Satellite and quasi-star cooperative train positioning method

Abstract

The application discloses a satellite and star-like cooperative train positioning method, and relates to the technical field of satellite positioning. A differential base station is arranged outside a tunnel, a plurality of star-like base stations for emitting star-like signals are arranged in the tunnel, and a vehicle-mounted terminal for receiving satellite signals and star-like signals is arranged on a train. The method comprises the following steps: distinguishing signals, establishing a pseudo-range equation, screening a pseudo-range equation solution ideal pseudo-range initial value, and then solving train positioning by using a least square method and Kalman filtering according to the pseudo-range initial value, so as to realize the purpose of cooperative and accurate train positioning.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of train positioning technology, in particular to a satellite and star-like cooperative train positioning method. BACKGROUND

[0002] Train positioning is the most important part of automatic control of rail trains. A patent with publication number CN110208835A discloses a cross-system tight combination differential positioning method based on ionosphere cancellation combination. The differential base station uses a base station end receiver and a user end receiver to receive satellite signals. A pseudo-range double difference method is used to estimate the deviation between multiple satellite navigation systems. The differential base station broadcasts differential correction information to the user, which includes double-frequency ionosphere cancellation pseudo-range differential correction, satellite navigation system deviation, and the position of the differential base station. The user uses the received satellite signals and differential correction information to achieve differential positioning in a cross-system tight combination mode and obtains the positioning result.

[0003] However, there are open areas and tunnel areas in the actual operation of rail trains. However, it is difficult to obtain accurate satellite signals to achieve positioning in the tunnel area, resulting in inaccurate positioning of the train when entering and exiting the tunnel and running in the tunnel. SUMMARY

[0004] To solve the above technical problems, the present application provides a satellite and star-like cooperative train positioning method.

[0005] To solve the above technical problems, the present application adopts the following technical scheme: the present application provides a satellite and star-like cooperative train positioning method, characterized in that it comprises:

[0006] Step 1: device arrangement: a differential base station is pre-set outside the tunnel, a plurality of star-like base stations for transmitting star-like signals are pre-set inside the tunnel, and a vehicle-mounted terminal for receiving satellite signals and star-like signals is pre-set on the train;

[0007] Step 2: the vehicle-mounted terminal and the differential base station receive the same received satellite signals, and the vehicle-mounted terminal also needs to receive the differential signals output by the differential base station and the star-like signals;

[0008] Step 3: the vehicle-mounted terminal distinguishes between satellite signals and star-like signals,

[0009] If it is a satellite signal, the satellite position information is obtained in combination with the differential signal;

[0010] If it is a star-like signal, the star-like base station position information is obtained;

[0011] The pseudo-range measurement value p is obtained in combination with the position information c .

[0012] Step 4: Select four equations from the positioning equation set in step 3 to construct multiple pseudo-range equation sets, and combine the least square method to obtain the pseudo-range initial value;

[0013] Step 5: Select the pseudo-range initial value corresponding to the position information group with the highest positioning accuracy as the ideal pseudo-range;

[0014] Step 6: Combine the ideal pseudo-range, pseudo-range measurement value ρ c , EKF gain, and Kalman filter to obtain the optimal estimation value of the pseudo-position;

[0015] Step 7: Perform divergence judgment on the optimal estimation value of the position,

[0016] If divergence occurs, correct and output the new pseudo-range prediction value by combining the least square method;

[0017] If non-divergence occurs, output the optimal estimation value of the position again.

[0018] Preferably, step 3 comprises:

[0019] 3.1 Pseudo-range positioning

[0020] Eliminate ionospheric delay error, tropospheric delay error, and clock error to obtain the pseudo-range measurement value of the corresponding satellite;

[0021] Eliminate the clock error to obtain the pseudo-range measurement value of the corresponding satellite-like base station;

[0022] Combine the coordinates of the satellite or satellite-like base station to construct a positioning equation set:

[0023]

[0024] ρ is the pseudo-range measurement value, (x u ,y u ,z u ,t u ) is the coordinate of the train at time t u , (x, y, z) is the coordinate of the satellite or satellite-like base station, δt u is the initial clock error, n is the number of received satellite signals and satellite-like signals, and c is the speed of light.

[0025] Preferably, step 4 specifically comprises:

[0026] 4.1: Select four equations from the positioning equation set in step 3.1 to construct multiple pseudo-range equation sets;

[0027] 4.2: Solve the pseudo-range equation set by the least square method as follows:

[0028] Set the initial solution: the position (x k-1 ,y k-1z k-1 ) and clock error initial value δt u,k-1 as the initial value of the first iteration;

[0029] Using the first-order Taylor series expansion, the nonlinear equation set is linearized to obtain the linearized matrix equation about the change amount. The first-order Taylor series expansion formula for the initial value of the observation equation is:

[0030]

[0031]

[0032] Substitute the pseudo-range equation set:

[0033]

[0034] Solve the pseudo-range equation set:

[0035] GX = b,

[0036]

[0037] G is the system observation matrix, b is the observation vector, and r is the distance between the satellite or star-like base station and the vehicle-mounted receiving terminal;

[0038] 4.3: Obtain multiple pseudo-range initial values by fitting the pseudo-range initial value in step 4.2,

[0039] J(X) is the quadratic form of X

[0040] J(X) = (b-GX) Τ (b-GX)

[0041] J(X) = b Τ b-b Τ GX-X Τ G Τ b+X Τ G Τ X

[0042] = b Τ b-2b Τ GX+X Τ G Τ GX

[0043]

[0044] When J(X) takes the extreme value, let

[0045] -2G Τ b+2G Τ GX = 0 ​

[0046] X = (G Τ G) -1 G Τ b

[0047]

[0048]

[0049] Preferably, step 6 comprises:

[0050] 6.1 : Obtain the nonlinear system model for cooperative navigation:

[0051] The state transition equation of the system x k = Ax k-1 ;

[0052] where the state transition matrix is A, and set The measurement equation can be expressed by the pseudo-range equation:

[0053]

[0054] 6.2: Prediction process:

[0055]

[0056]

[0057] P k-1 is the initial value of the state error covariance;

[0058] VarΔx = E(ΔxΔx Τ )

[0059] = (G Τ G) -1 G Τ E{bb Τ}G(G Τ G) -1

[0060] = (G Τ G) -1 G Τ P k-1 G(G Τ G) -1

[0061]

[0062] Obtain the process noise vector ω k :

[0063] cov(ω k ) = E(ω k ωk T ) = Q

[0064] Q is an n×n symmetric matrix, and is a fixed value. The process noise covariance matrix is ​​set as follows:

[0065] 6.3: Calibration

[0066] Calculate the least squares observation matrix C

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] Set V=1, and measure the noise covariance R=200.0

[0073] K k It's P k The Kalman filter gain at its smallest value

[0074]

[0075] Nonlinear systems Treat as measurement vector y k The predicted value and the measured residual vector are:

[0076]

[0077] Optimal estimate of system state

[0078]

[0079] Mean square error matrix of posterior estimation error

[0080]

[0081] Preferably, the specific method for determining divergence in step 7 is as follows:

[0082] judge If the value is greater than the threshold, continue iterating until it is less than the threshold, then terminate the iteration and output the corresponding optimal position estimate and clock difference.

[0083] Preferably, the iterative method in step 7 is as follows:

[0084] Will middle As an initial value, the following is brought in in

[0085] The pseudo-range prediction value is obtained

[0086] The present application has the following advantages:

[0087] 1. The satellite and star-like base station cooperatively send information to the train, so as to realize positioning of the train in various regions (such as relatively closed space, tunnel, etc.).

[0088] 2. The optimal estimation value is diverged to determine, so as to realize the purpose of improving the positioning accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0089] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0090] Fig. 1 A satellite and star-like cooperative train positioning method provided by the embodiment of the present application is shown in the schematic diagram.

[0091] Fig. 2 The positioning method is shown in the schematic diagram.

[0092] Fig. 3 The positioning method is shown in the schematic diagram. DETAILED DESCRIPTION

[0093] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments only constitute some embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0094] As shown in the drawings, the present application provides a satellite and star-like cooperative train positioning method, including the following steps: Figs. 1-3 Step 1: Arranging equipment, including Beidou satellite, differential base station located in open area, star-like base station located in tunnel and vehicle terminal located on train, wherein the vehicle terminal includes satellite receiver and star-like receiver.

[0095]

[0096] ​Step 2: During the train operation, there are three environmental conditions: 1. In the open area, the Beidou satellite signals and the differential correction values output by the differential base station can be effectively received by the satellite receiver to calculate the train position information; 2. Between the open area and the tunnel, the satellite receiver and the quasi-star receiver need to work together to calculate the train position information; 3. In the tunnel, the quasi-star receiver needs to receive the quasi-star signals to calculate the train position information.

[0097] In order to facilitate a complete understanding of the positioning method of the present application, the following describes the state of the train between the open area and the tunnel.

[0098] Step 3: The signals received by the vehicle terminal are divided into satellite signals and quasi-star signals, and the satellite position information and the position information of the quasi-star base station are obtained in combination with the differential correction values, and the pseudo-range measurement value is calculated in combination with the position information;

[0099] Wherein, when the satellite signal is used to calculate the pseudo-range measurement value, the ionospheric delay, the tropospheric delay and the clock difference need to be overcome, and the quasi-star signal does not have the influence of the ionosphere and the troposphere, and the calculation is as follows:

[0100] Satellite pseudo-range measurement value ρ

[0101] ρ = c (t u -t (s) ) - c (δt u -δt (s) ) - cI - cT - ε p

[0102] ρ - cδt (s) + cI + cT + ε p = c (t u -t (s) ) - cδt u

[0103] Wherein, the ionospheric delay is I, and the tropospheric delay is T.

[0104] Since the satellite initial clock difference, the ionospheric delay and the tropospheric delay can be regarded as known, they can be moved to the same side and simplified as

[0105] ρ - ε p = c (t u -t (s) ) - cδt u

[0106] Quasi-star pseudo-range measurement value ρ

[0107] ρ = c (t u -t (s) ) - c (δt u -δt (s) )

[0108] And then the positioning equation group is constructed as follows:

[0109]

[0110] (x u ,y u ,z u ,t u ) is the coordinate of the train at t u time, (x, y, z) is the coordinate of the satellite or satellite-like base station, δt u is the initial clock error, n is the number of received satellite signals and satellite-like signals, and c is the speed of light.

[0111] Step 4: Select four equations from the positioning equation group in step 3 to construct multiple pseudo-range equation groups, and solve the position coordinates by least squares as follows:

[0112] Set the initial solution: the position of the vehicle terminal (x k-1 , y k-1 , z k-1 ) and the initial value of the clock error δt u,k-1 as the initial value of the first iteration;

[0113] Use the first-order Taylor series expansion to linearize the nonlinear equation group, and obtain the linearized matrix equation about the change amount. The first-order Taylor series expansion formula for the initial value of the observation equation is:

[0114]

[0115]

[0116] Substitute the pseudo-range equation group:

[0117]

[0118] Solve the solution of the pseudo-range equation group:

[0119] GX=b,

[0120]

[0121] G is the system observation matrix, b is the observation vector, and r is the distance between the satellite or satellite-like base station and the vehicle-mounted receiving terminal.

[0122] Fit the above N pseudo-range initial values X, as follows:

[0123] J(X) is the quadratic form of X

[0124] J(X)=(b-GX) Τ (b-GX)

[0125] J(X) = b Τ b - b Τ GX - X Τ G Τ b + X Τ G Τ X

[0126] = b Τ b - 2b Τ GX + X Τ G Τ GX

[0127]

[0128] At the extreme value of J(X), let get

[0129] -2G Τ b + 2G Τ GX = 0

[0130] X = (G Τ G) -1 G Τ b

[0131]

[0132]

[0133] Step 5: Screen the pseudo-range initial value corresponding to the position information group with the highest positioning accuracy as the ideal pseudo-range, and the specific solution is as follows:

[0134] The pseudo-range initial value X in step 4 is brought into GX = b to get:

[0135] The measurement error term ε p is the pseudo-range observation error caused by introducing other error factors when calculating the positioning error. The measurement error ε p causes the positioning error to be ε x , ε y , ε z , and ε δtu .

[0136] The difference with GX = b is obtained:

[0137]

[0138] The vector value of the error value solution is:

[0139]

[0140] Calculate the covariance matrix:

[0141]

[0142] The covariance matrix of the positioning error is

[0143]

[0144] wherein the weight coefficient matrix is H = (G T G) -1 ;

[0145] The weight coefficient matrix H is calculated:

[0146]

[0147] The accuracy factor is calculated:

[0148] The horizontal accuracy factor is:

[0149] The height accuracy factor is:

[0150] The spatial position accuracy factor is:

[0151] The clock error accuracy factor is:

[0152] The geometric accuracy factor is:

[0153] Compare all the pseudorange initial values X corresponding to each type of accuracy factor, and select the pseudorange initial value corresponding to the minimum accuracy factor as the ideal pseudorange initial value.

[0154] Step 6: Combine the ideal pseudorange, the pseudorange measurement value ρ c , the EKF gain, and the Kalman filter to obtain the optimal estimation value of the pseudoposition, and the specific solution is as follows:

[0155] The nonlinear system model of cooperative navigation is obtained:

[0156] The state transition equation of the system is x k = Ax k-1 ;

[0157] wherein the state transition matrix is A, and A = (B

[0158] The measurement equation can be expressed by the pseudorange equation:

[0159]

[0160] The prediction process is:

[0161]

[0162]

[0163] P k-1 is the initial value of the state error covariance;

[0164] VarΔx = E(ΔxΔx Τ )

[0165] = (G Τ G) -1 G Τ E{bb Τ}G(G Τ G) -1

[0166] = (G Τ G) -1 G Τ P k-1 G(G Τ G) -1

[0167]

[0168] Obtain ω k is the process noise vector:

[0169] cov(ω k ) = E(ω k ω k T ) = Q

[0170] Q is an n x n symmetric matrix, is a fixed value, set the process noise covariance matrix as:

[0171] Correct

[0172] Calculate the least squares calculation observation matrix C

[0173]

[0174]

[0175]

[0176]

[0177]

[0178] Set V = 1, the measurement noise covariance R = 200.0

[0179] K k is the Kalman filter gain when the value of P k is the smallest

[0180]

[0181] Nonlinear system The prediction value of the measurement vector y k is the measurement residual vector:

[0182]

[0183] Optimal estimation value of system state

[0184]

[0185] Mean square error matrix of posteriori estimation error

[0186]

[0187] Step 7: divergence judgment is performed on the optimal estimation value of position,

[0188] If divergence occurs, iteration is performed, and a new pseudo-range prediction value is corrected and output by combining the least square method;

[0189] If non-divergence occurs, the optimal estimation value of position is output again;

[0190] Wherein, the divergence judgment is solved as follows:

[0191] Judgment whether it is greater than a threshold value, if it is greater than the threshold value, iteration is continued until it is less than the threshold value, and the corresponding optimal estimation value of position and clock difference are output;

[0192] Wherein, the iteration solving method is as follows:

[0193] The is taken as an initial value, and is brought into

[0194] to obtain a pseudo-range prediction value

[0195] The pseudo-range prediction value is brought into step 6 to re-solve the optimal estimation value

[0196] The above only describes the preferred embodiments of the present application and is not used to limit the present application, although the foregoing embodiments of the present application are described in detail, those skilled in the art can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to some technical features. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.​​

Claims

1. A method for cooperative train positioning of satellites and quasi-satellites, characterized in that, Comprise: Step 1: Device arrangement: preset differential base station outside the tunnel, preset several star-like base stations for transmitting star-like signals inside the tunnel, and preset vehicle-mounted terminal on the train for receiving satellite signals and star-like signals; Step 2: The vehicle-mounted terminal receives the same received satellite signals as the differential base station, and the vehicle-mounted terminal also needs to receive the differential signals output by the differential base station and the star-like signals; Step 3: The vehicle-mounted terminal distinguishes satellite signals and star-like signals, If it is a satellite signal, combine the differential signal to obtain satellite position information; If it is a star-like signal, obtain the position information of the star-like base station; Acquiring pseudorange measurement values in conjunction with position information ; Step 4: In the positioning equation set in step 3, four equations are selected to construct multiple pseudo-range equation sets, and the least square method is used to obtain the pseudo-range initial value; Step 5: Select the pseudo-range initial value corresponding to the position information set with the highest positioning accuracy as the ideal pseudo-range; Step 6: Incorporate the ideal pseudo-range, pseudo-range measurement , EKF gain and Kalman filter to obtain the optimal estimate of pseudo-position Step 7: Perform divergence judgment on the optimal position estimate value, If it diverges, combine the least square method to correct and output a new pseudo-range prediction value; If it is not divergent, output the optimal position estimate value again.

2. The method of claim 1, wherein the satellite and star-like cooperative train positioning method is characterized by, Wherein step 3 comprises: 3.1 Pseudo-range positioning Eliminate ionospheric delay error, tropospheric delay error and clock error to obtain pseudo-range measurement value of corresponding satellite; Eliminate clock error to obtain pseudo-range measurement value of corresponding satellite-like base station; Combine the coordinates of the satellite or satellite-like base station to construct a positioning equation set: is a pseudo-range measurement value, is a coordinate of the train at time, is a coordinate of a satellite or satellite-like base station, is an initial clock difference, n is a number of received satellite signals and satellite-like signals, and c is a speed of light.

3. The method of claim 2, wherein the satellite and star-like cooperative train positioning method is characterized by, Wherein step 4 specifically comprises: 4.1: Construct multiple pseudo-range equation sets by selecting four equations in the positioning equation set in step 3.1; 4.2: Solve the pseudo-range equation set by the least square method as follows: Set initial solution: vehicle terminal position (x0, y0) and initial value of clock error as initial value of first iteration; Use first-order Taylor series expansion to linearize the nonlinear equation set to obtain a linearized matrix equation about the change amount, and the first-order Taylor series expansion formula for the initial value of the observation equation is: ， ； Substitute the pseudo-range equation set: ； Solve the solution of the pseudo-range equation set: ， , , ; G is a system observation matrix, b is an observation vector, and r is the distance between the satellite or star-like base station and the vehicle-mounted receiving terminal. 4.3: Fit the pseudo-range initial value in step 4.2 to obtain multiple pseudo-range initial values, quadratic form for X In Taking the extreme value, let , get 。 4. The method of claim 3, wherein the satellite and star-like cooperative train positioning method is characterized by, Step 6 comprises: 6.1: Obtain the nonlinear system model of cooperative navigation: State transition equation of the system ; where the state transition matrix is A, and let ; The measurement equation can be expressed by the pseudo-range equation: 6.2: Prediction process: is the state error covariance initial value; ； acquire for the process noise vector: Q is The symmetric matrix Q is a fixed value, and the process noise covariance matrix is set as: ； 6.3: Correction Calculate the least square calculation observation matrix C Set V=1, measurement noise covariance R=200.0 That is Kalman filter gain at the time of the minimum value Non-linear system The measurement residual vector is seen as a prediction of the measurement vector The measurement residual vector is seen as a prediction of the measurement vector Optimal estimate value of system state Mean square error matrix of posteriori estimation error 。 5. The method of claim 4, wherein the satellite and star-like cooperative train positioning method is characterized by, The divergence judgment method in step 7 is: determining whether the value is greater than a threshold value, and if so, continuing the iteration until the value is less than the threshold value, and outputting a corresponding position estimate and clock bias.

6. The method of claim 5, wherein the satellite and star-like cooperative train positioning method is characterized by, The iteration method in step 7 is: Will middle As initial values, substitute... middle obtaining a pseudorange prediction value .

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