A star-inertial installation error calibration method and system based on iterative filtering

Abstract

The application provides a kind of star inertial installation error calibration method and system based on iterative filtering, for the installation error between inertial navigation and star sensor affects the problem of star-sensitive attitude determination accuracy, the state space model and measurement model of iterative extended Kalman filter are constructed through the star vector under the body coordinate system of star sensor, ephemeris star vector and inertial information under the inertial coordinate system, the measurement jacobian matrix is obtained by derivation and calculation, the measurement jacobian matrix is substituted into the measurement model of iterative extended Kalman filter to iteratively estimate the installation error of inertial celestial combined navigation system, i.e. the installation error of inertial celestial combined navigation system, the function of calibrating the installation error of inertial celestial combined navigation system is realized.The application eliminates the influence of the installation error between inertial navigation system and star sensor on star-sensitive attitude determination, is suitable for combined navigation application occasion, and has good adaptability and high precision.

Description

Technical Field

[0001] The present invention belongs to the field of surveying and mapping technology, and in particular relates to a satellite inertial installation error calibration method and system based on iterative filtering. Background Art

[0002] Inertial navigation systems (INS) are widely used due to their advantages of all-day autonomous navigation. However, their navigation errors diverge over time. Star sensors (STARs), as high-precision optical sensors for attitude measurement, are a crucial component of astronomical navigation systems. They measure the vector orientation of stars in the STAR coordinate system, providing high-precision attitude reference information for the vehicle's attitude control and the astronomical navigation system. However, star sensor attitude measurement is affected by observation conditions such as weather, making it impossible to continuously output attitude information. Therefore, combining an INS with a star sensor can complement the advantages of both. The difference between the attitude information provided by the star sensor and the attitude information obtained by the INS solution is used as measurement information. Kalman filtering is then applied to estimate and correct the attitude misalignment angle calculated by the INS solution, thereby constructing an INS-astronomical integrated navigation system, effectively improving the navigation system's attitude determination and positioning accuracy.

[0003] However, during equipment installation, the installation error between the star sensor and the inertial navigation system will affect the attitude accuracy provided by the star sensor. Therefore, in order to eliminate the influence of the installation error on star sensor attitude measurement, it is necessary to accurately calibrate the installation error between the inertial navigation system and the star sensor, that is, to calibrate the installation error of the inertial astronomical integrated navigation system. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method and system for calibrating the installation error of an inertial astronomical integrated navigation system based on iterative filtering.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a satellite inertial installation error calibration method based on iterative filtering, comprising the following steps:

[0006] S0: Obtain the star vector in the star sensor body coordinate system through the star sensor, obtain the corresponding ephemeris star vector in the inertial coordinate system, and obtain inertial information through the inertial navigation system;

[0007] S1: Construct the state space model and measurement model of iterative extended Kalman filter based on the star vector in the star sensor body coordinate system, the ephemeris star vector in the inertial coordinate system and the inertial information;

[0008] S2: Based on the state space model and measurement model of the iterative extended Kalman filter, the measurement Jacobian matrix is ​​derived and calculated;

[0009] S3: Substitute the measurement Jacobian matrix into the measurement model of the iterative extended Kalman filter to iteratively estimate the installation error of the inertial astronomical integrated navigation system.

[0010] According to the above scheme, in step S1, the specific steps are:

[0011] S11: Select the three-dimensional installation error angle between the star sensor and the inertial navigation system as the system state variable of the input model; the system state variable at the current moment includes the product of the system state variable at the previous moment and the system state transfer matrix; the system state transfer matrix is ​​a third-order identity matrix;

[0012] S12: The measurement information output by the model at a certain moment is a nonlinear vector function of the system state variables, specifically expressed as the difference between the star vector in the star sensor body coordinate system and the star vector in the inertial navigation system coordinate system.

[0013] Furthermore, in step S11, the three-dimensional installation error angle includes a pitch direction installation error angle, a roll direction installation error angle, and a heading direction installation error angle.

[0014] Furthermore, in step S12, the star vector in the inertial navigation system coordinate system is the product of the attitude matrix obtained by pure inertial navigation, the matrix of the earth coordinate system represented by local longitude and latitude relative to the geographic coordinate system, the matrix of the inertial system represented by Greenwich sidereal time relative to the earth system, and the ephemeris star vector in the inertial coordinate system corresponding to the star sensor body coordinate system.

[0015] Furthermore, in step S12, the product is expressed as the product of the attitude matrix of the star sensor body coordinate system relative to the inertial navigation system coordinate system and the star vector in the star sensor body coordinate system; the attitude matrix of the star sensor body coordinate system relative to the inertial navigation system coordinate system is an attitude matrix represented by a three-dimensional installation error angle, i.e., a system state variable.

[0016] Furthermore, in the step S1,

[0017] The system state variables also include system noise; the system noise is the product of the system noise distribution matrix and the system noise vector;

[0018] The measurement information of the system at a certain moment also includes measurement noise;

[0019] Both the system noise and the measurement noise are zero-mean Gaussian white noise.

[0020] According to the above scheme, in step S2, the specific steps are:

[0021] S21: Obtaining one-step state prediction in iterative extended Kalman filter based on system state variables;

[0022] S22: Substitute the one-step state prediction in the iterative extended Kalman filter into the nonlinear vector function and derive the measurement Jacobian matrix.

[0023] According to the above scheme, in step S3, the specific steps are:

[0024] S31: Substitute the measurement Jacobian matrix into the measurement model of the iterative extended Kalman filter and perform pre-filtering according to the ordinary extended Kalman filter method;

[0025] S32: Perform iterative filtering to complete the calibration of the installation error of the inertial astronomical integrated navigation system.

[0026] A satellite inertial installation error calibration system based on iterative filtering,

[0027] The data acquisition submodule is used to obtain the star vector in the star sensor body coordinate system through the star sensor, obtain the corresponding ephemeris star vector in the inertial coordinate system, and obtain inertial information through the inertial navigation system;

[0028] The model construction submodule is used to construct the state space model and measurement model of the iterative extended Kalman filter based on the star vector in the star sensor body coordinate system, the ephemeris star vector in the inertial coordinate system and the inertial information;

[0029] The matrix calculation submodule is used to derive and calculate the measurement Jacobian matrix based on the state space model and measurement model of the iterative extended Kalman filter;

[0030] The error estimation submodule is used to substitute the measurement Jacobian matrix into the measurement model of the iterative extended Kalman filter to iteratively estimate the installation error of the inertial astronomical integrated navigation system.

[0031] A computer memory stores a computer program executable by a computer processor. The computer program executes a satellite inertial installation error calibration method based on iterative filtering.

[0032] The beneficial effects of the present invention are:

[0033] 1. The present invention provides a method and system for calibrating the star-inertial navigation system installation error based on iterative filtering. This method addresses the problem that the installation error between an inertial navigation system and a star sensor affects the accuracy of star-sensor attitude measurement. The method constructs a state space model and a measurement model of an iterative extended Kalman filter using a star vector in a star sensor body coordinate system, an ephemeris star vector in an inertial coordinate system, and inertial information. The measurement Jacobian matrix is ​​then derived and calculated to obtain the measurement Jacobian matrix. The measurement Jacobian matrix is ​​then substituted into the measurement model of the iterative extended Kalman filter to iteratively estimate the installation error of an inertial astronomical integrated navigation system, thereby achieving a function of calibrating the installation error of the inertial astronomical integrated navigation system.

[0034] 2. The application eliminates the influence of installation error between inertial navigation system and star sensor on star-sensitive attitude measurement, is suitable for combined navigation application occasions, and is good in adaptability and high in precision.

[0035] Of course, implementing any product of the application does not necessarily need to achieve all the advantages mentioned above at the same time. BRIEF DESCRIPTION OF DRAWINGS

[0036] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without any creative effort.

[0037] Figure 1 is a flowchart of an embodiment of the present application.

[0038] Figure 2 is a flowchart of iterative filtering of an embodiment of the present application. DETAILED DESCRIPTION

[0039] In order to make the objects, technical solutions and advantages of the present application more clear, the following will further describe the present application in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and are not used to limit the present application.

[0040] Embodiment 1

[0041] Referring to Figure 1 The specific steps of a star-inertial installation error calibration method based on iterative filtering are as follows:

[0042] S0: obtaining a star vector in a star sensor body coordinate system through a star sensor, obtaining a ephemeris star vector in an inertial coordinate system correspondingly, and obtaining inertial information through an inertial navigation system;

[0043] S1: constructing a state space model and a measurement model of an iterative extended Kalman filter according to the star vector in the star sensor body coordinate system, the ephemeris star vector in the inertial coordinate system and the inertial information;

[0044] S2: deriving and calculating a measurement Jacobian matrix based on the state space model and the measurement model of the iterative extended Kalman filter;

[0045] S3: substituting the measurement Jacobian matrix into the measurement model of the iterative extended Kalman filter, and iteratively estimating an installation error of an inertial astronomical combined navigation system.

[0046] Further, in step S1, the specific steps are as follows:

[0047] S11: Select the three-dimensional installation error angle between the star sensor and the inertial navigation system as the system state variable of the input model; the system state variable at the current moment includes the product of the system state variable at the previous moment and the system state transfer matrix; the system state transfer matrix is ​​a third-order identity matrix;

[0048] S12: The measurement information output by the model at a certain moment is a nonlinear vector function of the system state variables, specifically expressed as the difference between the star vector in the star sensor body coordinate system and the star vector in the inertial navigation system coordinate system.

[0049] Furthermore, in step S11 , the three-dimensional installation error angle includes a pitch direction installation error angle, a roll direction installation error angle, and a heading direction installation error angle.

[0050] Furthermore, in step S12, the star vector in the inertial navigation system coordinate system is the product of the attitude matrix obtained by pure inertial navigation, the matrix of the earth coordinate system represented by local longitude and latitude relative to the geographic coordinate system, the matrix of the inertial system represented by Greenwich sidereal time relative to the earth system, and the ephemeris star vector in the inertial coordinate system corresponding to the star sensor body coordinate system.

[0051] Furthermore, in step S12, the product is expressed as the product of the attitude matrix of the star sensor body coordinate system relative to the inertial navigation system coordinate system and the star vector in the star sensor body coordinate system; the attitude matrix of the star sensor body coordinate system relative to the inertial navigation system coordinate system is an attitude matrix represented by a three-dimensional installation error angle, i.e., a system state variable.

[0052] In step S1, the system state variables also include system noise; the system noise is the product of the system noise distribution matrix and the system noise vector; the measurement information of the system at a certain moment also includes measurement noise; the system noise and measurement noise are both zero-mean Gaussian white noise.

[0053] In step S2, the specific steps are:

[0054] S21: Obtaining one-step state prediction in iterative extended Kalman filter based on system state variables;

[0055] S22: Substitute the one-step state prediction in the iterative extended Kalman filter into the nonlinear vector function and derive the measurement Jacobian matrix.

[0056] In step S3, the specific steps are:

[0057] S31: Substitute the measurement Jacobian matrix into the measurement model of the iterative extended Kalman filter and perform pre-filtering according to the ordinary extended Kalman filter method;

[0058] S32: Perform iterative filtering to complete the calibration of the installation error of the inertial astronomical integrated navigation system.

[0059] This embodiment addresses the issue of the installation error between the inertial navigation system and the star sensor affecting the accuracy of star sensor attitude measurement. By constructing a state space model and a measurement model of an iterative extended Kalman filter using the star vector in the star sensor's coordinate system, the ephemeris star vector in the inertial coordinate system, and inertial information, the state space model and measurement model of the iterative extended Kalman filter are derived and calculated. The measurement Jacobian matrix is ​​then substituted into the measurement model of the iterative extended Kalman filter to iteratively estimate the installation error of the inertial astronomical integrated navigation system, thereby achieving the function of calibrating the installation error of the inertial astronomical integrated navigation system.

[0060] Example 2

[0061] The steps of this embodiment are the same as those of embodiment 1, except that each step is applied to a specific example. Specifically, the following steps are included:

[0062] S1: Based on the star vector in the star sensor body coordinate system and the ephemeris star vector and inertial information obtained by the star sensor, the state space model and measurement model of the iterative extended Kalman filter are constructed. Specifically:

[0063]

[0064] Where, For the system The state variable at time t is selected as the three-dimensional installation error angle between the star sensor and the inertial navigation system, as follows:

[0065]

[0066] in They are the pitch direction installation error angle, roll direction installation error angle, and heading direction installation error angle between the two respectively. That is the system The state of the moment.

[0067] is the system state transfer matrix. Since the inertial navigation system and the star sensor are installed in a fixed connection manner in the inertial astronomical integrated navigation system, the installation error angle is a constant, that is, is the third-order identity matrix.

[0068] is the system noise allocation matrix, is the system noise vector.

[0069] for The measurement information at the moment is expressed as follows:

[0070]

[0071] in is the star sensor body coordinate system, The system is an inertial coordinate system, is the inertial navigation system coordinate system, The coordinate system is the Earth coordinate system, The system is the navigation coordinate system (select the geographic coordinate system), It is the star vector in the star sensor body coordinate system measured by the star sensor. That is the ephemeris star vector in the corresponding inertial system, is the attitude matrix obtained by pure inertial navigation, is the matrix of the earth coordinate system expressed by the local longitude and latitude relative to the geographic coordinate system, is the matrix of the inertial system expressed in Greenwich sidereal time relative to the Earth's system.

[0072] For measurement information About system state variables The nonlinear vector function is expressed as follows:

[0073]

[0074] in is the attitude matrix of the star sensor body coordinate system relative to the inertial navigation system coordinate system, which is composed of the three-dimensional installation error angle The posture matrix represented by is as follows:

[0075]

[0076] is the measurement noise vector, and both the system noise and the measurement noise are zero-mean Gaussian white noise, that is:

[0077]

[0078] in is the system noise variance matrix, To measure the noise variance matrix, it is generally required is positive definite and is non-negative definite.

[0079] S2: Based on the state space model and measurement model of iterative extended Kalman filter, the measurement Jacobian matrix is ​​derived and calculated. for:

[0080]

[0081] in For the one-step prediction of the state in the iterative extended Kalman filter, it is expressed as follows:

[0082]

[0083] is a nonlinear vector function The dimension in which it is located.

[0084] S3: Substitute the measurement Jacobian matrix into the measurement model of the iterative extended Kalman filter to iteratively estimate the installation error of the inertial astronomical integrated navigation system.

[0085] The filtering equation is as follows:

[0086] First, pre-filtering is performed according to the ordinary extended Kalman filter method, as follows:

[0087]

[0088] in .

[0089] Then perform iterative filtering as follows:

[0090]

[0091] in .

[0092] This completes the calibration of the installation error of the inertial astronomical integrated navigation system.

[0093] This embodiment eliminates the influence of the installation error between the inertial navigation system and the star sensor on the star sensor attitude measurement, is suitable for the application of combined navigation, and has good adaptability and high precision.

[0094] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0095] Example 3

[0096] This embodiment is used to implement the principle of the above method embodiment to construct a satellite inertial installation error calibration system based on iterative filtering, including a data acquisition submodule, a model construction submodule, a matrix calculation submodule and an error estimation submodule;

[0097] The data acquisition submodule is used to obtain the star vector in the star sensor body coordinate system through the star sensor, obtain the corresponding ephemeris star vector in the inertial coordinate system, and obtain inertial information through the inertial navigation system;

[0098] The model construction submodule is used to construct the state space model and measurement model of the iterative extended Kalman filter based on the star vector in the star sensor body coordinate system, the ephemeris star vector in the inertial coordinate system and the inertial information;

[0099] The matrix calculation submodule is used to derive and calculate the measurement Jacobian matrix based on the state space model and measurement model of the iterative extended Kalman filter;

[0100] The error estimation submodule is used to substitute the measurement Jacobian matrix into the measurement model of the iterative extended Kalman filter to iteratively estimate the installation error of the inertial astronomical integrated navigation system.

[0101] Each sub-module is mainly used to implement each step of the method embodiment, which will not be described in detail here.

[0102] It should be pointed out that, according to the needs of implementation, the various steps / components described in this application can be split into more steps / components, or two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of the present invention.

[0103] This embodiment also includes a processor, a communication interface, a memory, and a communication bus; wherein the processor, the communication interface, and the memory communicate with each other via the communication bus; the memory stores a computer program, and when the program is executed by the processor, the processor executes the steps of a satellite inertial installation error calibration method based on iterative filtering.

[0104] This embodiment further provides a computer-readable storage medium having executable instructions stored thereon. When the instructions are executed by a processor, the processor implements a satellite inertial installation error calibration method based on iterative filtering.

[0105] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware.

[0106] Moreover, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0107] This application is described with reference to the flowchart of the method and computer program product according to Embodiment 1 of the application. It should be understood that each process in the flowchart or block diagram, as well as the combination of processes in the flowchart, can be implemented by computer program instructions.

[0108] These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce the instructions for implementing the process Figure 1A star inertial error calibration system based on iterative filtering and a function specified in one or more processes.

[0109] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A function specified in a process or multiple processes.

[0110] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 The invention provides steps of a method for calibrating a satellite inertial installation error based on iterative filtering specified in a process or multiple processes.

[0111] The above embodiments are intended only to illustrate the design concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. The scope of protection of the present invention is not limited to the above embodiments. Therefore, any equivalent changes or modifications made based on the principles and design concepts disclosed in the present invention are within the scope of protection of the present invention.

Claims

1. A method for calibrating satellite inertial installation error based on iterative filtering, characterized by: The following steps are involved: S0: Obtain the star vector in the star sensor body coordinate system through the star sensor, obtain the corresponding ephemeris star vector in the inertial coordinate system, and obtain inertial information through the inertial navigation system; S1: Construct the state space model and measurement model of iterative extended Kalman filter based on the star vector in the star sensor body coordinate system, the ephemeris star vector in the inertial coordinate system and the inertial information; the specific steps are: S11: Select the three-dimensional installation error angle between the star sensor and the inertial navigation system as the system state variable of the input model; the system state variable at the current moment includes the product of the system state variable at the previous moment and the system state transfer matrix; the system state transfer matrix is ​​a third-order identity matrix; S12: The measurement information output by the model at a certain moment is a nonlinear vector function of the system state variables, specifically expressed as the difference between the star vector in the star sensor body coordinate system and the star vector in the inertial navigation system coordinate system; S2: Based on the state space model and measurement model of the iterative extended Kalman filter, the measurement Jacobian matrix is ​​derived and calculated; S3: Substitute the measurement Jacobian matrix into the measurement model of the iterative extended Kalman filter to iteratively estimate the installation error of the inertial astronomical integrated navigation system.

2. The method for calibrating satellite inertial installation error based on iterative filtering according to claim 1, characterized in that: In step S11, the three-dimensional installation error angle includes a pitch direction installation error angle, a roll direction installation error angle, and a heading direction installation error angle.

3. The method for calibrating satellite inertial installation error based on iterative filtering according to claim 1, characterized in that: In step S12, the star vector in the inertial navigation system coordinate system is the product of the attitude matrix obtained by pure inertial navigation, the matrix of the earth coordinate system represented by local longitude and latitude relative to the geographic coordinate system, the matrix of the inertial system represented by Greenwich sidereal time relative to the earth system, and the ephemeris star vector in the inertial coordinate system corresponding to the star sensor body coordinate system.

4. The method for calibrating satellite inertial installation error based on iterative filtering according to claim 3, characterized in that: In step S12, the product is expressed as the product of the attitude matrix of the star sensor body coordinate system relative to the inertial navigation system coordinate system and the star vector in the star sensor body coordinate system; the attitude matrix of the star sensor body coordinate system relative to the inertial navigation system coordinate system is an attitude matrix represented by a three-dimensional installation error angle, i.e., a system state variable.

5. The method for calibrating satellite inertial installation error based on iterative filtering according to claim 1, characterized in that: In the step S1, The system state variables also include system noise; the system noise is the product of the system noise distribution matrix and the system noise vector; The measurement information of the system at a certain moment also includes measurement noise; Both the system noise and the measurement noise are zero-mean Gaussian white noise.

6. The method for calibrating satellite inertial installation error based on iterative filtering according to claim 1, characterized in that: In the step S2, the specific steps are: S21: Obtaining one-step state prediction in iterative extended Kalman filter based on system state variables; S22: Substitute the one-step state prediction in the iterative extended Kalman filter into the nonlinear vector function and derive the measurement Jacobian matrix.

7. The method for calibrating satellite inertial installation error based on iterative filtering according to claim 1, characterized in that: In the step S3, the specific steps are: S31: Substitute the measurement Jacobian matrix into the measurement model of the iterative extended Kalman filter and perform pre-filtering according to the ordinary extended Kalman filter method; S32: Perform iterative filtering to complete the calibration of the installation error of the inertial astronomical integrated navigation system.

8. A satellite inertial installation error calibration system based on iterative filtering, characterized by: The data acquisition submodule is used to obtain the star vector in the star sensor body coordinate system through the star sensor, obtain the corresponding ephemeris star vector in the inertial coordinate system, and obtain inertial information through the inertial navigation system; The model construction submodule is used to construct the state space model and measurement model of the iterative extended Kalman filter based on the star vector in the star sensor body coordinate system, the ephemeris star vector in the inertial coordinate system, and the inertial information. Specifically, it includes: The three-dimensional installation error angle between the star sensor and the inertial navigation system is selected as the system state variable of the input model; the system state variable at the current moment includes the product of the system state variable at the previous moment and the system state transfer matrix; the system state transfer matrix is ​​a third-order unit matrix; The measurement information output by the model at a certain moment is a nonlinear vector function of the system state variables, specifically expressed as the difference between the star vector in the star sensor body coordinate system and the star vector in the inertial navigation system coordinate system; The matrix calculation submodule is used to derive and calculate the measurement Jacobian matrix based on the state space model and measurement model of the iterative extended Kalman filter; The error estimation submodule is used to substitute the measurement Jacobian matrix into the measurement model of the iterative extended Kalman filter to iteratively estimate the installation error of the inertial astronomical integrated navigation system.

9. A computer memory, characterized in that: A computer program executable by a computer processor is stored therein, and the computer program executes a satellite inertial installation error calibration method based on iterative filtering as described in any one of claims 1 to 7.

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