A Beidou high-precision positioning method with an adaptive weight matrix

Abstract

A Beidou high-precision positioning method with an adaptive weight matrix, which relates to the field of communication technologies, especially the field of satellite navigation and positioning. The present invention considers the problem of low positioning accuracy caused by the equal processing of all visible satellite observables in traditional positioning algorithms, combines the spatial correlation between the base station and the observation station with the pseudorange differential positioning technology, and then establishes an adaptive weight matrix on the basis of introducing the weighted least squares algorithm to construct a Beidou high-precision positioning method with an adaptive weight matrix. This method can be applied to many application fields that require precise positioning, such as military, ports, and autonomous driving, to meet the positioning requirements at the sub-meter level. The present invention is applicable to satellite navigation receiving systems and devices.

Description

Technical Field

[0001] The present invention relates to the field of communication technologies, especially the field of satellite navigation and positioning. Specifically, it is a high-precision Beidou positioning method with an adaptive weight matrix. Background Technique

[0002] The Beidou satellite navigation system is a global satellite navigation system independently developed by China. An important function of the Beidou navigation system is to provide location information for users. When calculating the user's position through the received satellite navigation message and pseudorange information, the positioning method directly affects the positioning accuracy of the system. As an absolute positioning method, the pseudorange measurement positioning technology can estimate the position of the user receiver and the clock deviation only by the ranging code broadcast by the navigation satellite. Although it is vulnerable to error factors such as satellite orbits, satellite clock errors, space propagation, and ground environments, resulting in deviations in satellite positioning and low positioning accuracy, the pseudorange positioning method does not need to consider the integer ambiguity problem and does not have the problem of cycle slips in carrier phase positioning. It has significant advantages such as fast calculation speed, low method complexity, and low receiver price. Therefore, the research on high-precision pseudorange measurement positioning technology has always been a key technology for Beidou navigation and positioning, and it has great significance for promoting the application and industrial development of Beidou navigation. Summary of the Invention

[0003] A high-precision Beidou positioning method with an adaptive weight matrix, considering the problem of low positioning accuracy caused by the equal processing of all visible satellite observations in traditional positioning calculation methods, combines the spatial correlation between the base station and the observation station in pseudorange differential positioning technology. Furthermore, on the basis of introducing the weighted least squares algorithm, an adaptive weight matrix is established to construct a high-precision Beidou positioning method with an adaptive weight matrix. This method can be applied to many application fields that require precise positioning, such as military, ports, and autonomous driving, to meet the positioning requirements at the sub-meter level.

[0004] The technical solution adopted is as follows:

[0005] First, parse the received ephemeris file and observation file to obtain the parameters required for positioning calculation. According to the Beidou navigation ICD (Interface Control Document for Beidou navigation system space signal) standard, calculate the positions of Beidou navigation satellites.

[0006] Then, based on the principle of pseudorange differential positioning, deduce the pseudorange double-difference positioning error equation. Linearize the pseudorange double-difference equation to obtain the pseudorange error equation.

[0007] Secondly, improve the weight matrix and create an adaptive weighted least squares solution algorithm.

[0008] Finally, according to the improved algorithm, solve the three-dimensional coordinates of the observation station.

[0009] Its advantages are as follows:

[0010] This method considers the problem of low positioning accuracy caused by the equal processing of all visible satellite observations in traditional positioning algorithms, and combines the spatial correlation between the base station and the observation station in pseudorange differential positioning technology. On this basis, by introducing the weighted least squares algorithm, an adaptive weight matrix is established to construct a Beidou high-precision positioning method with an adaptive weight matrix. This method can be applied to many application fields that require precise positioning, such as military, ports, and autonomous driving, to meet the sub-meter positioning requirements. The present invention is applicable to satellite navigation receiving systems and devices. Brief Description of the Drawings

[0011] Figure 1 It is the schematic diagram of a Beidou high-precision positioning method with an adaptive weight matrix according to the present invention.

[0012] In the figure, Rinex is Receiver Independent Exchange Format. Detailed Embodiment

[0013] Step 1: Parse the received ephemeris file and observation file to obtain the parameters required for positioning calculation. Obtain the current observation time t of the base station and the observation station from the observation file b , t o ; the number of visible satellites N at the current moment b , N o , and the number of satellites jointly observed by the base station and the observation station at the same moment is N, (N = min{N b , N o}). The pseudorange observations of the visible satellites at the current moment

[0014] Step 2: Calculate the satellite positions of Beidou navigation according to the Beidou navigation ICD standard. The receiver calculates the spatial coordinates (X i , Y i , Z i ) of each navigation satellite using the orbital parameters in the ephemeris file.

[0015] Step 3: Derive the pseudorange double-difference positioning error equation according to the principle of pseudorange differential positioning. The position (x b , y b , z b ) of the reference station is accurately known. If the m-th satellite is observed at the base station (i.e., i = m), using the pseudorange observation value parsed from the base station observation file and the satellite spatial coordinates (X m , Ym , Z m ), the pseudorange formula (1) from the base station to the m-th satellite can be obtained.

[0016]

[0017] In the formula, is the true distance from the m-th satellite to the base station at time t b , δt b represents the clock error of the base station receiver, and δt m represents the satellite clock error, C represents the speed of light, represents the ionospheric error, represents the tropospheric error, represents the random error.

[0018] The pseudorange correction in differential positioning is obtained by taking the difference between the true distance from the satellite to the base station and the pseudorange . After rearranging formula (1), the pseudorange correction number from the base station to the m-th satellite is obtained

[0019]

[0020] Similarly, according to formula (1), if b is replaced by o, it represents the pseudorange from the observation station to the m-th satellite, which can be expressed as formula (3).

[0021]

[0022] In the formula, is the true distance from the m-th satellite to the observation station at time t o , δt o represents the clock error of the observation station receiver. Adding the pseudorange of the observation station to the pseudorange correction realizes pseudorange single-difference positioning, as shown in formula (4).

[0023]

[0024] Similarly, if m in formula (4) is replaced by n, it can represent that the base station and the observation station simultaneously observe the satellite numbered n (i.e., i = n). Then, the pseudorange single-difference positioning equation obtained by the observation station is formula (5).

[0025]

[0026] Performing a group difference on the pseudorange equations (4) and (5) after double-differencing the observation station to achieve double-difference processing, the pseudorange double-difference equation is obtained, as shown in formula (6).

[0027]

[0028] As can be seen from the above equation, after double-difference processing, the receiver clock error has been eliminated, and the unknowns in the equation are only the three-dimensional coordinates of the observation station to be solved. If the distance between the base station and the observation station is within 100 km, then the satellite clock error, receiver clock error, most of the errors of the troposphere, ionosphere and random errors can be eliminated, greatly improving the positioning accuracy.

[0029] Step 4: Linearize the pseudo-range double-difference equation to obtain the pseudo-range error equation. Since the least squares related algorithms can only solve linear equations, the formula (6) is linearized. Here, the first-order Taylor series expansion is used, and the coordinates of the observation station are set as unknowns (x o , y o , z o ), the satellite coordinates are (X i , Y i , Z i ), and the initial coordinates of the observation station are (x0, y0, z0). Taking

[0030]

[0031] Let Δx = x o - x0, Δy = y o - y0, Δz = z o - z0, δx = [Δx, Δy, Δz]T, and at the same time let After organizing formula (7), the pseudo-range difference error equation (8) is obtained.

[0032]

[0033] where Δv is a matrix of size m×1, representing the pseudo-range error. Let the pseudo-range observation matrix H = [p i , q i , s i , then formula (8) can be expressed as:

[0034] Δv = Hδx - b (9).

[0035] Step 5: Improve the weight matrix and create an adaptive weighted least squares solution algorithm. The traditional least squares algorithm defaults that the observations of all visible satellites by the receiver are of equal accuracy. However, in actual situations, the pseudo-range observations between the observed satellites are often uncorrelated and have different distributions. In this case, there will be large errors in the positioning of the least squares algorithm. Therefore, the weighted least squares estimation is used to find the optimal solution of the user's position and improve the effectiveness of the algorithm.

[0036] The weighted least squares method introduces a weight matrix W as shown in Equation (10) to solve the matrix equation. Since there is no correlation between individual measurement values, the weight matrix is usually a diagonal matrix.

[0037]

[0038] Multiply each term in Equation (9) by the corresponding weight coefficient to obtain the weighted least squares error matrix equation as shown in Equation (11).

[0039] W·Δv=W(Hδx - b) (11).

[0040] To improve the credibility of the pseudorange observations in the positioning solution, correct the pseudorange-related errors that have not been thoroughly corrected by the mathematical model for different satellites at the same moment. Therefore, an adaptive weight matrix is constructed using the magnitudes of the different pseudorange correction amounts of each satellite.

[0041] According to Equation (2), the pseudorange correction amount of the m-th satellite received by the observation station from the base station can be expressed as Δρ m , and the number of observed satellites is N. The pseudorange correction amounts for these satellites can form a correction amount array Δρ.

[0042] Δρ = [Δρ 1 , Δρ 2 , … Δρ N (12).

[0043] Considering that the pseudorange observations between satellites are uncorrelated, the variance of Δρ is denoted as Δρ m .

[0044]

[0045] Subtract Δρ m from each element in Δρ and take the absolute value to form a new array (14):

[0046] γ = [γ1, γ2, ..., γ N (14).

[0047] where γ m = |ρ m - Δρ m |. Using the γ array to construct the weight matrix, the weight coefficient of the m-th satellite can be expressed as ω m .

[0048]

[0049] Substitute Equation (17) into (11) to obtain the adaptive weight matrix (16).

[0050]

[0051] As can be seen from (16), the weight matrix is closely related to the pseudorange observables. The weight coefficient is not fixed and will be updated with the iteration of the pseudorange observations. The greater the weight, the more important the current observation value is in solving the pseudorange equation set, and the higher the positioning accuracy.

[0052] The improved adaptive weighted least squares error matrix equation is as shown in formula (17).

[0053]

[0054] Step 6: Solve the three-dimensional coordinates of the observation station according to the improved algorithm. According to formula (17), the positioning result of the pseudorange measurement double difference of the improved adaptive weighted least squares method is (18).

[0055] δx = (H T WH) -1 ×(H T Wb) (18).

[0056] where δx = [Δx, Δy, Δz] T . The correction amount obtained from the above formula is between the initial point and the true point and has passed through first-order linearization. Using this correction amount to update the initial point, the corrected solution, that is, the coordinates of the observation station, can be obtained.

[0057]

[0058] Using the corrected solution (x1, y1, z1) in formula (19) as the initial value for iteration, as the number of iterations increases, the accuracy of linearization will become higher and higher. The user can customize the number of iterations k (k takes positive integers) according to needs. The larger the value of k, the higher the positioning accuracy. Then, after iteratively updating k times, the coordinates of the observation station receiver are as shown in formula (20), that is, the final positioning coordinates.

[0059]

Claims

1. A Beidou high-precision positioning method with an adaptive weight matrix, characterized in that It includes the following steps: Step 1: Parse the received ephemeris file and observation file to obtain the parameters required for positioning calculation; obtain the current observation time t of the base station and the observation station from the observation file b , t o ; the number of visible satellites N at the current moment b , N o , the number of satellites jointly observed by the base station and the observation station at the same moment is N, (N = min{N b , N o}); the pseudorange observations of the visible satellites at the current moment Step 2: Calculate the satellite positions of Beidou Navigation according to the Beidou Navigation ICD standard; the receiver calculates the spatial coordinates (X i , Y i , Z i ) of each navigation satellite by using the respective orbital parameters in the ephemeris file; Step 3: Derive the pseudorange double-difference positioning error equation based on the principle of pseudorange differential positioning; the position of the reference station (x b , y b , z b ) is precisely known. If the m-th satellite is observed at the base station, i.e., i = m, the pseudorange observation value of the base station is obtained by parsing the base station observation file and the observation station observation file Pseudorange observation value of the observation station The satellite spatial coordinates (X m , Y m , Z m ) calculated using the ephemeris file; according to the differential positioning principle, calculate the pseudorange correction amount from the base station to the m-th satellite According to the principle of pseudorange single difference positioning, the pseudorange of the observation station is added with the pseudorange correction to obtain the pseudorange single difference positioning formula [1]; wherein, is the true distance from the satellite numbered m to the base station at time t, δt b is the clock error of the base station receiver, δt b represents the satellite clock error, C represents the speed of light, m and represent the ionospheric errors near the base station and the observation station respectively, and represent the tropospheric errors between the base station and the observation station respectively;represents the random error;​ Similarly, substituting m in formula [1] with n, it can represent that the base station and the observation station simultaneously observe the satellite numbered n, that is, i = n. Then the pseudo-range single-difference positioning equation obtained by the observation station is formula [2]; According to the principle of pseudo-range double-difference positioning, the pseudo-range equations [1] and [2] after double-differencing the observation station are grouped and differenced again to achieve double-difference processing, obtaining the pseudo-range double-difference equation, such as formula [3]; As can be seen from the above equation, after double-difference processing, the receiver clock error has been eliminated, and the unknowns in the equation are only the three-dimensional coordinates of the observation station to be solved; if the distance between the base station and the observation station is within 100 km, then the satellite clock error, receiver clock error, and most of the errors of the troposphere, ionosphere, and random errors can be eliminated; Step 4: Linearize the pseudorange double-difference equation to obtain the pseudorange error equation. Since the least squares related algorithms can only solve linear equations, the formula [3] is linearized. Here, the first-order Taylor series expansion is adopted, and the coordinates of the observation station are set as unknowns (x o , y o , z o ), the satellite coordinates are (X i , Y i , Z i ), and the initial coordinates of the observation station are (x0, y0, z0). is the initial pseudorange. Based on this starting value, the pseudorange equation [3] is expanded by the first-order Taylor series to obtain formula [4]. Let Δx = x o - x0, Δy = y o - y0, Δz = z o - z0, δx = [Δx, Δy, Δz] T , and at the same time let Rearranging formula [4] gives the pseudorange differential error equation [5]; where Δv is a matrix of size m×1, representing the pseudorange error; let the pseudorange observation matrix H = [p i , q i , s i , then Equation [5] can be expressed as: Δv = Hδx - b [6]; Step Five: Improve the weight matrix and create an adaptive weighted least squares solution algorithm; use weighted least squares estimation to find the optimal solution of the user's position; The weighted least squares method introduces a weight matrix W shown in formula [7] to solve the matrix equation. Since there is no correlation between each measurement value, the weight matrix is a diagonal matrix; Multiply each term in formula [6] by the corresponding weight coefficient to obtain the weighted least squares error matrix equation as formula [8]; W·Δv = W(Hδx - b) (8); In order to improve the credibility of the pseudo-range observables in the positioning solution and correct the pseudo-range related errors that have not been completely corrected by the established mathematical model for different satellites at the same moment, an adaptive weight matrix is constructed using the magnitudes of the different pseudo-range correction amounts of each satellite; According to Step 3, the pseudorange correction of the m-th satellite sent by the base station received by the observation station can be expressed as Δρ m , the number of observed satellites is N, and the pseudorange corrections for these satellites can form a correction array Δρ; Δρ = [Δρ 1 , Δρ 2 , … Δρ N [9]; Considering that the pseudorange observations between satellites are uncorrelated, the variance of Δρ is expressed as Δρ m ; Subtract each element in Δρ by Δρ m And take the absolute value to form a new array [11]: γ = [γ1, γ2, …, γ N [11]; Among them, γ m = |ρ m - Δρ m |; By using the γ array to construct a weight matrix, the weight coefficient of the m-th satellite can be expressed as ω m ; Substituting formula [12] into [7], the adaptive weight matrix [13] can be obtained; It can be seen from [13] that the weight matrix is closely related to the pseudo-range observables. The weight coefficient is not fixed and will be updated with the iteration of the pseudo-range observations. The greater the weight, the more important the current observation value is in solving the pseudo-range equation set, and the higher the positioning accuracy; The improved adaptive weighted least squares error matrix equation is as formula [14]; Step Six: Solve the three-dimensional coordinates of the observation station according to the improved algorithm; according to formula [14], the positioning result of the pseudo-range measurement double-difference of the improved adaptive weighted least squares method is [15]; δx=(H T WH) -1 ×(H T Wb) [15]; where δx = [Δx, Δy, Δz] T , the correction obtained from the above formula is between the initial point and the true point and has passed through one linearization. Using this correction to update the initial point, the corrected solution, that is, the coordinates of the observation station, can be obtained. Using the corrected solution (x1, y1, z1) in formula [16] as the initial value for iteration. As the number of iterations increases, the linearization accuracy will be higher and higher; the user can customize the number of iterations k as needed. k takes positive integers, and the larger the value of k, the higher the positioning accuracy. Then, after iterating and updating k times, the coordinate of the observation station receiver is shown in formula [17], that is, the final positioning coordinate;

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