferring time information by radio frequency. It relates in particular to a method for transmitting precise time information to a mobile or semi-mobile platform by radio broadcasting beacons whose positions are known with low precision. Prior art

[0002] Sharing a common time reference of good accuracy between several devices may prove essential. This is generally the case when it is necessary to synchronize equipment, such as for time division multiplexed (TDMA) or code division multiplexed (CDMA) radio transmissions, or using frequency hopping spread spectrum (FHSS). The desired accuracy depends on the intended application, but a standard order of magnitude for the desired accuracy is microseconds or less.

[0003] Generally, equipment seeking to determine precise time uses GNSS (Global Navigation Satellite Systems) positioning, which allows precise determination of position and time. However, in some cases, broadcasting a time by a satellite network is not possible, for example when satellite visibility conditions are poor, when there is no means of receiving signals from the satellites, or when one does not wish to rely on a GNSS network.

[0004] It is then possible to broadcast precise time information via wired channels, but this solution is not applicable when the equipment is mobile.

[0005] Another solution is to transmit a time marker by three or more terrestrial time transfer beacons over a radio channel. As long as the beacons are precisely synchronized (by wired channels or high-precision clocks) and their positions are transmitted or known to the equipment seeking to determine the network time, it is possible to calculate a distance to each beacon and to deduce the position of the equipment. This determination is made in a comparable manner to GNSS positioning, by estimating pseudo-distances with each of the beacons, obtained by measuring the propagation time, then by trilateration from the pseudo-distances.

[0006] This solution works in the case of a fixed network of terrestrial time transfer beacons whose position is perfectly known. This is no longer the case when there is a high inaccuracy in the position of the time transfer beacons. This application case is however frequent when it is a question of deploying a network temporarily on a site in the absence of GNSS service, or in the case of so-called "ad-hoc" networks (decentralized wireless network not based on a fixed architecture of access points). In these networks, each node can act as a time transfer beacon, and thus contributes to the synchronization of the other nodes in the network. Since the nodes can be mobile, their position is not necessarily known very precisely.The accuracy of the broadcast time may then not reach the desired requirement levels, especially if the nodes are distant, even when the time transfer beacons have very precise clocks.

[0007] Until now, the measures implemented to overcome this problem consist of adding an error post on the position of the time transfer beacons in the calculation of the variance of the time estimator, in the manner of a DOP (English acronym for Dilution Of Precision) calculation for GNSS links, which makes it possible to take into account an uncertainty on the time, but does not make it possible to improve the precision of the broadcast time.

[0008] An object of the invention is therefore to describe a method for transferring precise time information in a radiocommunications network from terrestrial beacons, taking into account the problem of the precision of their positioning. Summary of the invention

[0009] To this end, the present invention describes a method for transferring time to a receiver in radiofrequency connection with at least three synchronized terrestrial time transfer beacons each broadcasting a time message comprising a time marker and a transmission time. The method described comprises: - a first step of calculating an arrival time of the time messages transmitted by said terrestrial time transfer beacons, the positions of said terrestrial time transfer beacons being known by the receiver or transmitted to the receiver, and of determining a pseudodistance measurement Pdi associated with each time transfer beacon, - a second step of determining an initial position and an initial time offset of said receiver from the pseudo-distance measurements calculated during the first step, - a third step of calculating a fine time shift of said receiver, by implementing a resolution algorithm optimizing a maximum likelihood criterion using the values ​​calculated in the second step and jointly resolving the positions of the terrestrial time transfer beacons, the position of the receiver and the time shift of the receiver.

[0010] According to one embodiment, the third step comprises: - the construction of a state vector X comprising the estimated position of the receiver, the estimated time offset of the receiver, and the estimated positions of the terrestrial time transfer beacons, - the construction of an observation vector y comprising the known or transmitted positions of said at least three terrestrial time transfer beacons and the pseudo-distances calculated during the first step, the construction of a linearized observation vector Y comprising a difference between the known or transmitted positions of said at least three terrestrial time transfer beacons time and their estimated positions, and a difference between the pseudo-distances calculated during the first step (201) and the pseudo-distances constructed from the values ​​of the state vector X, - the construction of a Jacobian matrix H from the state vector X and the observation vector 2 such that u _ dy . and ôx - the resolution of the system, by calculating x — H Y-

[0011] Advantageously, the calculation of x = H*Y is iterated several times, the values ​​of the vector Y and matrix H being recalculated at each iteration based on the vector X determined at the previous iteration.

[0012] According to different embodiments, the algorithm using a maximum likelihood criterion implemented during the third step is a Gauss-Newton algorithm or a Levenberg-Marquardt algorithm.

[0013] Advantageously, the second step is implemented by a method of pseudo-linear estimation of the initial position and the initial time offset of said receiver.

[0014] According to one embodiment, the pseudo-linear estimation comprises: - the calculation of an initial position p of the receiver, with P- (G(R)lG(R))lG(R)1. pseudo-distance measurements Pd; calculated during the first step of the method and the known or transmitted positions of the terrestrial time transfer beacons, R is an observation vector comprising the pseudo-distance measurements Pd; made during the first step of the method, and / is a pseudo-measurement constructed from the pseudo-distance measurements Pd; made , where tr is a matrix constructed from during the first step of the process and the known or transmitted positions of the beacons, - the calculation of an initial time shift such that _ i || Z - P || ] ' with the number of land beacons of time transfer and a vector comprising the known or transmitted positions of the terrestrial time transfer beacons.

[0015] The method according to the invention is particularly suitable for use cases where the position of the terrestrial time transfer beacons is known imperfectly.

[0016] The invention also relates to radiocommunications equipment (or RF receiver) in radiofrequency connection with at least three synchronized terrestrial time transfer beacons each broadcasting a time message comprising a time marker and a transmission time. The radiocommunications equipment according to the invention comprises a radio chain configured to receive and interpret the time message transmitted by the beacons. It further comprises calculation means configured to implement a time transfer method according to one of the preceding claims.

[0017] Finally, the invention also relates to a computer program comprising program code instructions for executing the steps of the time transfer method according to the invention when said program is executed on a computer, and a computer-readable recording medium on which such a computer program is recorded. Brief description of the drawings

[0018] The invention will be better understood and other characteristics, details and advantages will appear more clearly on reading the following description, given without limitation, and thanks to the appended figures, given by way of example.

[0019] [Fig.l] [Fig.l] represents an equipment configuration in which a time transfer method of radio equipment according to the invention can be implemented.

[0020] [Fig.2] [Fig.2] schematically represents the steps of a time transfer method according to one embodiment of the invention.

[0021] [Fig.3] [Fig.3] represents an operational configuration in which a time transfer method according to the invention is implemented. Description of the embodiments

[0022] [Fig.l] represents an equipment configuration in which a time transfer method according to the invention can be implemented. It comprises equipment 101 seeking to synchronize temporally with at least three terrestrial time transfer beacons 102 to 104 with which it is in radio contact. The terrestrial time transfer beacons may be mobile or temporarily fixed but with approximate positions, so that their positions are only imperfectly known.

[0023] The beacons are synchronized very precisely, for example by incorporating high-precision clocks such as atomic clocks or by being connected to a wired network or a dedicated radio network implementing a precise synchronization mechanism.

[0024] Subsequently, the network will be considered to be planar, and the unknowns will only relate to orthogonal positions x and y in a horizontal plane. Only three time transfer beacons are therefore necessary to enable radio equipment to retrieve precise time information. However, the invention also applies outside a plane, by adding the dimension z orthogonal to x and y, in which case a minimum of four stations is required. Adding additional time transfer stations improves the quality of the time determination by smoothing out the measurement noise.

[0025] The time transfer method according to the invention consists in explicitly taking into account the positions of the time transfer beacons in an estimator implemented by the receiver, in order to jointly estimate the precise positions of the beacons, the position of the receiver and its time bias relative to the beacon network.

[0026] It assumes the existence of a radio waveform adapted to the need for time transfer by broadcasting, that is to say the transmission by the beacons of a time message and a periodic clock pulse, which the radio receiver to be synchronized knows how to receive and measure precisely. The time message contains the time of transmission of the clock pulse, defined according to the reference time of the beacon network. The position of each beacon (potentially imprecise) can be transmitted in the time message, stored in the receiver, or transmitted to the receiver by a data link.

[0027] The method according to the invention requires the measurement of the arrival times (TOA) of the time markers by the receiver. The accuracy of this measurement depends on the bandwidth of the waveform used to transmit the time information. It is a function of the product BT, with B the bandwidth and T the duration of a symbol, and the SNR (Signal to Noise Ratio). The maximum theoretical value of its variance, given by the Cramer-Rao bound, is:

[0028] , = —1— =... '............... TOA 27^B^2BTSNR,

[0029] with No the noise spectral density, and ^toa the variance of the arrival time measurement.

[0030] The parameters of the waveform used for the radio transmission of the time message and the clock pulse must therefore be sized so as to provide the desired precision. For example, for a bandwidth B of 1 MHz with a symbol duration T of 1 ms and an SNR of 10 dB, the variance of the time measurement ^toa will be 1.2 ns. As a general rule, variances gtoa of less than 30 ns, or even less than 10 ns, are targeted. Advantageously, the chosen waveform may be a spread spectrum waveform, for which the bandwidth is generally large and makes it possible to obtain accuracies of the order of a nanosecond for very low SNRs. For example, for B equal to 20 MHz, T equal to 1 ms and an SNR of -30 dB, ^toa is equal to 1.3 ns.

[0031] [Fig. 2] schematically represents the steps of a time transfer method according to an embodiment of the invention. It comprises the following steps: - a step 201 of pseudo-distance measurements with at least three terrestrial time transfer beacons, - a step 202 of calculating an initial position of the receiver, from the pseudo-distances. This step can advantageously implement an effective initial resolution based on a clause form, that is to say a form directly giving the desired solution in the absence of noise, - a step 203 of joint estimation of a clock bias of the receiver, by implementing a resolution algorithm optimizing a maximum likelihood criterion jointly resolving the position of the terrestrial time transfer beacons, the position of the receiver and the time offset of the receiver relative to the time transfer beacons.

[0032] Step 201 is a usual step for those skilled in the art, which consists of detecting the synchronization peaks in the signals transmitted by the beacons to determine an arrival time of the signal, and comparing them with their transmission times, transmitted in the time message contained in the signal, in order to calculate a time difference, and consequently a pseudo-distance between the receiver and the time transfer beacons with which it is in radio link.

[0033] The pseudo-distance Pd; measured between the time transfer beacon i and the receiver is Pdi = c(TOAi - Te; + At + e;) = d; + c. At + ce;, with: - TOAi the arrival time of the synchronization top in the signal coming from beacon i, measured by the receiver from its local clock, - Te; the time of transmission by the beacon of the synchronization top, time measured according to the time reference of the beacon system and transmitted in the time message, - At the receiver clock bias, i.e. the difference between the beacon system time and the receiver's local clock time, - e; a white Gaussian noise affecting the measurement, - c the speed of light (speed of propagation of the radio signal), and - di the distance between the beacon i and the receiver, - Pd the vector formed from the set of values ​​of the Pd;.

[0034] Step 202 consists, from N pseudo-distances Pd; obtained in the first step 201, in calculating an initial position of the receiver and an initial estimate of the clock bias of this equipment, N being greater than or equal to 3. For example, this position and this clock bias can be obtained by trilateration, by applying techniques well known to those skilled in the art.

[0035] At the end of step 202, an initial position p of the receiver and the clock bias are available. These values ​​are not very precise since the measurements are affected by positioning errors of the time transfer beacons (potentially significant) and white Gaussian noise e;.

[0036] Step 203 consists of estimating the clock bias At by an algorithm optimizing a maximum likelihood criterion jointly resolving the positions of the terrestrial time transfer beacons, the clock bias At and the position P of the receiver.

[0037] This step can be implemented for example by a Gauss-Newton algorithm, well known to those skilled in the art, or by an equivalent least squares resolution algorithm, for example a Levenberg-Marquardt algorithm.

[0038] The remainder of the description will be given using a Gauss-Newton algorithm, for illustrative purposes only. The following notations will be adopted: - Z; denotes the exact position of the time transfer beacon i, with ie [1, N], - denotes the known position of the time transfer beacon i, with — Zj + r}. with its positioning error, and M is the vector formed from the set of values ​​of the - denotes the estimated position of the time transfer beacon i, initialized to Z = Mp ct Z is the vector formed from the set of values ​​of the - denotes the estimation of the receiver clock bias.

[0039] All position notations can be decomposed along a first x-axis and a second y-axis orthogonal to x in a horizontal plane, for example Zxi and Zyi.

[0040] According to one embodiment, step 203 comprises the construction of a state vector A comprising the estimated position p of the receiver, initialized in step 202, the estimated clock bias and the estimated positions of the time transfer beacons, with for example:

[0041]

[0042] Step 203 also includes constructing an observation vector M from the known or transmitted positions of the beacons and pseudo- [Pdï distances calculated during the first step 201, and its linearized counterpart Y, which includes the discrepancy between the known positions of the time transfer beacons and their estimated positions, and the difference between the pseudo-distances calculated during the first step 201 and pseudo-distances constructed from the estimated positions of the receiver and terrestrial time transfer beacons, and the time difference between the receiver and the beacons:

[0043] MZ .Pd-dc.at t. m xN -z xN MyN ~ Zy N Pd^-d^cA t yPd n - dy - c. At1

[0044] with the distance between the estimated position p of the receiver and the estimated position of the terrestrial time transfer beacon of index i, and the vector constructed from the . During the first iteration, the estimated positions z of the terrestrial time transfer beacons are equal to their known or transmitted positions M, and the estimated time offset is zero.

[0045] Step 203 also includes the construction of the Jacobian matrix H from the vectors X and 3, with:

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] with atPd . dx . By construction, ^4« _ < and _ i. Therefore: az„ “ 1 dzyi ~ 1 ^ = [00 ... 0 10 -].^ = [o 0 - 0 0 1 -]By construction still: dpdj _ 1x~ ~ Xy-Py di ​​di 1 0 0 ZyrPy di ​​Z^ d< 0 0 ? so that: i 0 0 0 1 0 0 0 0 0 ■ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 H = 0 0 0 0 0 0 0 0 0 1 AAX « AAAZ ZyJ-Py ZrrPx ZyrPy Z. . AA 1 1 0 0 0 0 “T” di di T” • • • ■ • • • • Zy^Py ZxN-Px ” A 1 0 0 0 0 - ' v-7'. Z,N-PX i dN dN The solution of this system is calculated by a maximum likelihood estimator implemented for example with a Gauss-Newton algorithm initialized with the values ​​calculated during the second step 202 of the method according to the invention, by the formula: X = with Fs the observation covariance matrix, which allows us to characterize the precision of the estimator. The estimate of the state vector X, which contains in particular an estimate of the clock bias zlr of the receiver, can therefore be obtained very simply from the matrix H and the vector Y. Advantageously, this calculation is carried out iteratively, by updating at each iteration the observation vector Y and the matrix u —^y. with the dx values ​​of the state vector % calculated at the previous iteration, in order to linearize and improve the estimation of X at each iteration. The iterations can be stopped for example by evaluating a stopping criterion on the norm || -Xj || , with Xt the state vector X obtained at iteration l, and X / +1 the state vector X obtained at iteration / + 1. Advantageously, successive measurements of the vector X can address a filter recursive smoothing in particular to take into account the mobility of the receiver and / or time transfer beacons.

[0054] The calculation described above performs the joint optimization of the position of the receiver, its clock bias, and the positions of the terrestrial time transfer beacons. This joint optimization makes it possible to improve the quality of the measurement of the clock bias when the position of the time transfer beacons is imprecise.

[0055] The observation covariance matrix Fg is:

[0056] rr^ oi ig= L o rj

[0057] where: - is the error covariance matrix on the knowledge of the positions of the beacons. The position measurements of the beacons are generally assumed to be independent of each other. This matrix is ​​therefore made up of a diagonal of square matrices L;,.; of the position variances of each beacon i. The measurement noise is assumed to be known, Gaussian and centered, so thatp^ = with E() the mathematical expectation and the Gaussian noise vector on the position measurement Mi of beacon i - re is the observation matrix of the pseudo-distances Pdi. The measurement noise 8i is assumed to be known, Gaussian and centered, and P^ = E(e|), with F^ the value of F^ in row i and column i. The covariance matrix of the estimator is then:

[0058] The equations given above are formed from matrices arranged in a given organization for illustration purposes only. The same results can be achieved by arranging the matrices differently, for example by permuting their rows, without this affecting the accuracy of the calculations and the results obtained.

[0059] According to an advantageous embodiment, the second step 202 of the method, which aims to determine an initial position and an initial time offset of the receiver, is implemented by a pseudo-linear estimation based on a clause form.

[0060] This solution consists of traversing the _ N(N-\) {N-2) triplets (i, j, k) of tags of 6 time transfer, with i < j < k. For each triplet of index q ranging from 1 to Q, we then calculate a pseudo-measure fq such that: + rikM^^-ry^^

[0061] with O the center of the reference frame, and 7 the difference between the pseudo-distance Pd; and the pseudo-distance Pdj, or:

[0062] rij=PdrPdj.

[0063] The vector Gq is also calculated from the pseudo-distance measurements and the known position of the beacons, i.e.:

[0064] Finally, we construct the observation vector R from the pseudo distance measurements, i.e.:

[0065] Pd} ' R = : ■ PdN.

[0066] A pseudo-linear estimate of the initial position of the receiver and its clock bias At is obtained by minimizing the residues of the linear system f(R) - G(R)X, where / is a vector consisting of the set of pseudo measurements fq, and G a matrix constructed by concatenation of the vectors Gq.

[0067] For this, it is possible to pose:

[0068] , Tt^^Pdr 11?-^ Il )

[0069] The values ​​p of the receiver position and its clock bias are then used to initialize the state vector X during the third step 203 of the time transfer method according to the invention.

[0070] This embodiment is particularly interesting, since it makes it possible to obtain a very precise first approximation of the position and the clock bias of the receiver, which guarantees the correct operation of the algorithm optimizing a maximum likelihood criterion implemented during the third step 203 of the method according to the invention. Indeed, given the strong non-linearity of the estimation problem, the Gauss-Newton algorithm has a high probability of divergence in the absence of a precise initialization.

[0071] [Fig. 3] represents an operational configuration in which a time transfer method according to the invention can be implemented, in order to present the results that it allows to be achieved. The receiver 301 is in radio link with four terrestrial time transfer beacons 302 to 305, equally distributed on a circle centered around the equipment 301. This is a favorable case.

[0072] The position of the beacons is known with a CEP of 50% (English acronym for Circle Error Probable, or probable circular error) of 10 meters. Equipment 301 is capable of measuring the arrival times of time messages with a variance of 2 ns.

[0073] The implementation of the time transfer method according to the invention makes it possible to synchronize the equipment 301 with an accuracy of ±40 ns, for a confidence interval of 99%.

[0074] The invention therefore relates to a method for transferring time from a terminal in radiofrequency reception with at least three synchronized terrestrial time transfer beacons each broadcasting a time message comprising a time marker and a transmission time, but also on the terminal itself.

[0075] Such a terminal must have a radio channel enabling it to receive and interpret the time message broadcast by the beacons to determine an arrival time of time markers, and calculation means enabling it to implement the method, such as for example a microprocessor, a DSP (English acronym for Digital Signal Processor), an FPGA (English acronym for Field Programmable Gate Array), an ASIC (English acronym for Application-Specific Integrated Circuit), any combination of these means, or any hardware component enabling the aforementioned functions to be executed.

[0076] Finally, it relates to a computer program comprising program code instructions for executing the steps of the time transfer method according to the invention when said program is executed on a computer, as well as to a recording medium readable by a computer on which such a computer program is recorded.

Claims

Claims

1. Method for transferring time to a receiver (101) in radiofrequency connection with at least three synchronized terrestrial time transfer beacons (102, 103, 104) each broadcasting a time message comprising a time marker and a transmission time, the time transfer method comprising: - a first step (201) of calculating an arrival time of the time messages transmitted by said terrestrial time transfer beacons, the positions of said terrestrial time transfer beacons being known by the receiver or transmitted to the receiver, and of determining a pseudo-distance measurement Pd; associated with each time transfer beacon, - a second step (202) of determining an initial position of said receiver and an initial time offset between said receiver and the at least three terrestrial time transfer beacons from the pseudo-distance measurements calculated during the first step (201), the time transfer method being characterized in that it further comprises: - a third step (203) of calculating a fine time offset of said receiver, by implementing a resolution algorithm optimizing a maximum likelihood criterion using the values ​​calculated in the second step (202) and jointly resolving the positions of the terrestrial time transfer beacons, the position of the receiver and the time offset of the receiver.

2. A time transfer method according to claim 1, wherein said third step (203) comprises: - constructing a state vector X comprising the estimated position of the receiver, the estimated time offset of the receiver, and the estimated positions of said at least three terrestrial time transfer beacons, - constructing an observation vector V comprising the known or transmitted positions of said at least three terrestrial time transfer beacons and the pseudo-distances calculated during the first step (201), constructing a linearized observation vector Y comprising a difference between the known or transmitted positions of said at least three terrestrial time transfer beacons and their estimated positions, and a difference between the pseudo-distances calculated during the first step (201) and pseudo-distances constructed from the values ​​of the state vector X, -the construction of a Jacobian matrix H from the state vector X and the observation vector such that rj _ . and n ~ dx -the resolution of the system, by calculating x = H*Y-

3. A time transfer method according to claim 2, wherein the calculation of x = H*Y is iterated several times, the values ​​of the vector K and the matrix H being recalculated at each iteration based on the vector x determined at the previous iteration.

4. Time transfer method according to one of the preceding claims, in which the algorithm using a maximum likelihood criterion implemented during the third step (203) is a Gauss-Newton algorithm or a Levenberg-Marquardt algorithm.

5. Time transfer method according to one of the preceding claims, in which the second step (202) is implemented by a method of pseudo-linear estimation of the initial position and the initial time offset of said receiver.

6. Time transfer method according to claim 5, wherein the pseudo-linear estimation method comprises: - calculating an initial position p of the receiver, with P ~ (G (RG (R) )^G(R)r °ù is a matrix constructed from the pseudo-distance measurements Pd; calculated during the first step 201 of the method and the known or transmitted positions of the terrestrial time transfer beacons, R is an observation vector comprising the pseudo-distance measurements Pd; made during the first step (201) of the method, and / is a pseudo-measurement constructed from the pseudo-distance measurements Pd; made during the first step 201 of the method and the known or transmitted positions of the beacons, - calculating an initial time offset such that ^Xt = ^=i(Pdr || ZrP || ), with N the number of terrestrial time transfer beacons and 7. a vector comprising the known or transmitted positions of terrestrial time transfer beacons.

7. Time transfer method according to one of the preceding claims, in which the position of the terrestrial time transfer beacons is known imperfectly.

8. Radiocommunications equipment (101) in radiofrequency connection with at least three terrestrial time transfer beacons (102, 103, 104) synchronized each broadcasting a time message comprising a time marker and a transmission time, the radiocommunications equipment comprising a radio chain configured to receive and interpret the time message transmitted by the beacons, the radiocommunications equipment being characterized in that it further comprises calculation means configured to implement a time transfer method according to one of the preceding claims.

9. A computer program comprising program code instructions for executing the steps of the time transfer method according to one of claims 1 to 7 when said program is executed on a computer.

10. A computer-readable recording medium having a computer program recorded thereon according to claim 9.

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