CN115014393A - Dynamic time-varying observability degree analysis method and device suitable for inertial navigation system - Google Patents
Dynamic time-varying observability degree analysis method and device suitable for inertial navigation system Download PDFInfo
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Abstract
The application discloses a dynamic time-varying observability degree analysis method and device suitable for an inertial navigation system. Wherein, the method comprises the following steps: acquiring a discrete state space model of an inertial navigation system, and performing observable map analysis between each error state variable and an output measurement variable of the discrete state space model; based on the observability graph analysis, calculating and standardizing the observability degree of each inertial device error variable of the inertial navigation system to obtain an observability degree analysis graph of the inertial navigation system; and dynamically analyzing the observability degree change of each inertial device error in the inertial navigation system in a time-varying manner based on the observability degree analysis graph. The method and the device solve the technical problem that the analysis effect on the tiny errors of the inertial device is not obvious.
Description
Technical Field
The application belongs to the technical field of multi-source fusion navigation, and particularly relates to a dynamic time-varying observability degree analysis method and device suitable for an inertial navigation system.
Background
The inertial navigation is a completely autonomous navigation technology developed in the middle of the 20 th century, angular rate and acceleration information of a carrier relative to an inertial space are measured through an inertial measurement component, instantaneous speed and position information of the carrier are automatically calculated by utilizing the Newton's law of motion, and the inertial navigation system has the advantages of being independent of external information, free of energy radiation to the outside, free of external interference and good in concealment, can work on the surface of the earth or even underwater all day long and all the time, and continuously provides all navigation parameters (position, linear speed, angular speed and attitude angle) required by the carrier. For more than 30 years, inertial navigation technology in China has been rapidly developed and has been applied to navigation and positioning of aviation, aerospace, navigation and land vehicles.
Correspondingly, the inertial navigation system has many inertial device errors, such as gyroscope drift and accelerometer zero offset, which may cause navigation positioning errors of the inertial navigation system to accumulate over time, resulting in a decrease in the accuracy and reliability of the inertial navigation system in long-term operation. In order to overcome the defect of the inertial navigation system, at present, while the inherent advantages of the inertial navigation system are maintained, two technical approaches mainly exist to suppress the error of an inertial device: firstly, performing rotation modulation on an inertial device so as to construct a rotation modulation type strapdown inertial navigation system; and the second is a combined navigation technology, which realizes the error compensation of the inertial navigation system through combined navigation among a plurality of navigation systems. In order to verify the error suppression effect of different technologies on the inertial navigation system, observability analysis can be performed on the system.
The observability representation output can completely reflect the characteristics of the system state, and in a navigation system formed by an inertial device, since a plurality of error variables are difficult to directly measure and analyze, the observability degree analysis is a very intuitive and effective method. The traditional observability degree analysis method is complex in process, difficult to realize through programming, and insignificant in analysis effect on small errors of inertial devices.
In view of the above problems, no effective solution has been proposed.
Disclosure of Invention
The embodiment of the application provides a dynamic time-varying observability degree analysis method and device suitable for an inertial navigation system, and the method and device at least solve the technical problem that the analysis effect on small errors of an inertial device is not obvious.
According to an aspect of the embodiment of the application, a method for analyzing a dynamic time-varying observability measure of an inertial navigation system error is provided, and the method includes: acquiring a discrete state space model of an inertial navigation system, and performing observable map analysis between each error state variable and an output measurement variable of the discrete state space model; based on the observability graph analysis, calculating and standardizing the observability degree of each inertial device error variable of the inertial navigation system to obtain an observability degree analysis graph of the inertial navigation system; and dynamically analyzing the observability degree change of each inertial device error in the inertial navigation system in a time-varying manner based on the observability degree analysis graph.
According to another aspect of the embodiments of the present application, there is also provided an apparatus for analyzing dynamic time-varying observability of inertial navigation system error, including: the acquisition module is configured to acquire a discrete state space model of the inertial navigation system and perform observable map analysis between each error state variable and an output measurement variable of the discrete state space model; the calculation module is configured to calculate and standardize the observability degree of each inertial device error variable of the inertial navigation system based on the observability graph analysis to obtain an observability degree analysis graph of the inertial navigation system; an analysis module configured to dynamically time-varying analyze observability level changes of inertial device errors in the inertial navigation system based on the observability level analysis graph.
In the embodiment of the application, a discrete state space model of an inertial navigation system is obtained, and observable graph analysis is carried out between each error state variable and an output measurement variable of the discrete state space model; based on the observability graph analysis, calculating and standardizing the observability degree of each inertial device error variable of the inertial navigation system to obtain an observability degree analysis graph of the inertial navigation system; based on the observability degree analysis graph, the observability degree change of errors of each inertial device in the inertial navigation system is dynamically analyzed in a time-varying manner, the technical problem that the analysis effect of small errors of the inertial devices is not obvious is solved, and the method has the beneficial effect of obvious analysis effect of the small errors of the inertial devices.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the application and together with the description serve to explain the application and not to limit the application. In the drawings:
FIG. 1 is a flowchart of a method for analyzing a dynamic time-varying observability measure of an inertial navigation system error according to a first embodiment of the present application;
FIG. 2 is a flowchart of a method for analyzing a dynamic time-varying observability measure of an inertial navigation system error according to a second embodiment of the present application;
FIG. 3 is a flowchart of a method for analyzing a dynamic time-varying observability measure of an inertial navigation system error according to a third embodiment of the present application;
FIG. 4 is an observability graph analysis of an inertial navigation system according to an embodiment of the present application;
FIG. 5 is a graph of results of dynamic time-varying observability analysis of an inertial navigation system according to an embodiment of the present application;
FIG. 6 is a schematic structural diagram of an apparatus for analyzing a dynamic time-varying observability level of an inertial navigation system error according to an embodiment of the present application.
Detailed Description
In order to make the technical solutions better understood by those skilled in the art, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only partial embodiments of the present application, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
It should be noted that the terms "first," "second," and the like in the description and claims of this application and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the application described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Example 1
According to an embodiment of the application, a method for analyzing a dynamic time-varying observability measure of an inertial navigation system error is provided, as shown in fig. 1, the method includes:
step S102, obtaining a discrete state space model of the inertial navigation system, and performing observability graph analysis between each error state variable and each output measurement variable of the discrete state space model.
For example, an error model of the inertial navigation system is obtained; and selecting error variables of all inertial devices of the inertial navigation system as state variables, and discretizing the error model in continuous time to obtain the discrete state space model.
For example, in the ith row and jth column of the output matrix H of the discrete state space model ij Under the condition of not being zero, the j error state variable is shown to influence the i output variable measurement, and therefore each error state variable x of the inertial navigation system is determined k And an output variable z k Wherein the output matrix H is an n x m dimensional matrix.
And step S104, calculating and standardizing the observability degree of each inertial component error variable of the inertial navigation system based on the observability graph analysis to obtain an observability degree analysis graph of the inertial navigation system.
For example, based on the observability graph analysis, a higher order system dimension reduction decomposition is performed; calculating a state variable root mean square, an observability matrix and a measurement variable root mean square based on the high-order system dimensionality reduction decomposition; calculating the observability degree of each error state variable based on the calculated state variable root mean square, observability matrix and measurement variable root mean square; and normalizing the observability degrees of the error state variables to obtain the normalized observability degrees of the error state variables so as to obtain an observability degree analysis graph of the inertial navigation system.
In an exemplary embodiment, based on the observability graph analysis, performing a high-order system dimension reduction decomposition, comprising: decomposing the high-dimensional system of the discrete state space model into low-dimensional subsystems according to the error types of the inertial devices based on the analysis of the observability diagram, wherein the state transition matrix and the output matrix corresponding to the first subsystem are respectively F l And H l And the dimension l of each subsystem 1 +l 2 +.. ═ m, where l 1 Dimension representing the 1 st subsystem, l 2 Representing the dimension of the 2 nd subsystem, and m represents the number of columns of the output matrix H of the discrete state space model.
In an exemplary embodiment, calculating the state variable root mean square, the observability matrix and the measure variable root mean square based on the high-order system dimensionality reduction decomposition comprises: from said state transition matrix F l And the output matrix H l Computing observability matrices
And pseudo-inverse obtaining
Wherein "+" represents the pseudo-inverse; calculating an error state variable x from k-m to k i Root mean square e of the estimate k (x i ) As the state variable root mean square; calculating the output variable y from k-m to k i Root mean square e of the measured values k (y i ) As the root mean square of the measurement variable.
In one exemplary embodiment, calculating observability measures for respective error state variables based on the calculated state variable root mean square, observability matrix and measurand root mean square includes: calculating the observability matrix based on the calculated state variable root mean square, observability matrix and measuration variable root mean square
Row elements and square roots of
Obtaining the ith error state variable to obtain each error state variable; calculating the observability degree of each error state variable by adopting a logarithm mode based on the analysis result of the observability graph
In an exemplary embodiment, normalizing the observability measures of the respective error state variables to obtain normalized observability measures of the error state variables comprises: taking an absolute value of the calculation results of the observability degrees of all the error state variables; and setting the error state variable with the maximum absolute value as an unobservable quantity, and standardizing the calculation results of the observability degrees of all the error state variables by taking the set unobservable quantity as a reference to obtain the observability degrees of the error state variables after standardization.
And S106, dynamically analyzing the observability degree change of the errors of the inertial devices in the inertial navigation system in a time-varying manner based on the observability degree analysis graph.
For example, the observability measure of the normalized error state variable is analyzed; when the observable degree of the error state variable is 0, the error state variable is an unobservable quantity; a fully observable when the observable of the error state variable is 1; the higher the value of the observability measure of the error state variable, the stronger the observability of the error state variable.
The application discloses a method for analyzing dynamic time-varying observability degree of inertial navigation system errors, which is easy to realize system programming, is convenient for clearly analyzing the observability degree of each error variable of an inertial device, and has strong practical value in the analysis of the inertial navigation system errors.
Example 2
According to the embodiment of the application, another method for analyzing the dynamic time-varying observability degree of the inertial navigation system error is provided.
The method can analyze the problem of the change of the observable degree of each inertial device error in the inertial navigation system in a dynamic time-varying manner. And after the discrete state space model of the inertial navigation system is obtained, performing observable graph analysis between each error state variable and each output measurement variable, further calculating and standardizing the observable degree of each inertial device error variable, and obtaining an observable degree analysis graph of the inertial navigation system.
In an exemplary embodiment, the state transition matrix of the inertial navigation system determines the corresponding relationship between each error state variable and the output measurement variable of the system, so as to obtain the observability graph analysis.
In one exemplary embodiment, the high-dimensional system is decomposed into individual low-dimensional subsystems by inertial device error type based on observability graph analysis results.
In one exemplary embodiment, the observability matrix of the system is computed by the state transition matrix and the output matrix, and then pseudo-inverted.
In an exemplary embodiment, observability degrees of various error state variables of the system are calculated and standardized based on the observability graph analysis result, and an observability degree analysis graph of the inertial navigation system is obtained.
Specifically, as shown in fig. 2, the method for analyzing the dynamic time-varying observability of the inertial navigation system provided in this embodiment includes the following steps:
step S202, a discrete state space model is obtained.
Obtaining an error model of the inertial navigation system, and selecting errors of each inertial device as a state variable x k (m-dimension), discretizing the continuous time model to obtain a discrete state space model, wherein F is a state transition matrix (m × m), G is an input matrix, H is an output matrix (n × m), z is an output measurement variable (n-dimension), W is process noise, v is measurement noise, and k represents the kth moment;
in step S204, observability graph analysis is performed.
The output matrix H of the system is an n x m-dimensional matrix which reflects the relationship between the m-dimensional state variables and the n-dimensional output measurement variables if the output matrix H has the ith row and the jth column of the element H ij If not, it means that the jth error state variable will affect the ith output variable measurement, thereby determining each state variable x of the system k And an output variable z k Observability graph analysis in between.
And step S206, performing high-order system dimension reduction decomposition.
Decomposing a high-dimensional system into low-dimensional subsystems according to the error types of the inertial devices based on the analysis result of the observability diagram, wherein the state transition matrix and the output matrix corresponding to the first subsystem are respectively F l And H l And the dimension l of each subsystem 1 +l 2 +...＝m。
In step S208, an observability matrix is calculated.
From the state transition matrix F l And an output matrix H l Computing observability matrices
And calculating the pseudo-inverse to obtain
Wherein "+" represents the pseudo-inverse;
wherein the content of the first and second substances,
an output matrix representing the time instant of the/th subsystem k,
an output matrix representing the time instant k +1 of the ith subsystem,
representing the state transition matrix at the moment/subsystem k,
representing the state transition matrix at the moment/subsystem k,
representing the state transition matrix at the moment of the/subsystem k + n-1,
representing the state transition matrix at the moment of the/subsystem k + n-2.
In step S210, a state variable root mean square, a measureable variable root mean square, and an observability matrix are calculated.
Calculating an error state variable x from k-m to k i Root mean square e of the estimate k (x i )；
Wherein x is i Representing the ith error state variable, E k Indicating taking the average.
Calculating an output variable y from k-m to k i Root mean square e of the measured values k (y i )；
Computing observability matrices
Row elements and square roots of
It corresponds to the ith error state variable;
wherein the content of the first and second substances,
observability matrix representing the k-th instant
Line i and line j.
Step S212, an observability level of each error state variable is calculated.
Computing observability degrees of respective error state variables based on observability graph analysis results
Because the errors of the inertial devices are all tiny, the calculation result of the observability degree is more visualized by adopting a logarithm taking mode;
and step S214, standardization.
Taking the absolute value of the calculation results of the observability degrees of all the error state variables, setting the error variable with the largest observability degree as an unobservable quantity, and taking the unobservable degree calculation result as the reference to the calculation results of the observability degrees of all the error state variables
Standardized to obtain
And obtaining an observability degree analysis graph of the inertial navigation system.
In step S216, the normalized observability measure is analyzed.
After being standardizedDegree of observability of
Analyzing, wherein the analysis criterion is unobservable quantity when the observable degree of the error state variable is O; a completely observable measure is 1; the higher the observability degree is, the stronger the observability of the error state variable is, and the better the estimation and compensation effects are.
Example 3
According to the embodiment of the application, another method for analyzing the dynamic time-varying observability degree of the inertial navigation system error is provided. In this embodiment, a discrete error state space model of the inertial navigation system is first obtained, and then observability graph analysis is performed between each error state variable and the output measurement variable, so that the observability degree of each state variable is calculated and normalized, and an observability degree analysis graph of the inertial navigation system is obtained.
The method for analyzing the dynamic time-varying observability of the inertial navigation system in this embodiment, as shown in fig. 3, includes the following steps:
step S302, discretizing the continuous time model to obtain a discrete state space model.
Obtaining an error model of the inertial navigation system, and selecting the errors of the triaxial gyro drift, the scale factor and the installation angle of an inertial device as state variables x k (24 dimensions), and then discretizing the continuous-time model to obtain a discrete state space model, wherein F is a state transition matrix (24 × 24), G is an input matrix, H is an output matrix (2 × 24), z is an output measurement variable (2 dimensions, rotation angle measurement values of inertial navigation A and B), W is process noise, v is measurement noise, and k represents the kth moment.
Step S304, the observability graph is analyzed.
The output matrix H of the system is a 2 x 24 dimensional matrix reflecting the relationship between the 24 dimensional state variables and the 2 dimensional output measurement variables if the output matrix H is the ith row and the jth column of the element H ij Is not zero, and the power is not zero,it means that the jth error state variable will affect the ith output variable measurement, and thus the error state variables x of the system can be determined k And an output measurement variable z k Observability graph analysis in between.
In step S306, the higher-order system will be decomposed.
Decomposing the high-dimensional system into low-dimensional subsystems according to the error types of the inertial devices based on the analysis result of the observability diagram, wherein the state transition matrix and the output matrix corresponding to the first subsystem are respectively F as shown in FIG. 4 l And H l And the dimension l of each subsystem 1 +l 2 +...＝24。
In step S308, an observability matrix is calculated.
From the state transition matrix F l And an output matrix H l Computing observability matrices
And pseudo-inverse obtaining
Wherein "+" represents the pseudo-inverse;
in step S310, a state variable root mean square is calculated.
Calculating an error state variable x from k-m to k i Root mean square e of the estimate k (x i )。
In step S312, a root mean square of the measurement variable is calculated.
Calculating the output variable y from k-m to k i Root mean square e of measurement values k (y i )；
Step S314, the observability level is calculated.
Computing observability matrices
Row elements and square roots of
It corresponds to the ith error state variable;
computing observability degrees of respective error state variables based on observability graph analysis results
Because the errors of the inertial devices are all tiny, the calculation result of the observability degree is more visualized by adopting a logarithm taking mode;
step S316, the normalized observability matrix is calculated.
Taking the absolute value of the calculation results of the observability degrees of all the error state variables, setting the error variable with the largest observability degree as an unobservable quantity, and taking the unobservable degree calculation result as the reference to the calculation results of the observability degrees of all the error state variables
Standardized to obtain
Further obtaining an observability degree analysis graph of the inertial navigation system, as shown in fig. 5;
in step S318, observability degree analysis is performed.
For the normalized observability degree
Analyzing, wherein the analysis criterion is that the observable degree of the error state variable is 0, and the observable degree is unobservable; the complete observability is obtained when the observability degree is 1; the higher the observability degree is, the stronger the observability of the error state variable is, and the better the estimation and compensation effects are.
The method for analyzing the dynamic time-varying observability of the inertial navigation system error can calculate and standardize the observability of the scale factor error, the installation angle error and the gyroscope drift error of an inertial device in the inertial navigation system, and is convenient for visual analysis.
In addition, the complexity of observability degree analysis is simplified, the designed dynamic time-varying observability degree analysis method is easy to realize by system programming, the calculation result is convenient for clearly analyzing the observability degree change of each error state variable of the inertial device, and the method has strong practical value in the error analysis of the inertial navigation system.
It should be noted that, for simplicity of description, the above-mentioned method embodiments are described as a series of acts or combination of acts, but those skilled in the art will recognize that the present application is not limited by the order of acts described, as some steps may occur in other orders or concurrently depending on the application. Further, those skilled in the art should also appreciate that the embodiments described in the specification are preferred embodiments and that the acts and modules referred to are not necessarily required in this application.
Through the above description of the embodiments, those skilled in the art can clearly understand that the method according to the above embodiments can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware, but the former is a better implementation mode in many cases. Based on such understanding, the technical solutions of the present application may be embodied in the form of a software product, which is stored in a storage medium (e.g., ROM/RAM, magnetic disk, optical disk) and includes instructions for enabling a terminal device (e.g., a mobile phone, a computer, a server, or a network device) to execute the method according to the embodiments of the present application.
Example 4
According to an embodiment of the present application, there is further provided an apparatus for analyzing a dynamic time-varying observability measure of an inertial navigation system error, as shown in fig. 6, including: an acquisition module 62, a calculation module 64, and an analysis module 66.
The obtaining module 62 is configured to obtain a discrete state space model of the inertial navigation system, and perform observability map analysis between each error state variable and an output metrology variable of the discrete state space model.
For example, the obtaining module 62 is configured to obtain an error model of the inertial navigation system; and selecting error variables of all inertial devices of the inertial navigation system as state variables, and discretizing the error model in continuous time to obtain the discrete state space model.
In an exemplary embodiment, the obtaining module 62 is configured to obtain the ith row and the jth column of the output matrix H of the discrete state space model ij Under the condition of not being zero, the j error state variable is shown to influence the i output variable measurement, and therefore each error state variable x of the inertial navigation system is determined k And an output variable z k Wherein the output matrix H is an n x m dimensional matrix.
The calculation module 64 is configured to calculate and normalize observability levels of respective inertial device error variables of the inertial navigation system based on the observability graph analysis, obtaining an observability level analysis graph of the inertial navigation system.
For example, the calculation module 64 is configured to perform a higher order system dimension reduction decomposition based on the observability graph analysis; calculating a state variable root mean square, an observability matrix and a measurement variable root mean square based on the high-order system dimensionality reduction decomposition; calculating the observability degree of each error state variable based on the calculated state variable root mean square, observability matrix and measurement variable root mean square; and normalizing the observability degrees of the error state variables to obtain the normalized observability degrees of the error state variables so as to obtain an observability degree analysis graph of the inertial navigation system.
In an exemplary embodiment, calculation module 64 is configured to perform a higher order system dimension reduction decomposition based on the observability graph analysis, including: decomposing the high-dimensional system of the discrete state space model into low-dimensional subsystems according to the error types of the inertial devices based on the analysis of the observability diagram, wherein the state transition matrix and the output matrix corresponding to the first subsystem are respectively F l And H l And the dimension l of each subsystem 1 +l 2 +.. ═ m, where l 1 Dimension representing the 1 st subsystem, l 2 Representing the dimension of the 2 nd subsystem, and m represents the number of columns of the output matrix H of the discrete state space model.
In an exemplary embodiment, the calculation module 64 is configured to calculate the state variable root mean square, the observability matrix and the measure variable root mean square based on the high-order system dimensionality reduction decomposition, including: from said state transition matrix F l And the output matrix H l Computing observability matrices
And pseudo-inverse obtaining
Wherein "+" represents the pseudo-inverse; calculating an error state variable x from k-m to k i Root mean square e of the estimate k (x i ) As the state variable root mean square; calculating the output variable y from k-m to k i Root mean square e of the measured values k (y i ) As the root mean square of the measurement variable.
In one exemplary embodiment, the calculation module 64 is configured to calculate the root mean square, observability moments based on the calculated state variablesArray and measurement variable root mean square, calculating the observability degree of each error state variable, including: calculating the observability matrix based on the calculated state variable root mean square, observability matrix and measuration variable root mean square
Row elements and square roots of
Obtaining the ith error state variable to obtain each error state variable; calculating the observability degree of each error state variable by adopting a logarithm mode based on the analysis result of the observability graph
In an exemplary embodiment, the calculation module 64 is configured to normalize the observability measures of the respective error state variables to obtain normalized observability measures of the error state variables, including: taking absolute values of the calculation results of the observability degrees of all the error state variables; and setting the error state variable with the maximum absolute value as an unobservable quantity, and standardizing the calculation results of the observability degrees of all the error state variables by taking the set unobservable quantity as a reference to obtain the observability degrees of the error state variables after standardization.
The analysis module 66 is configured to dynamically time-varying analyze changes in the observability level of each inertial device error in the inertial navigation system based on the observability level analysis map.
In an exemplary embodiment, the analysis module 66 is configured to analyze the observability measure of the normalized error state variables; when the observable degree of the error state variable is 0, the error state variable is an unobservable quantity; a fully observable when the observable of the error state variable is 1; the higher the value of the observability measure of the error state variable, the stronger the observability of the error state variable.
Example 5
Embodiments of the present application also provide a storage medium. In the present embodiment, a storage medium is provided to store program codes for executing the steps in embodiments 1 to 3.
Optionally, in this embodiment, the storage medium may include, but is not limited to: a U-disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a removable hard disk, a magnetic or optical disk, and other various media capable of storing program codes.
The above-mentioned serial numbers of the embodiments of the present application are merely for description and do not represent the merits of the embodiments.
The integrated unit in the above embodiments, if implemented in the form of a software functional unit and sold or used as a separate product, may be stored in the above computer-readable storage medium. Based on such understanding, the technical solution of the present application may be substantially implemented or a part of or all or part of the technical solution contributing to the prior art may be embodied in the form of a software product stored in a storage medium, and including instructions for causing one or more computer devices (which may be personal computers, servers, network devices, or the like) to execute all or part of the steps of the method described in the embodiments of the present application.
In the above embodiments of the present application, the descriptions of the respective embodiments have respective emphasis, and for parts that are not described in detail in a certain embodiment, reference may be made to related descriptions of other embodiments.
In the several embodiments provided in the present application, it should be understood that the disclosed client may be implemented in other ways. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one type of division of logical functions, and there may be other divisions when actually implemented, for example, a plurality of units or components may be combined or may be integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, units or modules, and may be in an electrical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present application may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, and can also be realized in a form of a software functional unit.
The foregoing is only a preferred embodiment of the present application and it should be noted that those skilled in the art can make several improvements and modifications without departing from the principle of the present application, and these improvements and modifications should also be considered as the protection scope of the present application.
Claims (10)
1. A method for analyzing dynamic time-varying observability of inertial navigation system errors is characterized by comprising the following steps:
acquiring a discrete state space model of an inertial navigation system, and performing observable map analysis between each error state variable and an output measurement variable of the discrete state space model;
based on the observability graph analysis, calculating and standardizing the observability degree of each inertial device error variable of the inertial navigation system to obtain an observability degree analysis graph of the inertial navigation system;
and analyzing the change of the observability degree of the error of each inertial device in the inertial navigation system in a dynamic time-varying manner based on the observability degree analysis graph.
2. The method of claim 1, wherein obtaining a discrete state space model of an inertial navigation system comprises:
obtaining an error model of the inertial navigation system;
and selecting error variables of all inertial devices of the inertial navigation system as state variables, and discretizing the error model in continuous time to obtain the discrete state space model.
3. The method of claim 1, wherein performing observability graph analysis between error state variables and output metrology variables of the discrete state space model comprises:
in the ith row and the jth column of the output matrix H of the discrete state space model ij Under the condition of not being zero, the j error state variable is shown to influence the i output variable measurement, and therefore each error state variable x of the inertial navigation system is determined k And an output variable z k Wherein the output matrix H is an n x m dimensional matrix.
4. The method of claim 1, wherein the observability degree of each inertial device error variable of the inertial navigation system is calculated and normalized based on the observability graph analysis to obtain an observability degree analysis graph of the inertial navigation system, comprising:
performing high-order system dimension reduction decomposition based on the observability graph analysis;
calculating a state variable root mean square, an observability matrix and a measurement variable root mean square based on the high-order system dimensionality reduction decomposition;
calculating the observability degree of each error state variable based on the calculated state variable root mean square, observability matrix and measurement variable root mean square;
and normalizing the observability degrees of the error state variables to obtain the normalized observability degrees of the error state variables so as to obtain an observability degree analysis graph of the inertial navigation system.
5. The method of claim 4, wherein performing a higher order system dimensionality reduction decomposition based on the observability graph analysis comprises:
based on the observability graph analysis, willDecomposing the high-dimensional system of the discrete state space model into low-dimensional subsystems according to the error types of the inertial devices, wherein the state transition matrix and the output matrix corresponding to the first subsystem are respectively F l And H l And the dimension l of each subsystem 1 +l 2 +. ═ m, where l 1 Dimension representing the 1 st subsystem, l 2 Representing the dimension of the 2 nd subsystem, and m represents the number of columns of the output matrix H of the discrete state space model.
6. The method of claim 5, wherein computing a state variable root mean square, an observability matrix, and a measure variable root mean square based on the high-order system dimensionality reduction decomposition comprises:
from said state transition matrix F l And the output matrix H l Computing observability matrices
And pseudo-inverse obtaining
Wherein "+" represents the pseudo-inverse;
calculating an error state variable x from k-m to k i Root mean square e of the estimate k (x i ) As the state variable root mean square;
calculating the output variable y from k-m to k i Root mean square e of the measured values k (y i ) As the root mean square of the measurement variable.
7. The method of claim 6, wherein calculating the measure of observability of each error state variable based on the calculated state variable root mean square, observability matrix and measurand root mean square comprises:
calculating the observability matrix based on the calculated state variable root mean square, observability matrix and measuration variable root mean square
Row elements and square roots of
Obtaining the ith error state variable to obtain each error state variable;
calculating the observability degree of each error state variable by adopting a logarithm mode based on the analysis result of the observability graph
8. The method of claim 4, wherein normalizing the observability measure of each error state variable to obtain a normalized observability measure of the error state variable comprises:
taking an absolute value of the calculation results of the observability degrees of all the error state variables;
and setting the error state variable with the maximum absolute value as an unobservable quantity, and standardizing the calculation results of the observability degrees of all the error state variables by taking the set unobservable quantity as a reference to obtain the observability degrees of the error state variables after standardization.
9. The method of claim 1, wherein dynamically time-varying analyzing changes in observability of inertial device errors in the inertial navigation system based on observability analysis maps comprises:
analyzing the observability degree of the error state variable after standardization;
when the observable degree of the error state variable is 0, the error state variable is an unobservable quantity; a fully observable when the observable of the error state variable is 1; the higher the value of the observability measure of the error state variable, the stronger the observability of the error state variable.
10. An apparatus for analyzing dynamic time-varying observability of inertial navigation system error, comprising:
an obtaining module configured to obtain a discrete state space model of an inertial navigation system, and perform observability graph analysis between each error state variable and an output measurand of the discrete state space model;
a calculation module configured to calculate and normalize observability levels of error variables of inertial devices of the inertial navigation system based on the observability graph analysis to obtain an observability level analysis graph of the inertial navigation system;
an analysis module configured to dynamically time-varying analyze observability degree changes of errors of inertial devices in the inertial navigation system based on the observability degree analysis graph.
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