A weighted direct positioning solution method for multi-mode satellite navigation system

Abstract

The invention discloses a weighted direct positioning solution method for a multi-mode satellite navigation system. The method of the invention first processes a nonlinear pseudo-range observation equation to obtain a linear expression between a position parameter and a time parameter; based on the linear expression, a weighted matrix is ​​introduced to measure different measurement accuracies between different satellites to obtain a quadratic equation with a time parameter as an unknown variable, and the validity and uniqueness of the positioning result (including position information and time information) are judged by solving the quadratic equation and combining the actual physical meaning of the parameters and corresponding constraints, thereby completing the direct positioning solution function. The method of the invention does not require iterative calculation, direct positioning solution, and does not require the initial position of the terminal device. The three-dimensional position and time information of the terminal can be directly given to complete the positioning solution.

Description

Technical Field

[0001] The present invention belongs to the field of satellite navigation technology, and in particular relates to a direct positioning solution problem for terminal equipment in a multi-mode satellite navigation system. Background Art

[0002] Since satellite signals are susceptible to environmental obstruction and interference, it is difficult to guarantee positioning accuracy and reliability when using a single system, and it may even lead to the inability to perform positioning calculations. In fact, given the good compatibility between the above systems, combining them to form a multi-mode satellite navigation system can complement each other's advantages and achieve better accuracy and reliability than a single system.

[0003] In multi-mode satellite navigation system terminal equipment, the least squares method is usually used for positioning solution to obtain its three-dimensional position and time information. The least squares method has the following main problems: ① It is necessary to perform multiple iterative (or recursive) calculations based on the initial coordinates of the terminal. When the initial coordinate deviation is large, the number of iterations will increase significantly, thereby increasing the amount of calculation; ② It requires multiple matrix inversion operations, which also significantly increases the amount of calculation; ③ In some cases, when the geometric observation matrix is ​​ill-conditioned, the matrix inversion process is prone to numerical stability problems, which in turn affects the positioning stability.

[0004] In fact, in a multi-mode satellite navigation system, terminal users can receive multiple satellite signals, resulting in a significant increase in the number of available satellites. This improves the terminal positioning accuracy, availability, and integrity to a certain extent; but as a result, the more satellites there are, the greater the amount of calculation, which in turn leads to higher hardware costs for terminal devices. Therefore, for multi-mode satellite navigation system terminal devices, research on fast positioning technology (i.e., no initial coordinates, no iterative calculations, etc.) is of great significance in reducing the cost of equipment hardware design, improving the efficiency of positioning solution, and ensuring the real-time performance of positioning solution. Summary of the invention

[0005] In order to solve the problems of high requirements on initial coordinates and large amount of computation required for multiple iterative operations in the positioning solution process of terminal equipment in a multi-mode satellite navigation system using the traditional least squares method, the present invention proposes a weighted direct positioning solution method for a multi-mode satellite navigation system.

[0006] The specific technical solution of the present invention is: a weighted direct positioning solution method for a multi-mode satellite navigation system, which specifically includes the following steps:

[0007] Step 1. Obtain the nonlinear pseudorange observation equation of the satellite navigation system as:

[0008]

[0009] in, represents the pseudorange observation value between the terminal and the i-th satellite of the BD system, represents the pseudo-range observation value between the terminal and the jth satellite of the GPS system, represents the pseudorange observation value between the terminal and the kth satellite of the GLONASS system; r i C represents the three-dimensional coordinates of the i-th satellite in the BD system, represents the three-dimensional coordinates of the jth satellite in the GPS system, represents the three-dimensional coordinates of the kth satellite of the GLONASS system, r is the three-dimensional position coordinates of the terminal, α C Indicates the clock difference between the terminal and the BD system, α G Indicates the clock difference between the terminal and the GPS system, α R Indicates the clock difference between the terminal and the GLONASS system. represents the pseudorange measurement noise of the i-th satellite, the j-th satellite, and the k-th satellite,

[0010] Step 2. Perform transposition and square processing on the nonlinear pseudorange observation equation to obtain:

[0011]

[0012] Select a BD satellite, a GPS satellite and a GLONASS satellite as reference satellites respectively, perform differential processing on the above formula, eliminate the quadratic term of the clock error parameter, linearize the terminal position coordinates and the clock error parameter, select the first satellite as the reference satellite in each of the three subsystems, and obtain the following after differential processing:

[0013]

[0014] in,

[0015]

[0016] The formula after difference processing is transformed into:

[0017]

[0018] Select the first three equations for calculation, namely

[0019]

[0020] Step 3. Write equation (8) obtained in step 2 into matrix-vector form:

[0021] Ar=α C b+α Gc+d+e (9)

[0022] in, Multiply both sides of the above equation by a weighted matrix W, that is,

[0023] WAr=α C Wb+α G Wc+Wd+We (10)

[0024] After introducing the weighted matrix, the least squares solution, the position coordinate (r) can be expressed as:

[0025] r=[(WA) T (WA)] -1 (WA) T [α C Wb+α G Wc+Wd] (11)

[0026] Among them, when the least squares solution is optimal in the sense of minimizing the variance,

[0027]

[0028] When the pseudo-range measurement noise is assumed to be Gaussian noise,

[0029]

[0030] Formula (11) is simplified to:

[0031] r=α C μ+α G ν+ω (14)

[0032] in,

[0033]

[0034] Substitute equation (14) into the nonlinear pseudorange observation equation ρ1 C =||r1 C -r||+α C With ρ1 G =||r1 G -r||+α G , and after simplification, we get:

[0035]

[0036] Among them, e 11 =(ω-r C 1) T μ+ρ C , e 12 =(ω-r1 C ) Tν,f1=(ω-r1 C ) T (ω-r1 C )-(ρ1 C ) 2 , e 21 =(ω-r1 G ) T μ,e 22 =(ω-r1 G ) T ν+ρ1 G ,f2=(ω-r1 G ) T (ω-r1 G )-(ρ1 G ) 2 .

[0037] After further arrangement, formula (16) is transformed into:

[0038] (α C ) 2 -(α G ) 2 -2(e 11 -e 21 )α C +2(e 22 -e 12 )α G +(f2-f1)=0 (17) Substituting equation (14) into the fourth equation of equation (7), we obtain:

[0039]

[0040] Combining equations (17) and (18), the clock error parameter α C With α G It is expressed as:

[0041]

[0042] After rearranging formula (19), we get a quadratic equation, namely:

[0043] G(α C ) 2 +Hα C +I=0 (20)

[0044] in,

[0045] The clock error parameter α is calculated by using the root formula of the quadratic equation. C :

[0046]

[0047] Substituting equation (20) into equation (17), we get another clock error parameter α G ,Right now:

[0048]

[0049] Substituting equations (21) and (22) into equation (14), we can obtain the terminal location information r, namely:

[0050]

[0051] Substitute the position information r into the fifth equation in equation (7) and get the clock error information α R ,Right now:

[0052]

[0053] That is, the terminal location information and time information are obtained.

[0054] Beneficial effects of the present invention: The method of the present invention first processes the nonlinear pseudorange observation equation to obtain a linear expression between the position parameter and the time parameter; based on the linear expression, a weighting matrix is ​​introduced to measure the different measurement accuracies between different satellites, and a quadratic equation with the time parameter as an unknown is obtained. The validity and uniqueness of the positioning result (including the position information and the time information) are judged by solving the quadratic equation and combining the actual physical meaning of the parameters and the corresponding constraints, thereby completing the direct positioning solution function. The method of the present invention does not require iterative calculations, but directly locates and solves, does not require the initial position of the terminal device, and can directly give the three-dimensional position and time information of the terminal, thereby completing the positioning solution. In addition, considering that the measurement accuracy between different satellites (especially different satellites from different systems) is different, the present invention introduces a weighting matrix to measure the influence of the measurement accuracy of different satellites on the positioning process, and provides a fast positioning method for a terminal of a multi-mode satellite navigation system in a weighted sense. DETAILED DESCRIPTION

[0055] The method of the present invention is further described below:

[0056] Taking BD / GPS / GLONASS as an example, in the positioning solution process, it is necessary to solve the three-dimensional position information and three time information, so at least 6 satellites are needed. In fact, in order to ensure the reliability of positioning, it is usually necessary to introduce an autonomous integrity monitoring algorithm to detect and identify faulty satellites. This algorithm is based on redundant observation information, and at least 7 satellites are required for fault detection, and at least 8 satellites are required to eliminate faulty satellites. Therefore, for BD / GPS / GLONASS positioning, from the perspective of integrity monitoring, in order to ensure positioning reliability, the present invention considers 8 satellites.

[0057] In the BD / GPS / GLONASS positioning solution process, when 8 satellites are observed, if a subsystem has 4 or more satellites (such as 4 or more GPS satellites are observed), the terminal location information can be obtained using only the above satellites, thereby achieving positioning solution. Therefore, when 8 satellites are observed, the present invention only considers the "3+3+2" situation, that is, the three subsystems observe 3, 3 and 2 satellites respectively. Without loss of generality, the present invention assumes that 3 BD satellites, 3 GPS satellites and 2 GLONASS satellites are observed.

[0058] For BD / GPS / GLONASS positioning, when three BD satellites are observed, the nonlinear pseudorange observation equation can be expressed as:

[0059]

[0060] in: represents the pseudo-range observation value between the terminal and the i-th satellite; r i C represents the three-dimensional coordinates of the i-th satellite, which can be calculated based on the satellite ephemeris; r is the three-dimensional position coordinate of the terminal, α C Indicates the time information (clock difference) between the terminal and the BD system. represents the pseudorange measurement noise of the ith satellite, and Solve the position coordinate r and clock error α C The process is called positioning solution.

[0061] Similar to formula (25), for GPS satellites and GLONASS satellites, the nonlinear pseudorange observation equations are expressed as:

[0062]

[0063] Where: α G With α R Respectively represent the clock difference information between the terminal and the GPS system and the GLONASS system, which are unknown parameters to be solved. and represent the pseudorange measurement noise of the jth and kth satellites respectively.

[0064] Combining equation (25) with equation (26), the BD / GPS / GLONASS nonlinear pseudorange observation equation is:

[0065]

[0066] In formula (27), it is necessary to calculate the position coordinate (r) and the three clock errors (α C ,α G ,α R), a total of 6 parameters.

[0067] For BD / GPS / GLONASS positioning, when 8 satellites are observed, the specific implementation process of the direct positioning method proposed in the present invention is as follows:

[0068] The nonlinear pseudorange observation equation is subjected to transposition and square processing to obtain:

[0069]

[0070] A BD satellite, a GPS satellite and a GLONASS satellite are selected as reference satellites respectively, and differential processing is performed on equation (28) to eliminate the quadratic term of the clock error parameter, and the terminal position coordinates and the clock error parameter are linearly represented. Without loss of generality, the present invention selects the first satellite as the reference satellite in the above three subsystems respectively, and obtains after differential processing:

[0071]

[0072] Taking BD satellite as an example, the relevant parameters are as follows:

[0073]

[0074] For GPS satellites and GLONASS satellites, the calculation methods of relevant parameters are similar.

[0075] Furthermore, formula (29) can be transformed into:

[0076]

[0077] In equation (30), it is first assumed that the clock error parameters are known, and then the terminal location information is calculated based on the clock error parameters. Since the three-dimensional position coordinates (r) need to be solved, at least three equations are required. Without loss of generality, the first three equations are selected for calculation, namely

[0078]

[0079] Formula (31) is written in matrix-vector form as:

[0080] Ar=α C b+α G c+d+e (32)

[0081] In vector In , its elements are related to the pseudorange measurement noise. Due to the different measurement accuracy between different satellites (especially different satellites from different systems), the variance of each component in the vector e is different. Based on this, this embodiment adopts the least square method, that is, multiplying both sides of equation (32) by a weighting matrix W, that is,

[0082] WAr=α C Wb+α G Wc+Wd+We (33)

[0083] After introducing the weighted matrix, the least squares solution, the position coordinate (r) can be expressed as:

[0084] r=[(WA) T (WA)] -1 (WA) T [α C Wb+α G Wc+Wd] (34)

[0085] Among them, when the least squares solution is optimal in the sense of minimizing the variance,

[0086]

[0087] When the pseudo-range measurement noise is assumed to be Gaussian noise,

[0088]

[0089] Furthermore, formula (34) can be simplified as:

[0090] r=α C μ+α G ν+ω (37)

[0091] in:

[0092]

[0093] Substitute equation (37) into the nonlinear pseudorange observation equation ρ1 C =||r1 C -r||+α C With ρ1 G =||r1 G -r||+α G , and after simplification, we get:

[0094]

[0095] Among them, the parameter e 11 、e 12 、e 21 、e 22 , as well as f1 and f2 can be obtained by calculation, which will not be repeated here. After further arrangement, formula (39) can be transformed into:

[0096] (α C ) 2 -(α G )2 -2(e 11 -e 21 )α C +2(e 22 -e 12 )α G +(f2-f1)=0 (40)

[0097] On the other hand, substituting equation (37) into the fourth equation of equation (30), we obtain:

[0098]

[0099] Combining equation (40) and equation (41), the clock error parameter α C With α G It can be expressed as:

[0100]

[0101] After rearranging formula (42), we get a quadratic equation, namely:

[0102] G(α C ) 2 +Hα C +I=0 (43)

[0103] in,

[0104] The clock error parameter α can be calculated by using the root formula of the quadratic equation: C :

[0105]

[0106] Substituting equation (43) into equation (40), we get another clock error parameter α G ,Right now:

[0107]

[0108] Furthermore, by substituting equation (44) and equation (45) into equation (37), the terminal location information r can be obtained, namely:

[0109]

[0110] Substituting the position information r into the last equation in (30), we can get the clock error information α R ,Right now:

[0111]

[0112] Combining equations (44), (45), (46) and (47), the terminal location information and time information are obtained as follows:

[0113]

[0114] Formula (48) shows that the direct positioning solution method proposed in this invention needs to first calculate the clock error parameter α C , and then calculate the other two clock error parameters and position information in turn. In fact, when solving α C There are two alternative solutions. In order to determine the unique solution, it is necessary to combine the actual physical meaning of the parameters and the corresponding constraints to perform uniqueness diagnosis, which specifically includes the following process:

[0115] (1) According to the nonlinear pseudorange equation,

[0116]

[0117] It can be seen that the three clock error parameters should satisfy the following conditions respectively: as well as

[0118] (2) Furthermore, according to the Cauchy inequality, the clock error parameter should satisfy the following conditions:

[0119]

[0120] Combined with the above constraints, the uniqueness and validity of the position parameters and time parameters can be diagnosed, thereby completing the positioning solution function.

Claims

1. A weighted direct positioning solution method for a multi-mode satellite navigation system, comprising the following steps: Step 1. Obtain the nonlinear pseudorange observation equation of the satellite navigation system as: in, represents the pseudorange observation value between the terminal and the i-th satellite of the BD system, represents the pseudo-range observation value between the terminal and the jth satellite of the GPS system, represents the pseudorange observation value between the terminal and the kth satellite of the GLONASS system; r i C represents the three-dimensional coordinates of the i-th satellite in the BD system, represents the three-dimensional coordinates of the jth satellite in the GPS system, represents the three-dimensional coordinates of the kth satellite of the GLONASS system, r is the three-dimensional position coordinates of the terminal, α C Indicates the clock difference between the terminal and the BD system, α G Indicates the clock difference between the terminal and the GPS system, α R Indicates the clock difference between the terminal and the GLONASS system. represents the pseudorange measurement noise of the i-th satellite, the j-th satellite, and the k-th satellite, Step 2. Perform transposition and square processing on the nonlinear pseudorange observation equation to obtain: Select a BD satellite, a GPS satellite and a GLONASS satellite as reference satellites respectively, perform differential processing on the above formula, eliminate the quadratic term of the clock error parameter, linearize the terminal position coordinates and the clock error parameter, select the first satellite as the reference satellite in each of the three subsystems, and obtain the following after differential processing: in, The formula after difference processing is transformed into: Select the first three equations for calculation, namely Step 3. Write equation (8) obtained in step 2 into matrix-vector form: Ar−α C b+α G c+d+e (9) in, Multiply both sides of the above equation by a weighted matrix W, that is, WAr=a C Wb+a G Wc+Wd+We (10) After introducing the weighted matrix, the least squares solution, the position coordinate (r) can be expressed as: r=[(WA) T (W.A.)] -1 (W) T [α C Wb+α G Wc+Wd] (11) Among them, when the least squares solution is optimal in the sense of minimizing the variance, When the pseudo-range measurement noise is assumed to be Gaussian noise, Formula (11) is simplified to: r=a C m+a G n+w (14) in, Substitute equation (14) into the nonlinear pseudorange observation equation and After simplification, we get: among them, e 11 =(ω-r C 1) T m+r C ,e 12 =(ω-r1 C ) T n, e 21 =(ω-r1 G ) T m, After further arrangement, formula (16) is transformed into: (a C ) 2 -(a G ) 2 -2(e 11 -e 21 )a C +2(e 22 -e 12 )a G +(f2-f1)=0 (17) Substituting equation (14) into the fourth equation of equation (7), we obtain: Combining equations (17) and (18), the clock error parameter α C With α G It is expressed as: After rearranging formula (19), we get a quadratic equation, namely: G(a C ) 2 +Ha C +I=0 (20) in, The clock error parameter α is calculated by using the root formula of the quadratic equation. C : Substituting equation (20) into equation (17), we get another clock error parameter α G ,Right now: Substituting equations (21) and (22) into equation (14), we can obtain the terminal location information r, namely: Substitute the position information r into the fifth equation in equation (7) and get the clock error information α R ,Right now: That is, the terminal location information and time information are obtained.

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