CN117973429B - Model parameter ratio estimation method applied to non-Gaussian noise filtering - Google Patents
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Abstract
The invention discloses a model parameter ratio estimation method applied to non-Gaussian noise filtering, belonging to the technical field of information fusion calculation; the method comprises the following steps: initializing the position and speed of a motion unit, establishing a system model and an observation model, and performing primary filtering on the system model to obtain a linear state transfer matrix and a linear measurement matrix; initializing a goblet sea squirt swarm algorithm, and setting the population in the goblet sea squirt swarm algorithm to be initially uniformly distributed; the positions of the leader and the follower are updated, so that the searching speed is improved; obtaining a matrix Q and a matrix R by using all leaders and followers, respectively calculating norms of the innovation covariance matrix as fitness values, and then updating identities of leaders in the population; judging whether the maximum iteration number of the system running filter program is reached, if so, outputting matrixes Q and R; otherwise, returning to update the positions of the leader and the follower; finally, the parameter ratio of the model is output to reduce the acquisition error of the position and the speed of the motion unit.
Description
Technical Field
The invention belongs to the technical field of information fusion calculation, and particularly relates to a model parameter ratio estimation method applied to non-Gaussian noise filtering.
Background
Non-Gaussian noise is usually present in existing motion systems (such as aerospace missions, aircraft tests and unmanned craft sailing); when the unmanned plane, the unmanned ship and other motion units estimate the position, speed and other variables, the interference of the natural environment is often calculated by adopting Gaussian noise distribution, but the noise is known to have obvious non-Gaussian characteristics according to an actual ocean model and a wind power model. The newly proposed noise distribution generates a non-Gaussian environment filtering problem, so that the common parameters such as variance and the like of the noise of the motion unit are difficult to determine, and when the noise adopts t distribution, the parameters such as the degree of freedom are combined to estimate the variables such as the position, the speed and the like. For this purpose, a model parameter ratio estimation method applied to non-Gaussian noise filtering is provided.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a model parameter ratio estimation method applied to non-Gaussian noise filtering, which solves the problems in the prior art.
The aim of the invention can be achieved by the following technical scheme:
A model parameter ratio estimation method applied to non-Gaussian noise filtering comprises the following steps:
S1, initializing position and speed parameters of a motion unit, and establishing a system model and an observation model of the motion unit;
s2, filtering the system model once according to the observation model to respectively calculate linear state transition matrixes of the motion units And a linear measurement matrix/>；
S3, initializing a population of the goblet sea squirt swarm algorithm, and setting the population in the goblet sea squirt swarm algorithm to be initially uniformly distributed, wherein the population is divided into a leader and a follower;
s4, updating the positions of the leader and the follower, and then improving the searching speed by utilizing differential evolution;
S5, obtaining covariance matrixes respectively used in the motion unit model and the measurement by utilizing all leaders and followers And/>And then according to the linear state transition matrix/>, of the motion unitAnd/or linear measurement matrixAn innovation covariance matrix/>, which is obtained by estimation and measurement, of the position and the speed of the motion unit is calculated respectivelyTaking the norm of the population as a fitness value, and then updating the identity of a leader in the population;
S6, judging whether the maximum iteration number of the system running filter program is reached, and if so, outputting a matrix And/>Determining parameters of filtering; if not, the method goes to S4 to continue execution;
S7, inputting all obtained matrixes And/>And outputting the parameter ratio of the model to obtain the accurate position and speed of the motion unit.
Further, the system model of the motion unit is as follows:
Wherein, For/>A dimension state vector reflecting the position and speed of the motion unit; /(I)Reflecting the physical relationship of the motion units as a nonlinear transfer function; /(I)The noise is non-Gaussian process noise, and reflects the interference force of the motion unit on the position and the speed in the natural environment;
the observation model of the motion unit is as follows:
Wherein, For/>A dimension measuring vector reflects the position and the speed value measured by the motion unit; /(I)Reflecting the relation of the measurement process of the motion unit as a nonlinear observation function,/>The non-Gaussian observation noise reflects the thermal noise inside the measuring device when the motion unit is used for measuring.
Further, the linear state transition matrix of the motion unitThe calculation formula of (2) is as follows:
The linear measurement matrix The calculation formula is as follows:
Wherein, Error covariance matrix for non-linear transformed and untransformed motion element position and velocity,/>An inverse of the error covariance matrix for all untransformed motion element positions and velocities; /(I)Estimating an inverse of an error covariance matrix of the motion unit position and velocity for a next time,/>An error covariance matrix of the motion unit position and velocity is calculated for the inclusive measurements and the physical model.
Further, the population refers to: non-gaussian process noiseCovariance matrix/>Non-Gaussian observation noiseCovariance matrix/>The new vector, which is obtained by combining all elements on the diagonal, is divided into a leader and a follower.
Further, the formula for improving the search speed by adopting differential evolution is as follows:
wherein r1, r2, r3 are any non-repeating individuals in the population follower, b is the probability of controlling variation, Representing the original arbitrary population follower,/>Representing the population followers after differential evolution; the superscript i indicates that at the ith iteration, and the subscript j indicates the j-th dimension of the search.
Further, the estimated and measured innovation covariance matrix of the position and the speed of the motion unitThe calculation formula of (2) is as follows:
Wherein, The covariance matrix of the position and the speed error of the motion unit measured last time is represented, and the upper corner mark/>Representing the matrix transpose.
Further, in S7, the matrix of the minimum fitness value is selected to obtain the specific element of the corresponding matrix, and then the new covariance matrix of the position and the speed of the motion unit is obtained according to estimation and measurementAnd an innovation covariance matrix/>, of the position and the speed of the moving unit, which are obtained through actual measurementAnd (5) obtaining a proportionality coefficient, and correcting the parameter value by the proportionality coefficient.
Further, the actual measured position and velocity of the motion unit are an innovation covariance matrixThe calculation formula is as follows:
Wherein, Superscript indicates the actual value,/>Representing the number of defined components,/>Representing the i-th component,/>Representing the weight value.
Further, the calculation formula of the model parameter ratio is as follows:
Wherein, For model parameter ratio, reflecting the physical model of the motion unit and the variance value used in the measuring process,/>Representation matrix/>The element above, the subscript, the row and column number,/>Representation/>Degrees of freedom in the corresponding dimensions; /(I)Representation matrix/>Element above,/>Representation/>And degrees of freedom in the corresponding dimensions.
A model parameter ratio estimation system for non-gaussian noise filtering, comprising:
model construction module: initializing position and speed parameters of a motion unit, and establishing a system model and an observation model of the motion unit;
matrix calculation module: filtering the system model once according to the observation model to respectively calculate the linear state transition matrix of the motion unit And a linear measurement matrix/>；
Algorithm initialization module: initializing a population of the goblet sea squirt swarm algorithm, and setting the population in the goblet sea squirt swarm algorithm to be initially uniformly distributed, wherein the population is divided into a leader and a follower;
And a position updating module: updating the positions of the leader and the follower, and then improving the searching speed by utilizing differential evolution;
an identity updating module: obtaining covariance matrices used in the motion unit model and the measurement respectively by using all leaders and followers And/>And then according to the linear state transition matrix/>, of the motion unitAnd/or linear measurement matrixAn innovation covariance matrix/>, which is obtained by estimation and measurement, of the position and the speed of the motion unit is calculated respectivelyTaking the norm of the population as a fitness value, and then updating the identity of a leader in the population;
And an iteration judging module: judging whether the maximum iteration number of the system running filter program is reached, if so, outputting a matrix And/>Determining parameters of filtering; if not, the method goes to a position updating module to continue execution;
and a parameter ratio calculation module: inputting the obtained total matrix And/>And outputting the parameter ratio of the model to obtain the accurate position and speed of the motion unit.
The invention has the beneficial effects that:
the invention provides a model parameter ratio estimation method applied to non-Gaussian noise filtering, provides a calculation method of a system model parameter ratio related to non-linear and non-Gaussian noise, and provides an improved sea-squirt swarm algorithm, wherein the task of searching the model parameter ratio is optimized, and more accurate system parameters are searched more quickly; based on the model parameter ratio, when the noise covariance is inaccurate in practical application, the system can obtain the optimal state estimation; the result has minimum error in the statistical sense when the model is applied to the actual environment, and compared with the current position and speed of the motion unit obtained by a simple model calculation or measurement method, various errors of the motion unit after filtering increase to be close to zero along with time.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described, and it will be obvious to those skilled in the art that other drawings can be obtained according to these drawings without inventive effort.
FIG. 1 is a flow chart of a model parameter ratio estimation method of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, a model parameter ratio estimation method applied to non-gaussian noise filtering includes the following steps:
s1, initializing parameters
In an actual motion system (such as unmanned aerial vehicle or unmanned boat motion), the parameters refer to: the position and speed of the unmanned plane or unmanned plane in motion are used as state vectors, the state vectors are estimated, the influence of the natural world on the unmanned plane or unmanned plane is achieved in the process, various probability distribution is used for describing the unmanned plane or unmanned plane, a non-Gaussian distribution-t distribution is selected, variances and covariance of the unmanned plane or unmanned plane in the probability of existence of the position and the speed in all directions are obtained, and a covariance matrix is obtained according to the corresponding relation. The process is divided into a model calculation result and a measurement result, and the model calculation result and the measurement result are respectively described by a linear state transition matrix and a linear measurement matrix. If the rotation angle of the object itself can be added as a part of the state vector for different models and measurements, the method is taken as the basic theory of the filtering method; a high level of generalization of the system is required here.
Abstracting the system into a combination of the following parameters: the motion unit is interfered by natural environment as non-Gaussian process noiseInternal thermal noise of measuring device of motion unit as non-Gaussian observation noise/>The two are independent; establishing a nonlinear transfer function/>, of the position, speed and other changes of the motion unit, according to the physical relationshipNonlinear observation function/>, used for calculating in measuring angular distance with motion unit，/>To simplify the linear state transition matrix of the position and the speed of the motion unit,/>The linear measurement matrix is used by the simplified motion unit when measuring the angle distance; /(I)Finger/>Position, speed, etc. of the dimensional motion unit are used as state vectors,/>Finger/>The position speed and the like measured by the dimensional motion unit are used as measurement vectors; sampling period/>Is thatTo/>Is a time of (a) to be used.
S2, establishing a system model and an observation model of the motion unit based on the initialized parameters in the S1;
The system model of the motion unit is as follows:
Wherein, For/>A dimension state vector reflecting the position and speed of the motion unit; /(I)Reflecting the physical relationship of the motion units as a nonlinear transfer function; /(I)The noise is non-Gaussian process noise, and reflects the interference force of the motion unit on the position and the speed in the natural environment; the functional relation is based on different objects acted by physical theory, for example, the unmanned aerial vehicle can use a simple displacement formula according to the previous position and speed, and can also further add a square term related to the speed according to aerodynamics, or take an air simulation into account to establish a calculation model as the function;
the observation model of the motion unit is as follows:
Wherein, For/>A dimension measuring vector reflects the position and the speed value measured by the motion unit; /(I)Reflecting the relation of the measurement process of the motion unit as a nonlinear observation function,/>The non-Gaussian observation noise reflects the thermal noise inside the measuring device when the motion unit is used for measuring. The functional relation can directly measure the required quantity according to the different measuring equipment and methods, thereby changing into a simple diagonal matrix, or measuring the distance and angle between the measuring equipment and the measuring position, and calculating according to a trigonometric function.
S3, filtering the system model once according to the observation model of the motion unit at the current k moment, obtaining variances and covariances of the position and the speed of the motion unit which are non-linear transformation and non-transformation in the process, and writing the variances and covariances into an error covariances in a matrix form; Then the variance and covariance of all the untransformed motion unit positions and speeds are obtained and written as an inverse matrix/>, of the error covariance, in a matrix formCalculating the simplified position and speed change relation of the motion unit, namely an approximate linear state transition matrix; the variance and covariance of the position and the speed of the motion unit after the integrated physical model and the measurement method can be obtained, namely, the inverse matrix/>, of the covariance matrix of the estimated state errorAnd a cross covariance matrixCalculating an approximate linear measurement matrix used by the simplified motion unit in measuring the angular distance; and assume that the mobile unit is disturbed by the natural environment/>I.e. covariance matrix/>Elements on the middle diagonal; assume again that the motion unit measures the internal thermal noise/>I.e. covariance matrix/>Elements on the middle diagonal;
The primary filtering process includes the following operations:
from S2, an observation model and a system model of the motion unit are obtained, and then are calculated Is used for calculating the linear state transition matrix/>, and simplifying calculationAnd/or linear measurement matrix。
Linear state transition matrixThe calculation formula of (2) is as follows:
Linear measurement matrix The calculation formula is as follows:
Wherein it is necessary to hypothesize Covariance matrix/>Element sum/> on mid-diagonalCovariance matrix/>Elements on the middle diagonal.
S4, in order to find the matrix in S3And/>Firstly initializing a covariance matrix (population of a goblet sea squirt swarm algorithm) of the position and the speed of a motion unit, and setting the population in the goblet sea squirt swarm algorithm to be initially uniformly distributed;
Population refers to a matrix And/>New vector combined by all elements on diagonal is denoted/>Which in turn may be subdivided into a leader and follower.
S5, updating the positions of the leader and the follower in the S4, and then realizing differential evolution to improve the searching speed according to the following formula:
wherein r1, r2, r3 are any non-repeating individuals in the population follower, b is the probability of controlling variation, Representing the original arbitrary population follower,/>Representing the population followers after differential evolution; the superscript i indicates that at the ith iteration, and the subscript j indicates the j-th dimension of the search.
S6, utilizing the variances and covariances (populations) of all possible motion unit positions and velocities obtained in S5AndObtaining a matrix/>And/>Then according to the linear state transition matrix/>, in S3And/or linear measurement matrixThe fitness value is calculated respectively, namely, the innovation covariance matrix/>, of the position and the speed of the motion unit obtained by estimation and measurement is calculatedThen updating the identity of the leader in the population according to the fitness value;
The calculation formula of the innovation covariance matrix is as follows:
And/> According to calculation in S3,/>An error covariance matrix representing the combination of the variances and covariances of the motion unit position and velocity at the previous time, and an upper corner mark T represents the matrix transpose.
S7, after the S6 is completed, judging whether the maximum iteration number of the motion unit running filter program is reached, and if so, outputting a matrixAnd/>Determining parameters of filtering; if not, the process proceeds to S5 to continue execution.
S8, finishing S7 and inputting a variance and covariance matrix of the position and the speed of the motion unitAnd/>Outputting the parameter ratio of the model;
the variance and covariance of the position and the speed of the motion unit obtained in S7 are in one-to-one correspondence with the corresponding fitness value, wherein the specific element of the corresponding matrix can be obtained after selecting the matrix with the minimum fitness value, and then the estimated innovation covariance calculated in S6 is obtained And actual innovation covariance/>And (5) obtaining a proportionality coefficient, and correcting the parameter value by the proportionality coefficient.
Actual innovation covariance calculationThe method comprises the following steps:
the superscript indicates the actual value, which term can be pushed back to zero without deviation at the beginning according to time, but deviation gradually appears in continuous filtering, according to different filtering methods/> There are different estimation methods, here given an estimation method of unscented kalman filtering.
The calculation formula is as follows:
representing the number of defined components,/> Representing the i-th component,/>Representing the weight value.
Calculating a model parameter ratio of a system model and an observation model according to the following formula;
Wherein, Is the ratio of the variance to the covariance of the position and the speed of the motion unit, which is called as the model parameter ratio,/>Representation matrix/>The element above, the subscript, the row and column number,/>Representation/>Degrees of freedom in the corresponding dimensions; /(I)Representation matrix/>Element above,/>Representation/>And degrees of freedom in the corresponding dimensions.
Finally, the matrix is further corrected according to the model parameter ratio obtained in the step S8And/>I.e. multiply one of the terms by a more accurate matrix/>And/>According to the two newly obtained parameters, a more accurate result than the original assumption can be obtained, namely, an optimal filtering result is realized, the result has minimum error in statistical sense when the model is applied to an actual environment, and compared with the current position and speed of a motion unit (unmanned aerial vehicle or unmanned ship) obtained by a simple model calculation or measurement method, the error of the result is increased to be close to zero along with time.
In the description of the present specification, the descriptions of the terms "one embodiment," "example," "specific example," and the like, mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims.
Claims (6)
1. The model parameter ratio estimation method applied to non-Gaussian noise filtering is characterized by comprising the following steps of:
S1, initializing position and speed parameters of a motion unit, and establishing a system model and an observation model of the motion unit;
S2, filtering the system model once according to the observation model to calculate a linear state transition matrix of each motion unit And a linear measurement matrix/>；
S3, initializing a population of the goblet sea squirt swarm algorithm, and setting the population in the goblet sea squirt swarm algorithm to be initially uniformly distributed, wherein the population is divided into a leader and a follower;
s4, updating the positions of the leader and the follower, and then improving the searching speed by utilizing differential evolution;
S5, obtaining covariance matrixes respectively used in the motion unit model and the measurement by utilizing all leaders and followers And/>And then according to the linear state transition matrix/>, of the motion unitAnd/or linear measurement matrixAn innovation covariance matrix/>, which is obtained by estimation and measurement, of the position and the speed of the motion unit is calculated respectivelyTaking the norm of the population as a fitness value, and then updating the identity of a leader in the population;
S6, judging whether the maximum iteration number of the system running filter program is reached, and if so, outputting a matrix And/>Determining parameters of filtering; if not, the method goes to S4 to continue execution;
S7, inputting all obtained matrixes And/>Outputting the parameter ratio of the model to obtain the accurate position and speed of the motion unit;
The system model of the motion unit is as follows:
Wherein, For/>A dimension state vector reflecting the position and speed of the motion unit; /(I)Reflecting the physical relationship of the motion units as a nonlinear transfer function; /(I)The noise is non-Gaussian process noise, and reflects the interference force of the motion unit on the position and the speed in the natural environment;
the observation model of the motion unit is as follows:
Wherein, For/>A dimension measuring vector reflects the position and the speed value measured by the motion unit; /(I)Reflecting the relation of the measurement process of the motion unit as a nonlinear observation function,/>The non-Gaussian observation noise reflects the thermal noise in the measuring device during the measurement of the motion unit;
the population refers to: non-gaussian process noise Covariance matrix/>Non-Gaussian observed noise/>Covariance matrix/>The new vector obtained by combining all elements on the diagonal is divided into a leader and a follower;
the formula for improving the searching speed by adopting differential evolution is as follows:
wherein r1, r2, r3 are any non-repeating individuals in the population follower, b is the probability of controlling variation, Representing the original arbitrary population follower,/>Representing the population followers after differential evolution; the superscript i indicates that the iteration is in the ith round, and the subscript j indicates the j-th dimensional parameter of searching;
the calculation formula of the model parameter ratio is as follows:
Wherein, For model parameter ratio, reflecting the physical model of the motion unit and the variance value used in the measuring process,/>Representation matrix/>The element above, the subscript, the row and column number,/>Representation/>Degrees of freedom in the corresponding dimensions; /(I)Representation matrix/>Element above,/>Representation/>And degrees of freedom in the corresponding dimensions.
2. The method for estimating a model parameter ratio for non-Gaussian noise filtering according to claim 1, wherein said motion unit linear state transition matrixThe calculation formula of (2) is as follows:
The linear measurement matrix The calculation formula is as follows:
Wherein, For the non-linear transformed and untransformed motion unit position and velocity error covariance matrix,An inverse of the error covariance matrix for all untransformed motion element positions and velocities; /(I)Estimating an inverse of an error covariance matrix of the motion unit position and velocity for a next time,/>An error covariance matrix of the motion unit position and velocity is calculated for the inclusive measurements and the physical model.
3. The method of claim 1, wherein the estimating measures an innovation covariance matrix of the position and the velocity of the motion unitThe calculation formula of (2) is as follows:
Wherein, The covariance matrix of the position and the speed error of the motion unit measured last time is represented, and the upper corner mark/>Representing the matrix transpose.
4. The method for estimating a model parameter ratio for non-Gaussian noise filtering according to claim 3, wherein in S7, a matrix of minimum fitness value is selected to obtain a specific element of a corresponding matrix, and then an innovation covariance matrix of the position and the velocity of the motion unit is obtained according to estimation measurementAnd an innovation covariance matrix/>, of the position and the speed of the moving unit, which are obtained through actual measurementAnd (5) obtaining a proportionality coefficient, and correcting the parameter value by the proportionality coefficient.
5. The method of estimating a model parameter ratio for non-Gaussian noise filtering according to claim 4, wherein said actual measured innovation covariance matrix of motion element position and velocityThe calculation formula is as follows:
Wherein, Superscript indicates the actual value,/>Representing the number of defined components,/>Representing the i-th component,/>Representing the weight value.
6. A model parameter ratio estimation system for non-gaussian noise filtering, comprising:
model construction module: initializing position and speed parameters of a motion unit, and establishing a system model and an observation model of the motion unit;
matrix calculation module: filtering the system model once according to the observation model to respectively calculate the linear state transition matrix of the motion unit And a linear measurement matrix/>；
Algorithm initialization module: initializing a population of the goblet sea squirt swarm algorithm, and setting the population in the goblet sea squirt swarm algorithm to be initially uniformly distributed, wherein the population is divided into a leader and a follower;
And a position updating module: updating the positions of the leader and the follower, and then improving the searching speed by utilizing differential evolution;
an identity updating module: obtaining covariance matrices used in the motion unit model and the measurement respectively by using all leaders and followers And/>And then according to the linear state transition matrix/>, of the motion unitAnd/or linear measurement matrixAn innovation covariance matrix/>, which is obtained by estimation and measurement, of the position and the speed of the motion unit is calculated respectivelyTaking the norm of the population as a fitness value, and then updating the identity of a leader in the population;
And an iteration judging module: judging whether the maximum iteration number of the system running filter program is reached, if so, outputting a matrix And/>Determining parameters of filtering; if not, the method goes to a position updating module to continue execution;
and a parameter ratio calculation module: inputting the obtained total matrix And/>Outputting the parameter ratio of the model to obtain the accurate position and speed of the motion unit;
The system model of the motion unit is as follows:
Wherein, For/>A dimension state vector reflecting the position and speed of the motion unit; /(I)Reflecting the physical relationship of the motion units as a nonlinear transfer function; /(I)The noise is non-Gaussian process noise, and reflects the interference force of the motion unit on the position and the speed in the natural environment;
the observation model of the motion unit is as follows:
Wherein, For/>A dimension measuring vector reflects the position and the speed value measured by the motion unit; /(I)Reflecting the relation of the measurement process of the motion unit as a nonlinear observation function,/>The non-Gaussian observation noise reflects the thermal noise in the measuring device during the measurement of the motion unit;
the population refers to: non-gaussian process noise Covariance matrix/>Non-Gaussian observed noise/>Covariance matrix/>The new vector obtained by combining all elements on the diagonal is divided into a leader and a follower;
the formula for improving the searching speed by adopting differential evolution is as follows:
wherein r1, r2, r3 are any non-repeating individuals in the population follower, b is the probability of controlling variation, Representing the original arbitrary population follower,/>Representing the population followers after differential evolution; the superscript i indicates that the iteration is in the ith round, and the subscript j indicates the j-th dimensional parameter of searching;
the calculation formula of the model parameter ratio is as follows:
Wherein, For model parameter ratio, reflecting the physical model of the motion unit and the variance value used in the measuring process,/>Representation matrix/>The element above, the subscript, the row and column number,/>Representation/>Degrees of freedom in the corresponding dimensions; /(I)Representation matrix/>Element above,/>Representation/>And degrees of freedom in the corresponding dimensions.
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