Ionospheric scintillation process GNSS positioning model optimization based on weight superposition and singular decomposition method

Abstract

The application discloses an ionospheric scintillation process GNSS positioning model optimization based on weight superposition and singular decomposition method, and comprises the following steps: determining GNSS satellite observation; and designing a GNSS observation weight matrix by superposition of satellite elevation angles and ionospheric scintillation indexes. The application innovatively proposes to design a GNSS observation weight matrix by superposition of satellite elevation angles and ionospheric scintillation indexes, and then solve GNSS observation equations by using a method combining Tikhonov and singular decomposition, so as to solve the problem of the increase of the condition number of a normal equation coefficient matrix caused by ionospheric scintillation, change the ill-conditioned nature of the normal equation, and improve GNSS positioning precision and reliability.

Description

Technical Field

[0001] This invention relates to the field of model optimization technology, and in particular to an optimization of GNSS positioning model for ionospheric scintillation processes based on weighted superposition and singular decomposition methods. Background Technology

[0002] The ionosphere is one of the important sources affecting the performance of GNSS (Global Navigation Satellite System) services, especially since abnormal ionospheric activity can have an extremely unstable effect on radio signals.

[0003] Ionospheric scintillation causes rapid random fluctuations and attenuation in the amplitude and phase of received GNSS signals, even leading to bit errors and signal distortion, affecting signal quality. In severe cases, it can cause cycle slips in the carrier phase, even satellite lock-on failure, reducing the strength of the satellite's spatial geometry, increasing positioning errors, and even making positioning impossible. However, ionospheric scintillation is a complex random process caused by small- to medium-scale disturbances, and there is currently no model that can accurately correct it, nor can multi-frequency technology effectively reduce or eliminate its impact on GNSS positioning. Strong ionospheric scintillation reduces the number of effective GNSS satellites, increases the geometrical accuracy factor (GDOP), and increases positioning errors.

[0004] To address these issues, this invention innovatively proposes designing a GNSS observation weight matrix by superimposing satellite elevation angle and ionospheric scintillation index. Then, a method combining Tikhonov and singular decomposition is used to solve the GNSS observation equations, solving the problem of increased condition number of the normal equation coefficient matrix caused by ionospheric scintillation, changing the ill-conditioned nature of the normal equations, and improving the accuracy and reliability of GNSS positioning. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention provides an optimization of the GNSS positioning model for ionospheric scintillation processes based on weighted superposition and singular decomposition methods.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: an optimization of the GNSS positioning model for ionospheric scintillation processes based on weighted superposition and singular decomposition methods, comprising the following steps:

[0007] S1: Determine GNSS satellite observations;

[0008] S2: Design a GNSS observation weighting array by superimposing satellite elevation angle and ionospheric scintillation index;

[0009] S3: The GNSS observation equations are solved using a combination of Tikhonov and singular decomposition methods;

[0010] S4: Reduce the condition number of the coefficient matrix of the normal equation, change the ill-conditioned nature of the normal equation, and optimize the GNSS positioning model of the ionospheric scintillation process;

[0011] S5: Validation of the GNSS positioning model for ionospheric scintillation process.

[0012] As a preferred technical solution of the present invention, the determination of GNSS satellite observations in S1 is based on existing early warning information of disturbed satellites, and the GNSS satellite observations are selected preferentially.

[0013] As a preferred technical solution of the present invention, S2 uses the satellite elevation angle and the ionospheric scintillation index to design a GNSS observation weighting array, taking into account the impact of ionospheric scintillation on GNSS satellites. The GNSS observation weighting array that takes into account the impact of ionospheric scintillation is constructed using the ionospheric scintillation index ROTI and superimposed on the observation weighting array constructed by the elevation angle.

[0014] As a preferred embodiment of the present invention, step S3 employs a combination of Tikhonov and singular decomposition to solve the GNSS observation equations. This includes determining the condition number of the coefficient matrix of the algorithmic equations and assessing the ill-conditioned nature of the normal equations based on the condition number. If the normal equations are ill-conditioned, a regularization matrix is ​​constructed using singular decomposition based on the Tikhonov regularization principle. Appropriate regularization parameters are selected to improve the ill-conditioned nature of the equations, thereby obtaining the optimal solution result for the normal equations.

[0015] As a preferred technical solution of the present invention, S4 reduces the condition number of the coefficient matrix of the normal equation, changes the ill-conditioned nature of the normal equation, and optimizes the GNSS positioning model of the ionospheric scintillation process. This includes: constructing a regularization matrix using the singular decomposition method based on the Tikhonov regularization principle, selecting appropriate regularization parameters, changing the ill-conditioned nature of the equation, and obtaining the best solution result of the normal equation.

[0016] As a preferred technical solution of the present invention, the effectiveness verification of the S5 ionospheric scintillation process GNSS positioning model was carried out in the South my country Sea, Yunnan Province, and northern Australia to verify the effectiveness of the model.

[0017] Compared with the prior art, the beneficial effects that this invention can achieve are:

[0018] 1. This invention innovatively proposes to design a GNSS observation weight matrix by superimposing satellite elevation angle and ionospheric scintillation index, and then uses a combination of Tikhonov and singular decomposition to solve the GNSS observation equations. This solves the problem of increased condition number of the normal equation coefficient matrix caused by ionospheric scintillation, changes the ill-conditioned nature of the normal equations, and improves the accuracy and reliability of GNSS positioning.

[0019] 2. The positioning accuracy analysis of the GNSS positioning model for ionospheric scintillation process has not been fully and thoroughly studied, and no experimental verification has been carried out in the South China Sea and near the equator. While optimizing the model, this invention selects the South China Sea, Yunnan, and northern Australia to carry out experiments to verify the effectiveness and accuracy of the GNSS positioning model for ionospheric scintillation process. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the GNSS positioning solution process for ionospheric scintillation based on weighted superposition and singular decomposition.

[0021] Figure 2 This is the overall flowchart of the present invention. Detailed Implementation

[0022] To make the technical means, creative features, and achieved objectives and effects of this invention easier to understand, the invention is further described below with reference to specific embodiments. However, the following embodiments are merely preferred embodiments of this invention and not all of them. Other embodiments obtained by those skilled in the art based on the embodiments described herein without creative effort are all within the protection scope of this invention. Unless otherwise specified, the experimental methods in the following embodiments are conventional methods, and the materials and reagents used in the following embodiments are commercially available unless otherwise specified.

[0023] Example:

[0024] like Figure 1-2 As shown, an optimization of the GNSS positioning model for ionospheric scintillation processes based on weighted superposition and singular decomposition methods includes the following steps:

[0025] Step 1: Based on the existing early warning information of disturbed satellites, select the best GNSS satellite observations.

[0026] In this embodiment, the existing early warning information of disturbed satellites comes from the ionospheric scintillation spatial distribution grid map constructed based on the GISM (Global Ionospheric Scintillation Model) prediction model and the satellite spatial position predicted by the GNSS ephemeris, which identifies GNSS satellites whose ionospheric scintillation process is disturbed.

[0027] Step 2: Design a GNSS observation weighting array by superimposing satellite elevation angle and ionospheric scintillation index.

[0028] Typically, the GNSS observation weighting array is designed using satellite elevation angles:

[0029]

[0030] In the formula, E rFor reference satellite elevation angle, E k1 ,…,E k(n-1) The elevation angle of the other n-1 satellites.

[0031] Considering the impact of ionospheric scintillation on GNSS observations, the new observation weighting matrix after superimposing and optimizing the elevation angle and ionospheric scintillation weighting matrix is ​​as follows:

[0032]

[0033] In the formula, ROTI r Let ROTI be the ionospheric scintillation value of the reference satellite r, and ROTIk1,…,ROTIk(n-1) be the ionospheric scintillation values ​​of the other n-1 satellites.

[0034] Step 3: Solve the GNSS observation equations using a combination of Tikhonov and singular decomposition methods.

[0035] According to the Tikhonov regularization principle, when the condition number of the coefficient matrix of the normal equation is large, the equation may exhibit ill-conditioned behavior. Therefore, the optimal solution to the observation equation is to seek a solution that satisfies the following criterion:

[0036]

[0037] Where α is the regularization parameter and R is the regularization matrix. It is a stable functional, and ||·|| denotes the Euclidean 2-norm. As can be seen from the above equation, the key to solving the ill-conditioned equation is determining the regularization parameter α and the matrix R.

[0038] (1) Singular decomposition constructs a regularization matrix R

[0039] First, normalize the observation weight matrix P. R =CC T Multiply the coefficient matrix A of the normal equation by C T get And perform singular decomposition on it:

[0040]

[0041] In the formula, U and V are both orthogonal matrices, and D is... The singular value matrix.

[0042] Divide V and D into blocks:

[0043]

[0044]

[0045] make

[0046] Using S Q Construct the regularization matrix:

[0047]

[0048] The regularization matrix R is an m×m singular matrix, with the top-left 3×3 submatrix being non-zero and the rest being zero, and its rank is 3.

[0049] (2) Selecting an appropriate regularization parameter α

[0050] After determining the regularization matrix R, solving the ill-conditioned equation also requires determining a suitable regularization parameter α. Currently, the value of α is determined by empirical values ​​obtained from a large number of calculations, and different references provide different values. However, if α is different, the quality of the solution to the ill-conditioned equation will also be different. Therefore, it is necessary to select a suitable value for the regularization parameter α.

[0051] When the observation vector ||L δ When -L||≤δ, δ>0, the function for regularization parameter α>0 is:

[0052]

[0053] Where α * It is the conjugate operator of α; the constant E > 0. ||Y||≤E.

[0054] Then from α * The regularized solution Y obtained from (δ) and equation (3) α,δ The following convergence criterion must be met:

[0055]

[0056] Once the regularization parameter is determined, the error function of the best approximate solution to the ill-conditioned equation is:

[0057]

[0058] A * Let A be the conjugate operator of A. For positive constants p and s, let:

[0059]

[0060] The above formula has the following properties: 1) 2) α is strictly monotonically increasing and continuous; 3) The equation has a unique solution α = α(δ); 4)

[0061] There is currently no unified method for determining the value of α. In this embodiment, an iterative method will be adopted, which involves cyclically selecting different values ​​of α until the ill-conditioned equation is suppressed and becomes a benign equation, thus obtaining a reliable solution to the normal equation.

[0062] Once the value of α is determined, the optimal solution to the normal equation can be obtained as follows:

[0063]

[0064] in, For the estimated value of the coordinate vector, This is the estimate of the floating-point solution for ambiguity.

[0065] Step 4: Reduce the condition number of the coefficient matrix of the normal equations, change the ill-conditioned nature of the normal equations, and optimize the GNSS positioning model for the ionospheric scintillation process.

[0066] The condition number of the coefficient matrix of the normal equations is calculated, and the ill-conditioned nature of the normal equations is determined based on the condition number. If the normal equations are ill-conditioned, a regularization matrix is ​​constructed using the singular decomposition method according to the Tikhonov regularization principle. Appropriate regularization parameters are selected to improve the ill-conditioned nature of the equations, thereby obtaining the optimal solution result of the normal equations, improving positioning accuracy, and achieving reliable and accurate GNSS positioning.

[0067] Step 5: Validation of the GNSS positioning model for the ionospheric scintillation process.

[0068] In this embodiment, experiments were conducted in the South China Sea, Yunnan Province, and northern Australia to verify the effectiveness and accuracy of the GNSS positioning model for ionospheric scintillation processes, and further research on its practical application can be carried out.

[0069] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited thereto. Various changes can be made within the scope of knowledge possessed by those skilled in the art without departing from the spirit of the present invention.

Claims

1. A method for optimizing a GNSS positioning model of ionospheric scintillation processes based on weighted superposition and singular decomposition, characterized in that, Includes the following steps: S1: Determine GNSS satellite observations; S2: Design a GNSS observation weighting array by superimposing satellite elevation angle and ionospheric scintillation index; S3: The GNSS observation equations are solved using a combination of Tikhonov and singular decomposition methods; S4: Reduce the condition number of the coefficient matrix of the normal equation, change the ill-conditioned nature of the normal equation, and optimize the GNSS positioning model of the ionospheric scintillation process; S5: Validation of the GNSS positioning model for ionospheric scintillation process.

2. The method for optimizing the GNSS positioning model of ionospheric scintillation process based on weighted superposition and singular decomposition as described in claim 1, characterized in that, The determination of GNSS satellite observations in S1 is based on existing early warning information about disturbed satellites.

3. The method for optimizing the GNSS positioning model of ionospheric scintillation process based on weighted superposition and singular decomposition as described in claim 2, characterized in that, The S2 design uses the satellite elevation angle and the ionospheric scintillation index to design a GNSS observation weighting matrix, taking into account the impact of ionospheric scintillation on GNSS satellites. It uses the ionospheric scintillation index ROTI to construct a GNSS observation weighting matrix that takes into account the impact of ionospheric scintillation, and then superimposes it with the observation weighting matrix constructed by the elevation angle.

4. The method for optimizing the GNSS positioning model of ionospheric scintillation process based on weighted superposition and singular decomposition as described in claim 3, characterized in that, The S3 method uses a combination of Tikhonov and singular decomposition to solve the GNSS observation equations, including: calculating the condition number of the coefficient matrix of the normal equations, and judging the ill-conditioned nature of the normal equations based on the condition number.

5. The GNSS positioning model optimization method for ionospheric scintillation process based on weighted superposition and singular decomposition as described in claim 4, characterized in that, If the normal equation is ill-conditioned, according to the Tikhonov regularization principle, a regularization matrix is ​​constructed using the singular decomposition method, and appropriate regularization parameters are selected to improve the ill-conditioned nature of the equation and obtain the best solution result for the normal equation.

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