CN110514209B - Interactive multi-model combined navigation method - Google Patents

Interactive multi-model combined navigation method Download PDF

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CN110514209B
CN110514209B CN201910800501.0A CN201910800501A CN110514209B CN 110514209 B CN110514209 B CN 110514209B CN 201910800501 A CN201910800501 A CN 201910800501A CN 110514209 B CN110514209 B CN 110514209B
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徐晓苏
侯岚华
姚逸卿
王迪
潘绍华
吴贤
安仲帅
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Southeast University
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Abstract

The invention discloses an interactive multi-model integrated navigation method, which comprises the steps of firstly establishing a state equation according to an error model of an integrated navigation system, and secondly adopting a combined measurement noise variance matrix output by last state estimation
Figure DDA0002180493930000011
Adaptively establishing three models, and calculating the initial state and the estimation error variance matrix of the estimation according to the state of each model output by the last state estimation and the estimation error variance matrix; respectively carrying out Sage-Husa adaptive filtering on the three established models and updating the models by adopting a Bayesian hypothesis test method; and finally, carrying out an output interaction process according to the weight and outputting a final filtering result. The invention can estimate the measurement noise variance matrix in real time and effectively improve the precision and efficiency of the integrated navigation positioning.

Description

Interactive multi-model combined navigation method
The technical field is as follows:
the invention relates to an interactive multi-model integrated navigation method, belongs to the information fusion technology, and is particularly suitable for the field of integrated navigation.
Background art:
the Kalman filtering technology is widely applied in the field of integrated navigation as an optimal control. However, in the application process, the system model is required to be accurate, and the filtering precision is reduced by model errors. In this context, interactive multi-model algorithms and adaptive filtering have come into play. The interactive multi-model algorithm adopts a method of establishing a model set to cover a current model to eliminate model errors, but the efficiency of the algorithm is reduced due to filtering calculation of a plurality of models. The adaptive filtering improves the filtering precision by estimating a noise model, but has the problems of filtering divergence and noise error estimation delay. In view of the above, a more efficient filtering method is needed.
The invention content is as follows:
the invention provides an interactive multi-model combined navigation method in order to reduce the influence of model errors on filtering precision and effectively estimate a measured noise variance matrix in real time.
The above object of the present invention can be achieved by the following technical solutions:
an interactive multi-model combined navigation method specifically comprises the following steps:
s1: establishing a state equation according to the error model of the integrated navigation system;
s2: jointly measuring noise variance matrix output according to last state estimation
Figure BDA0002180493910000011
Establishing three models which respectively correspond to the measured noise variance matrix:
Figure BDA0002180493910000012
wherein sigma is a constant matrix and is set according to the system application environment;
s3: calculating the initial state of the estimation and the error variance matrix thereof by using the state estimation and the error variance matrix thereof of each model output by the last state estimation;
s4: respectively carrying out Sage-Husa self-adaptive filtering on the three established models;
s5: updating the model by adopting a Bayesian hypothesis testing method;
s6: and according to the weight, performing weighted fusion on output information of each model, calculating a joint state estimation, an estimation error variance matrix and a measurement noise variance matrix, and outputting a final result.
Further, the step S1 specifically includes the following steps:
establishing a state equation according to the error model of the integrated navigation system:
Figure BDA0002180493910000013
Z＝HX+V
wherein X is a state vector, F is a system matrix, W is a system noise vector, Z is a measurement vector, H is a measurement matrix, and V is a measurement noise vector.
Further, the step S2 specifically includes the following steps:
jointly measuring noise variance matrix output according to last state estimation
Figure BDA0002180493910000021
Three models are established
Figure BDA0002180493910000022
The measured noise variance matrix is respectively corresponding to:
Figure BDA0002180493910000023
wherein, the sigma is a constant matrix and is set according to the system application environment.
Further, the step S3 specifically includes the following steps:
s3.1, assuming that the model transition probability follows the Markov process, calculating the model prediction probability as follows:
Figure BDA0002180493910000024
P{mj(k)|mi(k-1)is the model m from the time k-1 to the time ki(k-1)To model mj(k)And Markov transition probability, abbreviated as Pi→j，μi(k-1)Is a model mi(k-1)The model matching probability of (2);
s3.2, the mixed initial state and the error variance matrix of each filter are given as follows:
Figure BDA0002180493910000025
Figure BDA0002180493910000026
Figure BDA0002180493910000027
wherein the content of the first and second substances,
Figure BDA0002180493910000028
for mixing the initial states, i.e. the state input, P, of the filter j at the present momentOj(k-1)For a hybrid initial state error variance matrix, i.e. an input state error variance matrix,
Figure BDA0002180493910000029
for the state estimation of the ith filter at the previous time, Pi(k-1)For its corresponding error variance matrix, mui→j(k-1)Probabilities are predicted for the model.
Further, the step S4 specifically includes the following steps:
and respectively carrying out Sage-Husa adaptive Kalman filtering on the three models:
s4.1 discretizing the state equation:
Figure BDA00021804939100000210
wherein j represents the jth filter, j is 1-3, k represents the kth time, and X representsj(k)Is a state vector, phij(k,k-1)For a state one-step transition matrix, Xj(k-1)Is the last moment filter state vector, Gj(k)For system noise input matrix, Wj(k)Is a systematic noise vector, Zj(k)For measuring the vector, Hj(k)For measuring the matrix, Vj(k)To measure the noise vector;
s4.2, calculating a Kalman filtering one-step prediction state vector and an error variance matrix:
Figure BDA00021804939100000211
Figure BDA0002180493910000031
wherein the content of the first and second substances,
Figure BDA0002180493910000032
for the state one-step prediction matrix, phij(k,k-1)In order to have a one-step transition matrix of states,
Figure BDA0002180493910000033
for mixing of the initial state, Pj(k,k-1)Predicting error variance matrix for state one step, POj(k-1)For mixed initial state error variance matrix, Gj(k)For system noise input matrix, Qj(k)Is a system noise error variance matrix;
s4.3, calculating Kalman filtering residual errors:
Figure BDA0002180493910000034
wherein epsilonj(k)Is a residual, Zj(k)For measuring the vector, Hj(k)In order to measure the matrix, the measurement matrix is,
Figure BDA0002180493910000035
the matrix is predicted for one step of the state,
Figure BDA0002180493910000036
estimating a mean value for the measured noise;
s4.4, calculating a Kalman filtering state gain matrix:
Figure BDA0002180493910000037
wherein, Kj(k)Is a state gain matrix, Pj(k,k-1)Error variance matrix for state one-step prediction, Hj(k)In order to measure the matrix, the measurement matrix is,
Figure BDA0002180493910000038
estimating a variance matrix for the measured noise;
s4.5, calculating Kalman filtering state estimation and a variance matrix thereof:
Figure BDA0002180493910000039
Pj(k)＝(I-Kj(k)Hj(k))Pj(k,k-1)
wherein the content of the first and second substances,
Figure BDA00021804939100000310
in order to estimate the vector for the state,
Figure BDA00021804939100000311
for a state one-step prediction matrix, Kj(k)Is a state gain matrix, epsilonj(k)Is a residual, Pj(k)To estimate the error variance matrix, Hj(k)For the measurement matrix, Pj(k,k-1)Predicting an error variance matrix for the state one step;
s4.6, calculating a measurement noise mean value and variance matrix:
Figure BDA00021804939100000318
Figure BDA00021804939100000312
wherein d isk＝(1-b)/(1-bk+1)，b＝0.95～0.99，
Figure BDA00021804939100000313
In order to measure the mean value of the noise estimate,
Figure BDA00021804939100000314
estimate the mean, Z, of the measured noise at the previous timej(k)For measuring the vector, Hj(k)In order to measure the matrix, the measurement matrix is,
Figure BDA00021804939100000315
the matrix is predicted for one step of the state,
Figure BDA00021804939100000316
to estimate the variance matrix for the measured noise,
Figure BDA00021804939100000317
estimating an array of variances, K, for the measured noise at the previous timej(k)Is a state gain matrix, epsilonj(k)Is a residual, Pj(k)To estimate an error variance matrix.
Further, the step S5 specifically includes the following steps:
and updating the model by adopting a Bayesian hypothesis testing method. And calculating a likelihood function according to the residual error of each model corresponding to the k moment of the filter and a variance matrix thereof:
Figure BDA0002180493910000041
Figure BDA0002180493910000042
wherein m is the dimension of the measurement vector, εj(k)Is a residual error, Aj(k)Is a residual variance matrix, Hj(k)For the measurement matrix, Pj(k)In order to estimate the error variance matrix,
Figure BDA0002180493910000043
estimating a variance matrix for the measured noise;
and calculating the weight of the model in the model set, and updating the model probability:
Figure BDA0002180493910000044
wherein, muj(k)Is the probability of the model, fj(k)As a likelihood function, Pi→jFor Markov transition probability, μi(k-1)Is the model match probability.
Further, the step S6 specifically includes the following steps:
and according to the weight, carrying out weighted fusion on the estimated values of the models, calculating a joint state estimation, a joint error variance matrix and a joint measurement noise variance matrix, and outputting an interactive multi-model final result:
Figure BDA0002180493910000045
Figure BDA0002180493910000046
Figure BDA0002180493910000047
wherein the content of the first and second substances,
Figure BDA0002180493910000048
in order to perform a joint state estimation,
Figure BDA0002180493910000049
for the state estimation vector, muj(k)As model probability, PkFor joint error variance matrix, Pj(k)In order to estimate the error variance matrix,
Figure BDA00021804939100000410
in order to jointly measure the noise variance matrix,
Figure BDA00021804939100000411
a variance matrix is estimated for the measured noise.
Advantageous effects
1. The noise statistical characteristic estimated by the Sage-Husa adaptive filter is weighted and averaged by the weight calculated by the interactive multi-model algorithm, so that the estimation precision of the noise statistical characteristic by the adaptive filter is improved, and the combined navigation precision is improved;
2. the method adopts the Sage-Husa adaptive filter to estimate the noise statistical characteristics in real time to establish the model set, and effectively reduces the calculated amount of the interactive multi-model algorithm caused by the complex model.
Drawings
FIG. 1 is a flow chart of the algorithm of the present invention.
Detailed Description
The technical solutions provided by the present invention will be described in detail below with reference to specific examples, and it should be understood that the following specific embodiments are only illustrative of the present invention and are not intended to limit the scope of the present invention.
The invention provides an interactive multi-model combined navigation method, the realization principle is shown in figure 1, and the flow mainly comprises the following steps:
step S1, establishing a state equation according to the error model of the integrated navigation system:
Figure BDA0002180493910000051
Z＝HX+V
wherein X is a state vector, F is a system matrix, W is a system noise vector, Z is a measurement vector, H is a measurement matrix, and V is a measurement noise vector.
Step S2, estimating the output joint measurement noise variance matrix R according to the last statekThree models are established. The method specifically comprises the following steps:
jointly measuring noise variance matrix output according to last state estimation
Figure BDA0002180493910000052
Three models are established { m1 m2 m3And } the measured noise variance matrixes are respectively corresponding to:
Figure BDA0002180493910000053
and sigma is a constant matrix and is set according to the system application environment.
Step S3, calculating the initial state of the current estimation and the error variance matrix thereof by using the state estimation and the error variance matrix thereof of each model output by the previous state estimation, which specifically includes the following steps:
s3.1, assuming that the model transition probability follows the Markov process, calculating the model prediction probability as follows:
Figure BDA0002180493910000054
P{mj(k)|mi(k-1)is the model m from the time k-1 to the time ki(k-1)To model mj(k)And Markov transition probability, abbreviated as Pi→jGenerally, a preset constant is used. Mu.si(k-1)Is a model mi(k-1)The model matching probability of (2).
S3.2, the mixed initial state and the error variance matrix of each filter are given as follows:
Figure BDA0002180493910000055
Figure BDA0002180493910000056
Figure BDA0002180493910000057
wherein the content of the first and second substances,
Figure BDA0002180493910000058
for mixing the initial states, i.e. the state input, P, of the filter j at the present momentOj(k-1)Is a mixed initial state error variance matrix, namely an input state error variance matrix.
Figure BDA0002180493910000059
For the state estimation of the ith filter at the previous time, Pi(k-1)Is its corresponding error variance matrix. Mu.si→j(k-1)Probabilities are predicted for the model.
And step S4, respectively carrying out Sage-Husa Kalman filtering on the three models. The method specifically comprises the following steps:
and respectively carrying out Sage-Husa adaptive Kalman filtering on the three models:
s4.1 discretizing the state equation:
Figure BDA00021804939100000510
wherein j represents the jth filter, j is 1-3, k represents the kth time, and X representsj(k)Is a state vector, phij(k,k-1)For a state one-step transition matrix, Xj(k-1)Is the last moment filter state vector, Gj(k)For system noise input matrix, Wj(k)Is a systematic noise vector, Zj(k)For measuring the vector, Hj(k)For measuring the matrix, Vj(k)To measure the noise vector.
S4.2, calculating a Kalman filtering one-step prediction state vector and an error variance matrix:
Figure BDA0002180493910000061
Figure BDA0002180493910000062
wherein the content of the first and second substances,
Figure BDA0002180493910000063
for the state one-step prediction matrix, phij(k,k-1)In order to have a one-step transition matrix of states,
Figure BDA0002180493910000064
for mixing of the initial state, Pj(k,k-1)Predicting error variance matrix for state one step, POj(k-1)For mixed initial state error variance matrix, Gj(k)For system noise input matrix, Qj(k)Is a systemNoise error variance matrix.
S4.3, calculating Kalman filtering residual errors:
Figure BDA0002180493910000065
wherein epsilonj(k)Is a residual, Zj(k)For measuring the vector, Hj(k)In order to measure the matrix, the measurement matrix is,
Figure BDA0002180493910000066
the matrix is predicted for one step of the state,
Figure BDA0002180493910000067
the mean is estimated for the measured noise.
S4.4, calculating a Kalman filtering state gain matrix:
Figure BDA0002180493910000068
wherein, Kj(k)Is a state gain matrix, Pj(k,k-1)Error variance matrix for state one-step prediction, Hj(k)In order to measure the matrix, the measurement matrix is,
Figure BDA0002180493910000069
a variance matrix is estimated for the measured noise.
S4.5, calculating Kalman filtering state estimation and a variance matrix thereof:
Figure BDA00021804939100000610
Pj(k)＝(I-Kj(k)Hj(k))Pj(k,k-1)
wherein the content of the first and second substances,
Figure BDA00021804939100000611
in order to estimate the vector for the state,
Figure BDA00021804939100000612
for a state one-step prediction matrix, Kj(k)Is a state gain matrix, epsilonj(k)Is a residual, Pj(k)To estimate the error variance matrix, Hj(k)For the measurement matrix, Pj(k,k-1)Error variance matrix is predicted for the state one step.
S4.6, calculating a measurement noise mean value and variance matrix:
Figure BDA00021804939100000613
Figure BDA00021804939100000614
wherein d isk＝(1-b)/(1-bk+1)，b＝0.95～0.99，
Figure BDA0002180493910000071
In order to measure the mean value of the noise estimate,
Figure BDA0002180493910000072
estimate the mean, Z, of the measured noise at the previous timej(k)For measuring the vector, Hj(k)In order to measure the matrix, the measurement matrix is,
Figure BDA0002180493910000073
the matrix is predicted for one step of the state,
Figure BDA0002180493910000074
to estimate the variance matrix for the measured noise,
Figure BDA0002180493910000075
estimating an array of variances, K, for the measured noise at the previous timej(k)Is a state gain matrix, epsilonj(k)Is a residual, Pj(k)To estimate an error variance matrix.
And step S5, updating the model by adopting a Bayesian hypothesis testing method. The method specifically comprises the following steps:
and updating the model by adopting a Bayesian hypothesis testing method. And calculating a likelihood function according to the residual error of each model corresponding to the k moment of the filter and a variance matrix thereof:
Figure BDA0002180493910000076
Figure BDA0002180493910000077
wherein m is the dimension of the measurement vector, εj(k)Is a residual error, Aj(k)Is a residual variance matrix, Hj(k)For the measurement matrix, Pj(k)In order to estimate the error variance matrix,
Figure BDA0002180493910000078
a variance matrix is estimated for the measured noise.
And calculating the weight of the model in the model set, and updating the model probability:
Figure BDA0002180493910000079
wherein, muj(k)Is the probability of the model, fj(k)As a likelihood function, Pi→jFor Markov transition probability, μi(k-1)Is the model match probability.
And step S6, outputting interaction and outputting a multi-model final result. The method specifically comprises the following steps:
and according to the weight, carrying out weighted fusion on the estimated values of the models, calculating a joint state estimation, a joint error variance matrix and a joint measurement noise variance matrix, and outputting the final result of the interactive multi-model.
Figure BDA00021804939100000710
Figure BDA00021804939100000711
Figure BDA00021804939100000712
Wherein the content of the first and second substances,
Figure BDA00021804939100000713
in order to perform a joint state estimation,
Figure BDA00021804939100000714
for the state estimation vector, muj(k)As model probability, PkFor joint error variance matrix, Pj(k)In order to estimate the error variance matrix,
Figure BDA00021804939100000715
in order to jointly measure the noise variance matrix,
Figure BDA00021804939100000716
a variance matrix is estimated for the measured noise.

Claims (6)

1. An interactive multi-model integrated navigation method is characterized by comprising the following steps:
s1: establishing a state equation according to the error model of the integrated navigation system;
s2: jointly measuring noise variance matrix output according to last state estimation
Figure FDA0002970225450000011
Establishing three models which respectively correspond to the measured noise variance matrix:
Figure FDA0002970225450000012
wherein sigma is a constant matrix and is set according to the system application environment;
s3: calculating the initial state of the estimation and the error variance matrix thereof by using the state estimation and the error variance matrix thereof of each model output by the last state estimation;
s4: respectively carrying out Sage-Husa self-adaptive filtering on the three established models;
s5: updating the model by adopting a Bayesian hypothesis testing method;
s6: according to the weight, performing weighted fusion on output information of each model, calculating a joint state estimation, an estimation error variance matrix and a measurement noise variance matrix, and outputting a final result;
the step S4 specifically includes the following steps:
and respectively carrying out Sage-Husa adaptive Kalman filtering on the three models:
s4.1 discretizing the state equation:
Figure FDA0002970225450000013
wherein j represents the jth filter, j is 1-3, k represents the kth time, and X representsj(k)Is a state vector, phij(k,k-1)For a state one-step transition matrix, Xj(k-1)Is the last moment filter state vector, Gj(k)For system noise input matrix, Wj(k)Is a systematic noise vector, Zj(k)For measuring the vector, Hj(k)For measuring the matrix, Vj(k)To measure the noise vector;
s4.2, calculating a Kalman filtering one-step prediction state vector and an error variance matrix:
Figure FDA0002970225450000014
Figure FDA0002970225450000015
wherein the content of the first and second substances,
Figure FDA0002970225450000016
the matrix is predicted for one step of the state,
Figure FDA0002970225450000017
for mixing of the initial state, Pj(k,k-1)For a state one step
Error variance matrix, POj(k-1)For mixed initial state error variance matrix, Gj(k)For system noise input matrix, Qj(k)Is a system noise error variance matrix;
s4.3, calculating Kalman filtering residual errors:
Figure FDA0002970225450000018
wherein
Figure FDA0002970225450000021
Estimating a mean value for the measured noise;
s4.4, calculating a Kalman filtering state gain matrix:
Figure FDA0002970225450000022
wherein, Kj(k)In the form of a matrix of state gains,
Figure FDA0002970225450000023
estimating a variance matrix for the measured noise;
s4.5, calculating Kalman filtering state estimation and a variance matrix thereof:
Figure FDA0002970225450000024
Pj(k)＝(I-Kj(k)Hj(k))Pj(k,k-1)
wherein the content of the first and second substances,
Figure FDA0002970225450000025
for state estimation vectors, Pj(k)An estimation error variance matrix is obtained;
s4.6, calculating a measurement noise mean value and variance matrix:
Figure FDA0002970225450000026
Figure FDA0002970225450000027
wherein d isk＝(1-b)/(1-bk+1)，b＝0.95～0.99，
Figure FDA0002970225450000028
In order to measure the mean value of the noise estimate,
Figure FDA0002970225450000029
the mean value of the measured noise estimates for the last time instant,
Figure FDA00029702254500000210
a variance matrix is estimated for the measured noise.
2. The interactive multi-model integrated navigation method according to claim 1, wherein the step S1 specifically includes the following procedures:
establishing a state equation according to the error model of the integrated navigation system:
Figure FDA00029702254500000211
Z＝HX+V
wherein X is a state vector, F is a system matrix, W is a system noise vector, Z is a measurement vector, H is a measurement matrix, and V is a measurement noise vector.
3. The interactive multi-model integrated navigation method according to claim 1, wherein the step S2 specifically includes the following procedures:
jointly measuring noise variance matrix output according to last state estimation
Figure FDA00029702254500000212
Three models are established { m1 m2 m3And the measured noise variance matrix is respectively corresponding to:
Figure FDA00029702254500000213
and sigma is a constant matrix and is set according to the system application environment.
4. The interactive multi-model integrated navigation method according to claim 1, wherein the step S3 specifically includes the following procedures:
s3.1, assuming that the model transition probability follows the Markov process, calculating the model prediction probability as follows:
Figure FDA0002970225450000031
P{mj(k)|mi(k-1)is the model m from the time k-1 to the time ki(k-1)To model mj(k)And Markov transition probability, abbreviated as Pi→jUsing a preset constant, mui(k-1)Is a model mi(k-1)The model matching probability of (2);
s3.2, the mixed initial state and the error variance matrix of each filter are given as follows:
Figure FDA0002970225450000032
Figure FDA0002970225450000033
Figure FDA0002970225450000034
wherein the content of the first and second substances,
Figure FDA0002970225450000035
for mixing the initial states, i.e. the state input, P, of the filter j at the present momentOj(k-1)For a hybrid initial state error variance matrix, i.e. an input state error variance matrix,
Figure FDA0002970225450000036
for the state estimation of the ith filter at the previous time, Pi(k-1)For its corresponding error variance matrix, mui→j(k-1)Probabilities are predicted for the model.
5. The interactive multi-model integrated navigation method according to claim 1, wherein the step S5 specifically includes the following procedures:
updating the models by adopting a Bayesian hypothesis test method, and calculating a likelihood function according to the residual error and the variance matrix of each model corresponding to the k moment of the filter:
Figure FDA0002970225450000037
Figure FDA0002970225450000038
where m is the dimension of the measurement vector, Aj(k)A residual variance matrix is obtained;
and calculating the weight of the model in the model set, and updating the model probability:
Figure FDA0002970225450000039
wherein, muj(k)Is the probability of the model, fj(k)As a likelihood function, Pi→jFor Markov transition probability, μi(k-1)Is a model mi(k-1)The model matching probability of (2).
6. The interactive multi-model integrated navigation method according to claim 1, wherein the step S6 specifically includes the following procedures:
and according to the weight, carrying out weighted fusion on the estimated values of the models, calculating a joint state estimation, a joint error variance matrix and a joint measurement noise variance matrix, and outputting an interactive multi-model final result:
Figure FDA0002970225450000041
Figure FDA0002970225450000042
Figure FDA0002970225450000043
wherein the content of the first and second substances,
Figure FDA0002970225450000044
in order to perform a joint state estimation,
Figure FDA0002970225450000045
for the state estimation vector, muj(k)As model probability, PkIs a joint error variance matrix.
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