Methods, equipment, and storage media for analyzing the observability evolution of radio navigation systems

Abstract

This invention relates to a method, apparatus, and storage medium for analyzing the observability evolution of a radio navigation system. The method includes: step S1, determining the error evolution of the spacecraft's state variables; step S2, obtaining the impact of each observation on the error covariance matrix based on the information gain from each observation; and step S3, calculating the error estimation matrix used to analyze system observability. This invention, by making the changes in estimation error caused by observation continuous and taking into account the accumulation of observation information, effectively solves the problem that the Fischer information matrix cannot reflect the differences between different orbiters when performing observability analysis on a single orbiter.

Description

Technical Field

[0001] This invention relates to the field of spacecraft autonomous navigation technology, and in particular to a method, device and storage medium for analyzing the observability evolution of a radio navigation system. Background Technology

[0002] Observability analysis is a crucial step in navigation system design and performance evaluation. It assesses the system's performance under varying observation conditions, providing vital guidance for system design. For spacecraft radio navigation schemes, existing qualitative observability analysis methods are mostly based on the Fischer information matrix. However, in most scenarios, this method only reflects the impact of observations at a single moment and fails to capture the long-term effects of observations from different orbiters. Furthermore, for observability analysis of a single orbiter, the eigenvalues ​​of its Fischer information matrix are fixed, failing to reflect the differences in radio observation performance between different orbiters. In addition, the stability of the dynamic model significantly influences the cumulative effect of observational information. Intuitively, the greater the error factor in the dynamic environment, the lower the reference value of information observed at previous moments, and the less pronounced the cumulative effect of observational information. Therefore, theoretically, to conduct observability analysis for more complex dynamic scenarios, it is necessary to consider both the cumulative effect of observational information and the coupling effects of the dynamic environment. Summary of the Invention

[0003] To address the technical problems existing in the prior art, the present invention aims to provide an analysis method, device, and storage medium for the observability evolution of a radio navigation system. This method helps to solve the problem that the Fischer information matrix cannot reflect the performance gap of a single orbiter, effectively reflects the evolution trend of the estimation error of system state variables, and combines the estimation error evolution of state variables in the dynamic model, which is beneficial for the observability analysis of navigation schemes under complex dynamic environments.

[0004] To achieve the above-mentioned objectives, this invention provides a method for analyzing the observability evolution of a radio navigation system, comprising the following steps:

[0005] Step S1: Determine the error evolution of the spacecraft's state variables themselves;

[0006] Step S2: Based on the information gain from each observation, obtain the impact of the observation on the error covariance matrix;

[0007] Step S3: Calculate the error estimation matrix used to analyze the observability of the system.

[0008] According to a technical solution of the present invention, step S1 specifically includes:

[0009] Step S11: Acquire spacecraft data and obtain the spacecraft's dynamic model;

[0010] Step S12: Use the Fock-Planck-Kármán equation to obtain the evolution of the state quantity estimation error over time.

[0011] According to one technical solution of the present invention, step S2 specifically includes:

[0012] Step S21: Calculate the information gain based on the observations obtained from each observation, according to the Fischer information matrix;

[0013] Step S22: By transforming the information matrix and the error covariance matrix, the influence of observation on the error covariance matrix is ​​obtained;

[0014] The observations refer to the relative distance and relative radial velocity between the detector and the radio orbiter, respectively.

[0015] According to one technical solution of the present invention, step S3 specifically includes:

[0016] Step S31: Perform continuous processing on the changes in estimation error caused by observation;

[0017] Step S32: Combine the influence of the dynamic part and the observation part obtained in steps S1 and S2 on the estimation error into the differential equation of the estimation error covariance matrix to obtain the evolution of the state quantity estimation error of the navigation process;

[0018] Step S33: Then, use Runge-Kutta to solve the differential equation to obtain the estimated value of the state quantity error covariance matrix;

[0019] Step S34: Calculate the eigenvalues ​​or diagonal elements of the estimated value of the state quantity error covariance matrix to effectively analyze the observability of the navigation system and obtain the evolution of the observability index in the x-direction.

[0020] According to a technical solution of the present invention, in step S22, the influence of observation on the error covariance matrix is ​​obtained through the transformation relationship between the information matrix and the error covariance matrix, as shown in the formula:

[0021]

[0022] in, Let be the state quantity estimation error covariance matrices before and after the observation update, and let I(t) be the Fisher information matrix of the observation equation.

[0023] According to a technical solution of the present invention, in step 31, the change in estimation error caused by observation is processed to be continuous, thereby obtaining the transformation rate of the state quantity covariance matrix brought about by observation at a fixed observation frequency:

[0024]

[0025] Where T represents the average interval of radio observations, and P(t) and I(t) represent the real-time state covariance matrix and the Fisher information matrix of the observation equation, respectively.

[0026] According to a technical solution of the present invention, in step S32, the calculation formula for the evolution of the state quantity estimation error is as follows:

[0027]

[0028] Where P(t) represents the state covariance matrix of the spacecraft, F(t) represents the Jacobian matrix of the state equation with respect to the state variables, Γ(t) is the Jacobian matrix of the state equation with respect to the unknown error terms, W(t) is the autocovariance matrix of the error terms, and F(t)P(t) and P(t)F(t) are also mentioned. T The state variable's own error evolves with the dynamic state equation, Γ(t)W(t)Γ(t). T This represents the estimation error caused by the inherent uncertainty of the state equation itself. This represents the impact of the amount of information from each observation on the state quantity estimation error.

[0029] According to one aspect of the present invention, an electronic device is provided, comprising: one or more processors, one or more memories, and one or more computer programs; wherein the processor is connected to the memory, and the one or more computer programs are stored in the memory; when the electronic device is running, the processor executes the one or more computer programs stored in the memory to cause the electronic device to perform an analysis method for the observability evolution of a radio navigation system as described in any of the above technical solutions.

[0030] According to one aspect of the present invention, a computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement a method for analyzing the observability evolution of a radio navigation system as described in any of the above technical solutions.

[0031] Compared with the prior art, the present invention has the following advantages:

[0032] This invention proposes an analysis method, device, and storage medium for the observability evolution of a radio navigation system. By making the estimation error changes caused by observation continuous and taking into account the accumulation of observation information, it effectively solves the problem that the Fisher information matrix cannot reflect the differences between different orbiters when performing observability analysis on a single orbiter.

[0033] Furthermore, by simultaneously calculating the cumulative effect of dynamic model and observation information on the error covariance matrix, this invention can more effectively reflect the evolution trend of state quantity errors, especially in environments with complex dynamic models.

[0034] Meanwhile, this invention, through the concept of information filtering and the Fisher information matrix of the observation equation, directly bypasses the nonlinear filtering process and obtains the influence of each observation on the estimated error covariance matrix. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described below. Obviously, the drawings described below are merely some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0036] Figure 1 This schematic diagram illustrates a flowchart of an analysis method for the observability evolution of a radio navigation system according to an embodiment of the present invention.

[0037] Figure 2 A schematic diagram illustrating the comparison between observability indicators and actual errors of one embodiment of the present invention;

[0038] Figure 3 The flowchart illustrates the specific steps of step S3 in one embodiment of the present invention. Detailed Implementation

[0039] The description of the embodiments in this specification should be taken in conjunction with the accompanying drawings, which should form part of the complete specification. In the drawings, the shape or thickness of the embodiments may be exaggerated and may be indicated in a simplified or convenient manner. Furthermore, parts of the various structures in the drawings will be described separately; it is worth noting that elements not shown in the figures or not described in words are in a form known to those skilled in the art.

[0040] The descriptions of the embodiments herein, including any references to directions and orientations, are for ease of description only and should not be construed as limiting the scope of the invention. The following description of preferred embodiments involves combinations of features, which may exist independently or in combination; the invention is not particularly limited to the preferred embodiments. The scope of the invention is defined by the claims.

[0041] like Figures 1 to 3 As shown, the present invention provides a method for analyzing the observability evolution of a radio navigation system, comprising the following steps:

[0042] Step S1: Based on the spacecraft's dynamic model, use the Fokker-Planck-Kármán equations to obtain the evolution of the state quantity estimation error over time;

[0043] In one embodiment of the present invention, preferably, step S1 specifically includes:

[0044] Step S11: Acquire spacecraft data and obtain the spacecraft's dynamic model;

[0045] Step S12: Use the Fock-Planck-Kármán equation to obtain the evolution of the state quantity estimation error over time.

[0046] Specifically, taking the spacecraft data from the Curiosity rover's approach to Mars as an example, and using the Mars central inertial coordinate system as the reference coordinate system, its dynamic model is as follows:

[0047]

[0048] Where r and v represent the spacecraft's position and velocity vectors in the Mars central inertial coordinate system, respectively. Vector r it The vector r represents the position vector of the i-th celestial body relative to Mars. ir μ represents the position vector of the i-th star relative to the detector. a μ is the gravitational constant of Mars. i Let represent the gravitational constant of the i-th celestial body, and w represent unmodeled terms such as solar radiation pressure, which are considered as systematic errors. In the formula, each term represents the force received by the spacecraft from Mars and other surrounding celestial bodies, respectively. Let the state variable be x = [r T v T ] T Then, under the influence of the dynamic model, the evolution of the state variable x covariance matrix P satisfies:

[0049]

[0050] in, W is the covariance matrix of the noise w.

[0051] Step S2: Based on the Fischer information matrix, obtain the information gain brought by each observation, and through the transformation relationship between the information matrix and the error covariance matrix, obtain the influence of the observation on the error covariance matrix;

[0052] In one embodiment of the present invention, preferably, step S2 specifically includes:

[0053] Step S21: Calculate the information gain based on the observations obtained from each observation, according to the Fischer information matrix;

[0054] Step S22: By transforming the information matrix and the error covariance matrix, the influence of observation on the error covariance matrix is ​​obtained;

[0055] The observations refer to the relative distance and relative radial velocity between the detector and the radio orbiter, respectively.

[0056] Specifically, taking the approach phase of a Mars exploration mission as an example, the radio measurement model for a single orbiter is as follows:

[0057]

[0058] Where r and v represent the spacecraft's position and velocity vectors in the Mars central inertial coordinate system, respectively, and v o Let r be the velocity of the Mars orbiter in the Martian inertial frame. o Let be the position of the Mars orbiter in the Martian inertial coordinate system, u represent the observation noise term, and the observations be the relative distance and relative radial velocity between the probe and the radio orbiter, respectively. The Fischer information matrix of the observations is calculated as follows:

[0059]

[0060] Where R represents the autocovariance matrix of the observation noise, and the change in the information matrix of the state variables caused by each observation state update during the filtering process is: Based on the transformation relationship between the information matrix and the state quantity estimation error covariance matrix, the change of the covariance matrix before and after observation is obtained as follows:

[0061]

[0062] Step S3: Integrate the results by combining the error evolution effect brought about by the dynamic model and observation to obtain the error estimation matrix used to analyze the observability of the system.

[0063] like Figure 3 As shown, in one embodiment of the present invention, preferably, step S3 specifically includes:

[0064] Step S31: Perform continuous processing on the changes in estimation error caused by observation;

[0065] Step S32: Combine the influence of the dynamic part and the observation part obtained in steps S1 and S2 on the estimation error into the differential equation of the estimation error covariance matrix to obtain the evolution of the state quantity estimation error of the navigation process;

[0066] Step S33: Then, use Runge-Kutta to solve the differential equation to obtain the estimated value (matrix) of the state quantity error covariance matrix;

[0067] Step S34: Calculate the estimated value of the state quantity error covariance matrix (matrix) and the eigenvalues ​​or diagonal elements to effectively analyze the observability of the navigation system, and obtain the evolution of the observability index in the x direction.

[0068] Specifically, the changes in estimation error caused by observation are processed to be continuous, and then the influence of the dynamic part and the observation part obtained in the first two steps on the estimation error are combined into the differential equation of the estimation error covariance matrix to obtain the evolution of the state quantity estimation error in the navigation process:

[0069]

[0070] Where P(t) represents the state covariance matrix of the spacecraft, F(t) represents the Jacobian matrix of the state equation with respect to the state variables, Γ(t) is the Jacobian matrix of the state equation with respect to the unknown error terms, W(t) is the autocovariance matrix of the error terms, and F(t)P(t) and P(t)F(t) are also mentioned. T The state variable's own error evolves with the dynamic state equation, Γ(t)W(t)Γ(t). T This represents the estimation error caused by the inherent uncertainty of the state equation itself. These represent the impact of the amount of information from each observation on the state quantity estimation error. These items respectively show the influence trend of different factors on the evolution of the state quantity estimation error.

[0071] The differential equation is solved using Runge-Kutta or other numerical methods to obtain estimates of the state error covariance matrix. Then, the eigenvalues ​​or diagonal elements of this matrix are calculated to effectively analyze the observability of the navigation system. The final evolution of the observability index in the x-direction is shown in the appendix. Figure 2 As shown.

[0072] According to one aspect of the present invention, an electronic device is provided, comprising: one or more processors, one or more memories, and one or more computer programs; wherein the processor is connected to the memory, and the one or more computer programs are stored in the memory; when the electronic device is running, the processor executes the one or more computer programs stored in the memory to cause the electronic device to perform an analysis method for the observability evolution of a radio navigation system as described in any of the above technical solutions.

[0073] According to one aspect of the present invention, a computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement an analysis method for the observability evolution of a radio navigation system as described in any of the above technical solutions.

[0074] This invention discloses a method, device, and storage medium for analyzing the observability evolution of a radio navigation system. The method includes: step S1, determining the error evolution of the spacecraft's state variables; step S2, obtaining the impact of observations on the error covariance matrix based on the information gain from each observation; and step S3, calculating the error estimation matrix used to analyze system observability. By making the changes in the estimation error caused by observations continuous and taking into account the accumulation of observation information, this invention effectively solves the problem that the Fischer information matrix cannot reflect the differences between different orbiters when performing observability analysis on a single orbiter.

[0075] Furthermore, by simultaneously calculating the changes in the error covariance matrix caused by the accumulation of dynamic model and observation information, this invention can more effectively reflect the evolution trend of state quantity errors and more effectively and intuitively reflect the impact of each radio observation, especially in environments with relatively complex dynamic models.

[0076] Meanwhile, this invention, through the concept of information filtering and the Fisher information matrix of the observation equation, directly bypasses the nonlinear filtering process and obtains the influence of each observation on the estimated error covariance matrix.

[0077] Furthermore, it should be noted that the present invention can be provided as a method, apparatus, or computer program product. Therefore, embodiments of the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, embodiments of the present invention can take the form of a computer program product implemented on one or more computer-usable storage media containing computer-usable program code.

[0078] Embodiments of the present invention are described with reference to flowchart illustrations and / or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0079] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing terminal equipment to cause a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0080] It should also be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0081] Finally, it should be noted that the above description represents a preferred embodiment of the present invention. It should be pointed out that although preferred embodiments have been described, those skilled in the art, once they understand the basic inventive concept of the present invention, can make various improvements and modifications without departing from the principles described herein. These improvements and modifications should also be considered within the scope of protection of the present invention. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the embodiments of the present invention.

Claims

1. A method for analyzing the observability evolution of a radio navigation system, characterized in that, Includes the following steps: Step S1: Determine the error evolution of the spacecraft's state variables themselves; Step S2: Based on the information gain from each observation, obtain the impact of the observation on the error covariance matrix; Step S3: Calculate the error estimation matrix used to analyze the observability of the system, specifically including: Step S31: Perform continuous processing on the estimation error changes caused by observation; Step S32: Combine the influence of the dynamic part and the observation part obtained in steps S1 and S2 on the estimation error into the differential equation of the estimation error covariance matrix to obtain the evolution of the state quantity estimation error of the navigation process; Step S33: Then, use Runge-Kutta to solve the differential equation to obtain the estimated value of the state quantity error covariance matrix; Step S34: Calculate the eigenvalues ​​or diagonal elements of the estimated value of the state quantity error covariance matrix, and conduct an effective analysis of the observability of the navigation system to obtain the evolution of the observability index in the x direction.

2. The method for analyzing the observability evolution of a radio navigation system according to claim 1, characterized in that, Step S1 specifically includes: Step S11: Acquire spacecraft data and obtain the spacecraft's dynamic model; Step S12: Use the Fock-Planck-Kármán equation to obtain the evolution of the state quantity estimation error over time.

3. The method for analyzing the observability evolution of a radio navigation system according to claim 1, characterized in that, Step S2 specifically includes: Step S21: Calculate the information gain based on the observations obtained from each observation, according to the Fischer information matrix; Step S22: By transforming the information matrix and the error covariance matrix, the influence of observation on the error covariance matrix is ​​obtained; The observations refer to the relative distance and relative radial velocity between the detector and the radio orbiter, respectively.

4. The method for analyzing the observability evolution of a radio navigation system according to claim 3, characterized in that, In step S22, the influence of observations on the error covariance matrix is ​​obtained through the transformation relationship between the information matrix and the error covariance matrix, as shown in the formula: in, , These are the covariance matrices of the state quantity estimation errors before and after the observation update. Let be the Fisher information matrix of the observation equation.

5. The method for analyzing the observability evolution of a radio navigation system according to claim 4, characterized in that, In step S31, the variation in estimation error caused by observation is processed to be continuous, and the transformation rate of the state quantity covariance matrix brought about by observation at a fixed observation frequency is obtained: in, This represents the average interval between radio observations. , Let represent the real-time state covariance matrix and the Fisher information matrix of the observation equation, respectively.

6. The method for analyzing the observability evolution of a radio navigation system according to claim 1 or 5, characterized in that, In step S32, the formula for calculating the evolution of the state quantity estimation error is: in, This represents the covariance matrix of the spacecraft's state variables. This represents the Jacobian matrix of the state equation with respect to the state variables. Let be the Jacobian matrix of the state equation with respect to the unknown error term. Let be the autocovariance matrix of the error term. and T This represents the evolution of the error of the state variables themselves with the dynamic state equation. T This represents the estimation error caused by the inherent uncertainty of the state equation itself. This represents the impact of the amount of information from each observation on the state quantity estimation error.

7. An electronic device, characterized in that, include: One or more processors, one or more memories, and one or more computer programs; wherein the processor is connected to the memory, and the one or more computer programs are stored in the memory, and when the electronic device is running, the processor executes the one or more computer programs stored in the memory to cause the electronic device to perform the method for analyzing the observability evolution of a radio navigation system as described in any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, implement the method for analyzing the observability evolution of a radio navigation system as described in any one of claims 1 to 6.

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