Satellite navigation receiver positioning method based on multivariate polynomial principal term decoupling and elimination

Abstract

The present invention discloses a satellite navigation receiver positioning method based on multivariate polynomial principal term decoupling elimination. The method uses satellite ephemeris data sampled by the receiver to obtain pseudorange observation data, obtaining a pseudorange observation equation. The pseudorange observation equation is then converted into a multivariate polynomial form. Elimination is performed to obtain a principal term decoupled trigonometric polynomial. The decoupled equations are then solved in reverse order to obtain user coordinates and system clock errors. The method utilizes the concept of elimination and approaches the solution of a multivariate polynomial system. Because it does not involve the discarding of higher-order terms and iterative calculation operations required in linearization, it can reduce the amount of computation while ensuring positioning accuracy.

Description

Technical Field

[0001] The invention belongs to the technical field of satellite navigation, and in particular relates to a satellite navigation receiver positioning method based on multivariate polynomial principal term decoupling and elimination. Background Art

[0002] Satellite navigation systems are widely used in various important fields and are an important basic construction for measuring a country's comprehensive national strength and scientific and technological development level.

[0003] In addition to the Beidou system, other satellite navigation systems already in operation or with mature development plans include GPS, GLONASS, and Galileo. Because satellite signals are susceptible to environmental obstruction and interference, using any single system alone can be difficult to guarantee accuracy and reliability, and may even render positioning impossible. Given the excellent compatibility between these four systems, combining them into a multi-mode satellite navigation system (hereinafter referred to as a multi-system) can complement each other's strengths and achieve superior accuracy and reliability compared to a single system. However, a larger number of satellites increases the computational complexity, leading to higher receiver hardware costs. Therefore, high-performance multi-mode receiver fast positioning technology is crucial for reducing receiver hardware design costs, improving positioning efficiency, and ensuring real-time positioning.

[0004] Whether for single or multiple systems, existing positioning solutions (based on least squares or Kalman filtering) linearize the pseudorange observation equation, discarding higher-order terms (second-order and above), resulting in a certain loss of accuracy. Furthermore, both methods require iterative operations, which are computationally expensive. Summary of the Invention

[0005] To solve the above technical problems, the present invention proposes a satellite navigation receiver positioning method based on multivariate polynomial principal term decoupling elimination, adopting a dual-system two-three star selection method (i.e., two stars from system one and the other three stars from system two), and obtaining the principal term decoupled trigonometric polynomial after elimination using the equation group, and then solving each decoupled equation in reverse order to obtain the user coordinates and system clock error.

[0006] The technical solution of the present invention is: a satellite navigation receiver positioning method based on multivariate polynomial principal term decoupling and elimination, the specific steps are as follows:

[0007] Step 1: Obtain pseudo-range observation data through satellite ephemeris data sampled by the receiver, and obtain the pseudo-range observation equation;

[0008] The pseudorange observation equation is expressed as:

[0009]

[0010]

[0011] Among them, [x,y,z] is unknown and represents the receiver coordinates, [x i ,y i ,z i ] and [x j ,y j ,z j ] represent the coordinates of satellites from different systems, and i = 1, 2; j = 3, 4, 5. δ1 represents the clock error of system 1, δ2 represents the clock error of system 2, and ρ i and ρ j represent the pseudoranges of the i-th star and the j-th star respectively.

[0012] Step 2: transform the pseudorange observation equation into a multivariate polynomial form;

[0013] If five stars are selected using the existing star selection method, a multivariate polynomial equation system (PS) is obtained, and the undetermined variables, i.e., unknown parameters, are sorted as follows:

[0014] x>y>z>δ1>δ2 (3)

[0015]

[0016] Among them, x>y>z>δ1>δ2 means that the importance of the indeterminate element δ2 to x increases in sequence, f i Represents the i-th multivariate polynomial (i=1,2,3,4,5).

[0017] Step 3: Perform a linear transformation on the multivariate polynomial equations obtained in step 2 so that the main terms are different;

[0018] Eliminate x from f2 to f5 by f1 2 Eliminate the terms containing x from f3 to f5 by f2; eliminate the terms containing y from f4 to f5 by f3; and eliminate the terms containing z from f5 by f4. Then we can get the triangular polynomial system (TS), which is formula (5):

[0019]

[0020] Among them, a i ,b i ,c i ,d i ,e i ,g i ,h i ,C i All represent constant coefficients.

[0021] Step 4: Decouple and eliminate the main terms of the equation group obtained in step 3;

[0022] Select Collection BS1={f2,f3,f4,f5}, and find The remainder set {r1,r2,r3,r4} for BS1;

[0023] Let f6 = r4, then we can get:

[0024]

[0025] Perform the remainder operation of the polynomial to the polynomial group again, and then select PS2 = {f1, f2, f3, f4, f5, r1, r2, r3, f6}, And BS2={f2,f3,f4,f6}, find For the remainder set of BS2, we get:

[0026]

[0027] Among them, a, b, c, d, e, g, h, and C represent constant coefficients. Let:

[0028]

[0029] At this time, the principal decoupled triangular polynomial system (DTS) is obtained:

[0030]

[0031] Step 5: Solve the principal decoupled triangular polynomial group obtained in step 4 to obtain the user coordinates and system clock error;

[0032] [x u ,y u ,z u ] represents the user coordinates, and four alternative solutions δ2 are obtained from f8 21 , δ 22 , δ 23 and δ 24 , let δ 24 To satisfy the truth value of practical significance; two alternative solutions δ1 are obtained from f5 11 and δ 12 , similarly, let δ 12 To satisfy the truth value of practical significance; from f4 we get the solution z=z u ; From f3 we get the solution y=y u ; From f2 we get the solution x=x u ; The final solution is obtained, and the user coordinates and system clock error are obtained:

[0033]

[0034] The present invention provides the following beneficial effects: The method uses satellite ephemeris data sampled by a receiver to acquire pseudorange observation data, obtain a pseudorange observation equation, and then transform the pseudorange observation equation into a multivariate polynomial form. Elimination is performed to obtain a principal-term decoupled trigonometric polynomial. The decoupled equations are then solved in reverse order to obtain user coordinates and system clock errors. The method utilizes elimination, approaching the solution of a multivariate polynomial system. Because it avoids the high-order term discarding and iterative computation required in linearization, it can reduce computational complexity while ensuring positioning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 The present invention is a flow chart of a satellite navigation receiver positioning method based on decoupling and elimination of principal terms of a multivariate polynomial. DETAILED DESCRIPTION

[0036] To facilitate the description of the method of the present invention, some definitions involved in the present invention are explained:

[0037] 1. Triangular Polynomial System (TS):

[0038]

[0039] Where i represents a positive integer, f i represents the i-th multivariate polynomial, x i represents the i-th undetermined element, It means A is defined by B. When f i When =constant and constant ≠ 0, it is called TS contradiction and TS=0 has no solution, constant represents a constant.

[0040] 2. Principal Decoupled Triangular Polynomial System (DTS):

[0041]

[0042] Among them, a i represents a constant coefficient, represents the highest power of the i-th important undetermined element, Q i Represents x i The lower order terms.

[0043] The present invention will be further described below with reference to the accompanying drawings and examples.

[0044] This embodiment takes the dual-system two-three star selection (i.e., two stars come from system one and the other three stars come from system two) as an example to further illustrate the method of the present invention.

[0045] like Figure 1As shown in FIG, a flow chart of a satellite navigation receiver positioning method based on multivariate polynomial principal term decoupling and elimination of variables of the present invention is shown, and the specific steps are as follows:

[0046] Step 1: Obtain pseudo-range observation data through satellite ephemeris data sampled by the receiver, and obtain the pseudo-range observation equation;

[0047] The pseudorange observation equation is expressed as:

[0048]

[0049]

[0050] Among them, [x,y,z] is unknown and represents the receiver coordinates, [x i ,y i ,z i ] and [x j ,y j ,z j ] represent the coordinates of satellites from different systems, i = 1, 2; j = 3, 4, 5; δ1 represents the clock error of system 1, δ2 represents the clock error of system 2, ρ i and ρ j denote the pseudoranges of the i-th star and the j-th star respectively;

[0051] Step 2: transform the pseudorange observation equation into a multivariate polynomial form;

[0052] If five stars are selected using the existing star selection method, a multivariate polynomial equation system (PS) is obtained, and the undetermined variables, i.e., unknown parameters, are sorted as follows:

[0053] x>y>z>δ1>δ2 (15)

[0054]

[0055] Among them, x>y>z>δ1>δ2 means that the importance of the indeterminate element δ2 to x increases in sequence, f i represents the i-th multivariate polynomial (i=1,2,3,4,5);

[0056] Step 3: Perform a linear transformation on the multivariate polynomial equations obtained in step 2 so that the main terms are different;

[0057] Eliminate x from f2 to f5 by f1 2 Eliminate the terms containing x from f3 to f5 by f2; eliminate the terms containing y from f4 to f5 by f3; and eliminate the terms containing z from f5 by f4. Then we can get the triangular polynomial system (TS), which is formula (17):

[0058]

[0059] Among them, a i ,b i ,c i ,d i ,e i ,g i ,h i ,C i are all constant coefficients.

[0060] Step 4: Decouple and eliminate the main terms of the equation group obtained in step 3;

[0061] Select Collection BS1={f2,f3,f4,f5}, and find The remainder set {r1,r2,r3,r4} for BS1;

[0062] Let f6 = r4, then we can get:

[0063]

[0064] Perform the remainder operation of the polynomial to the polynomial group again, and then select PS2 = {f1, f2, f3, f4, f5, r1, r2, r3, f6}, And BS2={f2,f3,f4,f6}, find For the remainder set of BS2,

[0065]

[0066] Among them, a, b, c, d, e, g, h, and C represent constant coefficients. Let:

[0067]

[0068] At this time, the principal decoupled triangular polynomial system (DTS) is obtained:

[0069]

[0070] Step 5: Solve the principal decoupled triangular polynomial system (DTS) obtained in step 4 to obtain the user coordinates and system clock error.

[0071] [x u ,y u ,z u ] represents the user coordinates, and four alternative solutions δ2 are obtained from f8 21 , δ 22 , δ 23 and δ 24 , let δ 24 To satisfy the truth value of practical significance; two alternative solutions δ1 are obtained from f5 11 and δ12 , similarly, let δ 12 To satisfy the truth value of practical significance; from f4 we get the solution z=z u ; From f3 we get the solution y=y u ; From f2 we get the solution x=x u ; The final solution is obtained, and the user coordinates and system clock error are obtained:

[0072]

[0073] In summary, the method of the present invention utilizes the idea of ​​elimination and starts from the perspective of solving a multivariate polynomial equation system. Since it does not involve the operation of discarding high-order terms and iterative calculation operations in linearization, it can reduce the amount of calculation while ensuring positioning accuracy.

[0074] Those skilled in the art will appreciate that the above-described embodiments are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art will readily appreciate that the present invention is susceptible to various modifications and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention are intended to be included within the scope of the claims of the present invention.

Claims

1. A satellite navigation receiver positioning method based on multivariate polynomial principal term decoupling and elimination, comprising the following steps: Step 1: Obtain pseudo-range observation data through satellite ephemeris data sampled by the receiver, and obtain the pseudo-range observation equation; The pseudorange observation equation is expressed as: in, [x,y,z] is unknown and represents the receiver coordinates, [x i ,y i ,z i ] and [x j ,y j ,z j ] represent the coordinates of satellites from different systems, i = 1, 2; j = 3, 4, 5; δ1 represents the clock error of system 1, δ2 represents the clock error of system 2, ρ i and ρ j denote the pseudoranges of the i-th star and the j-th star respectively; Step 2: transform the pseudorange observation equation into a multivariate polynomial form; If five stars are selected using the existing star selection method, a multivariate polynomial equation system is obtained, and the undetermined variables, i.e., unknown parameters, are sorted as follows: x>y>z>δ1>δ2 (3) Among them, x>y>z>δ1>δ2 means that the importance of the indeterminate element δ2 to x increases in sequence, f i represents the i-th multivariate polynomial, i = 1, 2, 3, 4, 5; Step 3: Perform a linear transformation on the multivariate polynomial equations obtained in step 2 so that the main terms are different; Eliminate x from f2 to f5 by f1 2 Eliminate the terms containing x from f3 to f5 by f2; eliminate the terms containing y from f4 to f5 by f3; and eliminate the terms containing z from f5 by f4. Then we can get the triangular polynomial group, namely formula (5): Among them, a i ,b i ,c i ,d i ,e i ,g i ,h i ,C i All represent constant coefficients; Step 4: Decouple and eliminate the main terms of the equation group obtained in step 3; Select Collection BS1={f2,f3,f4,f5}, and find The remainder set {r1,r2,r3,r4} for BS1; Let f6 = r4, then we can get: Perform the remainder operation of the polynomial to the polynomial group again, and then select PS2 = {f1, f2, f3, f4, f5, r1, r2, r3, f6}, And BS2={f2,f3,f4,f6}, find For the remainder set of BS2, we get: Among them, a, b, c, d, e, g, h, and C represent constant coefficients. Let: At this time, the main term decoupled triangular polynomial group is obtained: Step 5: Solve the principal decoupled triangular polynomial group obtained in step 4 to obtain the user coordinates and system clock error; [x u ,y u ,z u ] represents the user coordinates, and four alternative solutions δ2 are obtained from f8 21 , δ 22 , δ 23 and δ 24 , let δ 24 To satisfy the truth value of practical significance; two alternative solutions δ1 are obtained from f5 11 and δ 12 , similarly, let δ 12 To satisfy the truth value of practical significance; from f4 we get the solution z=z u ; From f3 we get the solution y=y u ; From f2 we get the solution x=x u ; The final solution is obtained, and the user coordinates and system clock error are obtained:

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