CN111310110B - Hybrid state estimation method for high-dimensional coupling uncertain system - Google Patents

Hybrid state estimation method for high-dimensional coupling uncertain system Download PDF

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CN111310110B
CN111310110B CN202010205361.5A CN202010205361A CN111310110B CN 111310110 B CN111310110 B CN 111310110B CN 202010205361 A CN202010205361 A CN 202010205361A CN 111310110 B CN111310110 B CN 111310110B
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CN111310110A (en
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焦玉召
王晓雷
娄泰山
赵红梅
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Zhengzhou University of Light Industry
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G06—COMPUTING; CALCULATING OR COUNTING
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Abstract

The invention provides a method for estimating a mixed state of a high-dimensional coupling uncertain system, which comprises the following steps: firstly, constructing Gao Weishen coupled uncertain system states, parameters and measured models, and designing corresponding observer models to obtain estimated values of the states and the parameters; secondly, decomposing the system discretization into a low-dimensional discretization mixed model, and further obtaining the low-dimensional discretization mixed model and a parameter model; and finally, taking the output estimated value of the observer as an auxiliary signal, and respectively carrying out filtering treatment on the state estimated value of the low-dimensional discretization mixed model by utilizing a volume Kalman filtering algorithm to output the state value of the low-dimensional discretization mixed model. The invention corrects the system model by the estimated value output by the observer, can effectively improve the system state estimation precision on the premise of ensuring the system stability, and simultaneously reduces the calculation dimension of the filtering calculation process by the low-dimensional volume Kalman filtering algorithm, thereby being applicable to the high-dimensional, coupled and nonlinear system state estimation with uncertainty.

Description

Hybrid state estimation method for high-dimensional coupling uncertain system
Technical Field
The invention relates to the technical field of hybrid state estimation, in particular to a hybrid state estimation method of a high-dimensional coupling uncertain system.
Background
For a linear accurate model, a linear Kalman filtering algorithm provides an optimal recursive solution for the system. For practical complex engineering systems, however, the system model is typically nonlinear, high-dimensional, coupled, and there is a parameter uncertainty in the system model. At this time, the classical model-based estimation method has the problems of overlarge calculated amount, reduced estimation accuracy and even divergence. There is no effective state estimation method for high-dimensional, nonlinear, uncertain systems. Therefore, the state estimation method under the high-dimensional, nonlinear and uncertain system model has certain frontier property and practical application value.
Disclosure of Invention
Aiming at the technical problems of large calculated amount, low estimation precision and divergent results of the existing state estimation method, the invention provides a mixed state estimation method of a high-dimensional coupling uncertain system, which can realize accurate, effective and stable state and parameter estimation of the high-dimensional, nonlinear and uncertain nonlinear system, reduce the calculation dimension of the estimation process and improve the precision of the state estimation of the system on the premise of ensuring the stability of the estimation process.
The technical scheme of the invention is realized as follows:
a method for estimating the mixed state of a high-dimensional coupling uncertain system comprises the following steps:
s1, constructing Gao Weishen coupling uncertain system state models, parameter models and measurement models;
s2, respectively constructing observer models of states and parameters according to the system state model, the parameter model and the measurement model, and estimating estimated values of the states and the parameters of the system by using the observer models of the states and the parameters;
s3, discretizing the system state model, the parameter model and the measurement model in the step S1 by using an Euler method to obtain a low-dimensional discretized mixed model, and modeling uncertain parameters in the low-dimensional discretized mixed model to obtain a parameter discrete model;
s4, based on the system state and the estimated value of the parameter in the step S2, respectively carrying out filtering processing on the low-dimensional discretization mixed model and the parameter discrete model in the step S3 by utilizing a volume Kalman filtering algorithm, and outputting the state value of the low-dimensional discretization mixed model.
Gao Weishen in the step S1, the uncertain system state model, the parameter model and the measurement model are respectively:
Figure BDA0002419320900000011
Figure BDA0002419320900000012
y(t)＝h(x(t),t)+υ(t) (3)，
wherein ,
Figure BDA0002419320900000021
representing the first derivative of the system state, f (·) is a nonlinear state transition matrix, x (t) represents a state variable that varies with time t, θ (t) represents an uncertainty parameter, u (t) represents a system input variable, ω 1 (t) is state process noise, +.>
Figure BDA0002419320900000022
Representing the first derivative, ω, of a system uncertainty parameter 2 (t) is the parameter process noise, y (t) is the measured value, h (·) is the measurement transfer matrix, and v (t) is the measurement noise. />
The observer models respectively constructing states and parameters according to the system state model, the parameter model and the measurement model are respectively as follows:
Figure BDA0002419320900000023
Figure BDA0002419320900000024
wherein ,
Figure BDA0002419320900000025
first derivative representing system state estimate,/->
Figure BDA0002419320900000026
Representing a linear state estimate,/>
Figure BDA0002419320900000027
Representing the first derivative of the parameter estimate, +.>
Figure BDA0002419320900000028
Representing the estimated value of the input variable, K 1 and K2 Representing a corresponding matrix of observer gains,
Figure BDA0002419320900000029
representing the deviation between the actual measurement of the system and the output measurement of the observer,/>
Figure BDA00024193209000000210
Representing the output measurement of the observer.
The low-dimensional discretized mixed model is as follows:
Figure BDA00024193209000000211
Figure BDA00024193209000000212
Figure BDA00024193209000000213
wherein ,
Figure BDA00024193209000000214
representing the nonlinear state component at time k +.>
Figure BDA00024193209000000215
Representing the nonlinear state component at time k-1, and (2)>
Figure BDA00024193209000000216
Representing the linear state component at time k +.>
Figure BDA00024193209000000217
Representing the linear state component at time k-1, < ->
Figure BDA00024193209000000218
Nonlinear state uncertainty parameter representing time k-1,/>
Figure BDA00024193209000000219
Represents k-linear state uncertainty parameter at time-1, < ->
Figure BDA00024193209000000220
Input variable representing the relation of time k to the state of the nonlinear system,/->
Figure BDA00024193209000000221
Input variable representing k time correlated with the state of the linear system,/->
Figure BDA00024193209000000222
Representing process noise associated with a nonlinear system state, < +.>
Figure BDA00024193209000000223
Representing process noise associated with a linear system state, < + >>
Figure BDA00024193209000000224
Representing a nonlinear state transition matrix,>
Figure BDA00024193209000000225
representing a linear state transition matrix associated with a non-linear state, < >>
Figure BDA00024193209000000226
Representing a linear state transition matrix->
Figure BDA00024193209000000227
Representing a nonlinear state transition matrix associated with a linear state, h k (. Cndot.) represents a measurement transfer matrix associated with a nonlinear state, B k (. Cndot.) represents the measurement transfer matrix associated with the linear state.
When the nonlinear state uncertain parameter and the linear state uncertain parameter are dynamic variable parameters, the parameter discrete model is as follows:
Figure BDA00024193209000000228
Figure BDA00024193209000000229
wherein ,
Figure BDA00024193209000000230
uncertainty parameter indicating the relation of moment k to the non-linear state,/->
Figure BDA00024193209000000231
Uncertainty parameter indicating the time of k-1 in relation to the nonlinear state, < >>
Figure BDA00024193209000000232
Uncertainty parameter indicating the relation of the moment k to the linear state,/->
Figure BDA00024193209000000233
An uncertainty parameter related to the linear state, representing the moment k-1,/>
Figure BDA00024193209000000234
Representing uncertain parameters->
Figure BDA00024193209000000235
Transfer matrix of->
Figure BDA00024193209000000236
Representing uncertain parameters->
Figure BDA00024193209000000237
Is a transfer matrix, ζ k-1 and εk-1 All represent zero-mean gaussian white noise;
when the nonlinear state uncertain parameter and the linear state uncertain parameter are static constant parameters, the parameter discrete model is as follows:
Figure BDA0002419320900000031
Figure BDA0002419320900000032
the method for outputting the state value of the nonlinear state in the low-dimensional discretization mixed model comprises the following steps of:
s41, according to the initial filtering error covariance
Figure BDA0002419320900000033
And state observer estimate at time k-1 +.>
Figure BDA0002419320900000034
The nonlinear state filtering value and the filtering error covariance of the next moment are calculated, and the specific method is as follows:
s41.1, generating an initial volume point:
Figure BDA0002419320900000035
wherein ,[1]i Represents a set of n-dimensional state space unit vector points, i=1, 2..m represents weights, and m=2n, δ i Representing the point of the initial volume of the unit,
Figure BDA0002419320900000036
representing nonlinear state estimation value, S k-1 Square root, χ, representing the covariance of the estimation error i,k-1 An initial volume point representing a system state;
s41.2, calculating nonlinear state predicted value
Figure BDA0002419320900000037
Figure BDA0002419320900000038
wherein ,
Figure BDA0002419320900000039
representing the state transfer volume point, +.>
Figure BDA00024193209000000310
Representing the linear state component at time k-1, < ->
Figure BDA00024193209000000311
Represents an uncertainty parameter related to a non-linear state, < ->
Figure BDA00024193209000000312
Representing an input variable associated with a nonlinear state;
s41.3, according to the nonlinear state predicted value in step S41.2
Figure BDA00024193209000000313
Calculating prediction error covariance +.>
Figure BDA00024193209000000314
Figure BDA00024193209000000315
wherein ,Qn Representing process noise
Figure BDA00024193209000000316
Is a variance of (2);
s42, according to the prediction error covariance
Figure BDA00024193209000000317
And nonlinear state predictor +>
Figure BDA00024193209000000318
Calculating a measurement prediction value->
Figure BDA00024193209000000319
And measurement estimation error covariance->
Figure BDA00024193209000000320
The specific method comprises the following steps:
s42.1, generating a predicted volume point χ i,k|k-1 ：
Figure BDA00024193209000000321
wherein ,Sk|k-1 Square root factor, delta, representing estimation error covariance i Representing a unit initial volume point;
s42.2, calculating a measurement predicted value
Figure BDA00024193209000000322
Figure BDA00024193209000000323
wherein ,
Figure BDA0002419320900000041
representing the measurement transfer volume point +.>
Figure BDA0002419320900000042
Representing the linear state component at time k, h k (. Cndot.) represents a measurement transfer matrix associated with a nonlinear state, B k (-) represents a measurement transfer matrix associated with a linear state;
s42.3, according to the measured predicted value
Figure BDA0002419320900000043
Calculating the measurement prediction error covariance +.>
Figure BDA0002419320900000044
Figure BDA0002419320900000045
Wherein R is measurement noise v k Is a variance of (2);
s43, predicting value according to the nonlinear state in the step S41.2
Figure BDA0002419320900000046
And measurement prediction value +.in step S42.2>
Figure BDA0002419320900000047
Calculating predictive cross-covariance +.>
Figure BDA0002419320900000048
Figure BDA0002419320900000049
S44, utilizing predictive cross-covariance
Figure BDA00024193209000000410
And measurement error covariance->
Figure BDA00024193209000000411
Updating the filter error covariance at time k
Figure BDA00024193209000000412
And uses the nonlinear state prediction value +>
Figure BDA00024193209000000413
Measurement value y k And measuring the predicted value->
Figure BDA00024193209000000414
Calculating the state value of the nonlinear state of a low-dimensional discretized hybrid model>
Figure BDA00024193209000000415
Figure BDA00024193209000000416
Figure BDA00024193209000000417
wherein ,
Figure BDA00024193209000000418
the technical scheme has the beneficial effects that:
(1) The invention is based on model parameter decoupling, can intuitively model the influence of uncertain parameters on the specific state of the system, and can solve the parameter modeling problem under the uncertain system model parameters;
(2) According to the invention, by constructing the low-dimensional discretization mixed model, the high-dimensional system can be decomposed into a mixed form of a plurality of low-dimensional systems, and the purpose of reducing the system dimension is achieved by the mixing, so that the calculation dimension of the subsequent estimation process is reduced;
(3) According to the invention, parameters in the mixed model are estimated through a design parameter observer, so that the problems of stability reduction and even divergence of a classical estimation theory under the condition that parameters of a system model are uncertain are overcome;
(4) The volume Kalman filtering algorithm based on the mixed model and the parameter observer overcomes the dependence of the traditional volume Kalman filtering algorithm on accurate system model parameters, and compared with the unscented Kalman filtering algorithm and the Monte Carlo particle filtering algorithm, the volume Kalman filtering algorithm based on the volume rule has fewer sample points and further reduces the calculated amount.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a flow chart of a parameter observer of the present invention;
FIG. 3 is a flow chart of a volume Kalman filtering algorithm based on the output of a parameter observer according to the 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 any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, the embodiment of the invention provides a method for estimating a hybrid state of a high-dimensional coupling uncertain system, which comprises the following specific steps:
s1, constructing a Gao Weishen coupling uncertain system state model, a parameter model and a measurement model, wherein the general form is as follows:
Figure BDA0002419320900000051
Figure BDA0002419320900000052
y(t)＝h(x(t),t)+υ(t) (3)，
wherein ,
Figure BDA0002419320900000053
representing the first derivative of the system state, f (·) is a nonlinear state transition matrix, x (t) represents a state variable that varies with time t, θ (t) represents an uncertainty parameter, u (t) represents a system input variable, ω 1 (t) is state process noise, +.>
Figure BDA0002419320900000054
Representing the first derivative, ω, of a parameter representing uncertainty of the system 2 (t) is Ginseng radixAnd (3) counting process noise, wherein y (t) is a measured value, h (·) is a measurement transfer matrix, and v (t) is measurement noise.
S2, respectively constructing observer models of states and parameters according to the system state model, the parameter model and the measurement model, and estimating estimated values of the states and the parameters of the system by using the observer models of the states and the parameters; it is assumed that the system is fully controllable and observable. The observer models as shown in fig. 2 can be designed separately based on observer theory. Wherein the observer gains correspond to different observers, respectively. The observer model is constructed as follows:
Figure BDA0002419320900000055
Figure BDA0002419320900000056
wherein ,
Figure BDA0002419320900000057
first derivative representing system state estimate,/->
Figure BDA0002419320900000058
Representing a nonlinear state estimate,/->
Figure BDA0002419320900000059
Representing the first derivative of the parameter estimate, +.>
Figure BDA00024193209000000510
Representing the estimated value of the input variable, K 1 and K2 Representing a corresponding matrix of observer gains,
Figure BDA00024193209000000511
representing the deviation between the actual measurement of the system and the output measurement of the observer,/>
Figure BDA00024193209000000512
Representing the output measurement of the observer.
S3, discretizing the system state model, the parameter model and the measurement model in the step S1 by using an Euler method to obtain a low-dimensional discretized mixed model:
Figure BDA0002419320900000061
Figure BDA0002419320900000062
Figure BDA0002419320900000063
wherein the nonlinear state and the linear state are mutually influenced,
Figure BDA0002419320900000064
representing the nonlinear state component at time k +.>
Figure BDA0002419320900000065
Representing the nonlinear state component at time k-1, and (2)>
Figure BDA0002419320900000066
Representing the linear state component at time k +.>
Figure BDA0002419320900000067
Representing the linear state component at time k-1, < ->
Figure BDA0002419320900000068
Representing nonlinear state uncertainty parameters, +.>
Figure BDA0002419320900000069
Representing a linear state uncertainty parameter, +.>
Figure BDA00024193209000000610
Input variable representing the relation of time k to the state of the nonlinear system,/->
Figure BDA00024193209000000611
Input variable representing k time correlated with the state of the linear system,/->
Figure BDA00024193209000000612
Mean value 0 and variance Q n Nonlinear process noise of>
Figure BDA00024193209000000613
Mean value 0 and variance Q l Linear process noise, < >>
Figure BDA00024193209000000614
Representing a nonlinear state transition matrix,>
Figure BDA00024193209000000615
representing a linear state transition matrix associated with a non-linear state, < >>
Figure BDA00024193209000000616
Representing a linear state transition matrix->
Figure BDA00024193209000000617
Representing a nonlinear state transition matrix associated with a linear state, h k (. Cndot.) represents a measurement transfer matrix associated with a nonlinear state, B k (. Cndot.) represents the measurement transfer matrix associated with the linear state.
When the nonlinear state uncertain parameters and the linear state uncertain parameters are dynamic variable parameters, modeling the uncertain parameters in the low-dimensional discretization mixed model, and obtaining a parameter discrete model which is:
Figure BDA00024193209000000618
/>
Figure BDA00024193209000000619
wherein ,
Figure BDA00024193209000000620
uncertainty parameter indicating the relation of moment k to the nonlinear state,/->
Figure BDA00024193209000000621
Uncertainty parameter indicating k time related to linear state, < ->
Figure BDA00024193209000000622
Representing uncertain parameters->
Figure BDA00024193209000000623
Transfer matrix of->
Figure BDA00024193209000000624
Representing uncertain parameters->
Figure BDA00024193209000000625
Is a transfer matrix, ζ k-1 and εk-1 All represent zero-mean gaussian white noise;
when the nonlinear state uncertain parameters and the linear state uncertain parameters are static constant parameters, modeling the uncertain parameters in the low-dimensional discretization mixed model, and obtaining a parameter discrete model which is:
Figure BDA00024193209000000626
Figure BDA00024193209000000627
s4, based on the system state and the estimated value of the parameter in the step S2, respectively performing a low-dimensional discretization mixed model and a parameter discrete model in the step S3 by using a volume Kalman filtering algorithmLine filtering processing to obtain state estimation value at k time according to formula (4)
Figure BDA00024193209000000628
and />
Figure BDA00024193209000000629
Obtaining a parameter estimation value according to formula (5)>
Figure BDA00024193209000000630
and />
Figure BDA00024193209000000631
And will->
Figure BDA00024193209000000632
and />
Figure BDA00024193209000000633
The volume Kalman filtering algorithm is modified as a modification signal of the low-dimensional discretized mixed model at the moment k, and finally the state value of the low-dimensional discretized mixed model is output, so that nonlinear state variable +.>
Figure BDA00024193209000000634
For example, as shown in fig. 3, the specific method is as follows:
s41, according to the initial estimation error covariance
Figure BDA00024193209000000635
And a nonlinear state estimation value +.f at time k-1>
Figure BDA00024193209000000636
Calculating a nonlinear state predicted value and an estimation error covariance, wherein the specific method comprises the following steps of:
s41.1, generating an initial volume point:
Figure BDA0002419320900000071
wherein ,[1]i represents a set of n-dimensional state space unit vector points, i=1, 2..m=2n represents weights, δ i Representing the point of the initial volume of the unit,
Figure BDA0002419320900000072
representing nonlinear state estimation value, S k-1 Representing the square root of the estimated error covariance via
Figure BDA0002419320900000073
Calculated, χ i,k-1 An initial volume point representing a system state;
s41.2, calculating nonlinear state predicted value
Figure BDA0002419320900000074
Figure BDA0002419320900000075
wherein ,
Figure BDA0002419320900000076
representing the state transfer volume point, +.>
Figure BDA0002419320900000077
Representing the linear state component at time k-1, < ->
Figure BDA0002419320900000078
Represents an uncertainty parameter related to a non-linear state, < ->
Figure BDA0002419320900000079
Representing an estimate of an input variable associated with a nonlinear state,/->
Figure BDA00024193209000000710
Output value of the corresponding non-linear state related visitor in step S3, +.>
Figure BDA00024193209000000711
Representing the output value of a linear state observer in the step S3 at the moment of k-1;
s41.3, according to the nonlinear state predicted value in step S41.2
Figure BDA00024193209000000712
Calculating prediction error covariance +.>
Figure BDA00024193209000000713
Figure BDA00024193209000000714
wherein ,Qn Representing process noise
Figure BDA00024193209000000715
Is a variance of (2);
s42, according to the prediction error covariance
Figure BDA00024193209000000716
And nonlinear state predictor +>
Figure BDA00024193209000000717
Calculating a measurement prediction value->
Figure BDA00024193209000000718
And measurement estimation error covariance->
Figure BDA00024193209000000719
The specific method comprises the following steps: />
S42.1, generating a predicted volume point χ i,k|k-1 ：
Figure BDA00024193209000000720
wherein ,Sk|k-1 Square root factor representing estimation error covariance via
Figure BDA00024193209000000721
Calculated, delta i Representing a unit initial volume point;
s42.2, calculating a measurement predicted value
Figure BDA00024193209000000722
Figure BDA00024193209000000723
wherein ,
Figure BDA00024193209000000724
representing the measurement transfer volume point +.>
Figure BDA00024193209000000725
Represents the linear state observer output value, h in step S3 at time k k (. Cndot.) represents a measurement transfer matrix associated with a nonlinear state, B k (-) represents a measurement transfer matrix associated with a linear state;
s42.3, according to the measured predicted value
Figure BDA0002419320900000081
Calculating measurement error covariance->
Figure BDA0002419320900000082
Figure BDA0002419320900000083
Wherein R is measurement noise v k Is a variance of (2);
s43, predicting value according to the nonlinear state in the step S41.2
Figure BDA0002419320900000084
And measurement prediction value +.in step S42.2>
Figure BDA0002419320900000085
Calculating predictive cross-covariance +.>
Figure BDA0002419320900000086
Figure BDA0002419320900000087
S44, utilizing predictive cross-covariance
Figure BDA0002419320900000088
And measurement error covariance->
Figure BDA0002419320900000089
Updating the estimated error covariance at time k
Figure BDA00024193209000000810
And uses the nonlinear state prediction value +>
Figure BDA00024193209000000811
Measurement value y k And measuring the predicted value->
Figure BDA00024193209000000812
Calculating a nonlinear state estimate of a low-dimensional discretized hybrid model +.>
Figure BDA00024193209000000813
Figure BDA00024193209000000814
Figure BDA00024193209000000815
wherein ,
Figure BDA00024193209000000816
the state value of the low-dimensional discretized mixed model obtained in the step S44
Figure BDA00024193209000000817
Store and output the estimated error covariance +.>
Figure BDA00024193209000000818
Performing state estimation at the next moment by storing and feeding back to the step S41, and performing cyclic operation to realize Gao Weishen coupling uncertain system hybrid nonlinear state +.>
Figure BDA00024193209000000819
Is a function of the estimate of (2).
Similarly, the processing method from step S41 to step S44 can obtain the mixed linear state of the high-dimensional deep coupling uncertain system
Figure BDA00024193209000000820
Is a function of the estimate of (2).
Maneuvering target models based on the current statistical model are widely applied to the field of target tracking, and the position, the speed and the acceleration of the target in a three-dimensional space form a group of 9-dimensional space state models.
In order to illustrate the implementation process of the invention, a model in any one-dimensional space is selected for specific illustration:
1. the one-dimensional maneuvering target continuous state equation is as follows:
Figure BDA00024193209000000821
wherein ,
Figure BDA00024193209000000822
x (t) represents the position of the current target, < >>
Figure BDA00024193209000000823
Representing the speed of the current target,
Figure BDA00024193209000000824
representing the acceleration, ω, of the current target 1 (t) is state noise interference, and under the condition of a 'current' statistical model, when a target moves with a certain acceleration, a non-zero mean time correlation model can be generally adopted to represent the movement of the acceleration, and the specific steps are as follows:
Figure BDA00024193209000000825
a(t)＝-αa(t)+ω 2 (t) (24)，
wherein ,
Figure BDA0002419320900000091
for the average acceleration value, a (t) is zero-average colored noise interference of acceleration, alpha is the reciprocal of time constant, omega 2 (t) zero mean white noise.
2. The one-dimensional spatial measurement equation is:
y(t)＝h(X(t))+υ 1 (t) (25)，
wherein y (t) represents the measured position, v 1 (t) represents measurement noise interference, h (·) represents a measurement state transition matrix.
3. For the system models (22) and (24), the observer of the position, velocity, acceleration, and acceleration colored noise is designed as follows:
Figure BDA0002419320900000092
Figure BDA0002419320900000093
by selecting proper observer gain, the global stability of the observer is ensured, and then the observer estimates the position, speed, acceleration and state estimation value of acceleration interference of the target.
4. Then discretizing the formula (26), wherein the sampling time is delta t, and a discrete state system equation is obtained as follows:
Figure BDA0002419320900000094
the following mixed model state equation can be converted by transformation:
Figure BDA0002419320900000095
Figure BDA0002419320900000096
the discretization model of the acceleration dry colored noise interference is as follows:
a k+1 ＝a k +ω 6,k (31)；
the measurement discretization model is as follows:
y k ＝[1 0 0]X k +υ k (32)；
thus, the variables in the low-dimensional discretized hybrid model are known from equations (30), (31) and (32), respectively:
Figure BDA0002419320900000101
Figure BDA0002419320900000102
Figure BDA0002419320900000103
Figure BDA0002419320900000104
Figure BDA0002419320900000105
Figure BDA0002419320900000106
Figure BDA0002419320900000107
Figure BDA0002419320900000108
Figure BDA0002419320900000109
and finally, filtering the parameters by using a volume Kalman filtering algorithm to obtain the state value of the low-dimensional discretization mixed model.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.

Claims (3)

1. The method for estimating the mixed state of the high-dimensional coupling uncertain system is characterized by comprising the following steps of:
s1, constructing Gao Weishen coupling uncertain system state models, parameter models and measurement models;
s2, respectively constructing observer models of states and parameters according to the system state model, the parameter model and the measurement model, and estimating estimated values of the states and the parameters of the system by using the observer models of the states and the parameters;
the observer models for the states and parameters are respectively:
Figure FDA0004059086220000011
Figure FDA0004059086220000012
wherein ,
Figure FDA0004059086220000013
first derivative representing system state estimate, f (·) is a nonlinear state transition matrix,/-)>
Figure FDA0004059086220000014
Representing a linear state estimate,/>
Figure FDA0004059086220000015
Representing the first derivative of the parameter estimate, +.>
Figure FDA0004059086220000016
Representing the estimated value of the input variable, K 1 and K2 Representing a corresponding observer gain matrix, +.>
Figure FDA0004059086220000017
Representing the deviation between the actual measurement of the system and the output measurement of the observer, y (t) being the measurement,/->
Figure FDA0004059086220000018
Representing an output measurement of the observer;
s3, discretizing the system state model, the parameter model and the measurement model in the step S1 by using an Euler method to obtain a low-dimensional discretized mixed model, and modeling uncertain parameters in the low-dimensional discretized mixed model to obtain a parameter discrete model;
the low-dimensional discretized mixed model is as follows:
Figure FDA0004059086220000019
Figure FDA00040590862200000110
Figure FDA00040590862200000111
wherein ,
Figure FDA00040590862200000112
representing the nonlinear state component at time k +.>
Figure FDA00040590862200000113
Representing the nonlinear state component at time k-1, and (2)>
Figure FDA00040590862200000114
Representing the linear state component at time k +.>
Figure FDA00040590862200000115
Representing the linear state component at time k-1, < ->
Figure FDA00040590862200000116
Nonlinear state uncertainty parameter representing time k-1,/>
Figure FDA00040590862200000117
A linear state uncertainty parameter representing the time of k-1, and (2)>
Figure FDA00040590862200000118
Input variable representing the relation of time k to the state of the nonlinear system,/->
Figure FDA00040590862200000119
Representation ofInput variable associated with the state of the linear system at time k, < >>
Figure FDA00040590862200000120
Representing process noise associated with a nonlinear system state, < +.>
Figure FDA00040590862200000121
Representing process noise associated with a linear system state, < + >>
Figure FDA00040590862200000122
Representing a nonlinear state transition matrix,>
Figure FDA00040590862200000123
representing a linear state transition matrix associated with a non-linear state, < >>
Figure FDA00040590862200000124
Representing a linear state transition matrix->
Figure FDA00040590862200000125
Representing a nonlinear state transition matrix associated with a linear state, h k (. Cndot.) represents a measurement transfer matrix associated with a nonlinear state, B k (-) represents a measurement transfer matrix associated with a linear state;
when the nonlinear state uncertain parameter and the linear state uncertain parameter are dynamic variable parameters, the parameter discrete model is as follows:
Figure FDA00040590862200000126
Figure FDA00040590862200000127
wherein ,
Figure FDA00040590862200000128
uncertainty parameter indicating the relation of moment k to the non-linear state,/->
Figure FDA00040590862200000129
Uncertainty parameter indicating the time of k-1 in relation to the nonlinear state, < >>
Figure FDA0004059086220000021
Uncertainty parameter indicating the relation of the moment k to the linear state,/->
Figure FDA0004059086220000022
An uncertainty parameter related to the linear state, representing the moment k-1,/>
Figure FDA0004059086220000023
Representing uncertain parameters->
Figure FDA0004059086220000024
Transfer matrix of->
Figure FDA0004059086220000025
Representing uncertain parameters->
Figure FDA0004059086220000026
Is a transfer matrix, ζ k-1 and εk-1 All represent zero-mean gaussian white noise;
when the nonlinear state uncertain parameter and the linear state uncertain parameter are static constant parameters, the parameter discrete model is as follows:
Figure FDA0004059086220000027
Figure FDA0004059086220000028
s4, based on the system state and the estimated value of the parameter in the step S2, respectively carrying out filtering processing on the low-dimensional discretization mixed model and the parameter discrete model in the step S3 by utilizing a volume Kalman filtering algorithm, and outputting the state value of the low-dimensional discretization mixed model.
2. The method for estimating hybrid states of a high-dimensional coupled uncertainty system according to claim 1, wherein the Gao Weishen coupled uncertainty system state model, the parameter model and the measurement model in step S1 are respectively:
Figure FDA0004059086220000029
Figure FDA00040590862200000210
y(t)＝h(x(t),t)+υ(t) (3)，
wherein ,
Figure FDA00040590862200000211
representing the first derivative of the system state, f (·) is a nonlinear state transition matrix, x (t) represents a state variable that varies with time t, θ (t) represents an uncertainty parameter, u (t) represents a system input variable, ω 1 (t) is a state process noise,
Figure FDA00040590862200000212
representing the first derivative, ω, of a system uncertainty parameter 2 (t) is the parameter process noise, y (t) is the measured value, h (·) is the measurement transfer matrix, and v (t) is the measurement noise.
3. The method for estimating a hybrid state of a high-dimensional coupled uncertainty system according to claim 1, wherein the method for filtering the low-dimensional discretized hybrid model and the parameter discrete model and outputting the state value of the nonlinear state in the low-dimensional discretized hybrid model comprises the steps of:
s41, according to the initial filtering error covariance
Figure FDA00040590862200000213
And state observer estimate at time k-1 +.>
Figure FDA00040590862200000214
The nonlinear state filtering value and the filtering error covariance of the next moment are calculated, and the specific method is as follows:
s41.1, generating an initial volume point:
Figure FDA00040590862200000215
wherein ,[1]i Represents a set of n-dimensional state space unit vector points, i=1, 2..m represents weights, and m=2n, δ i Representing the point of the initial volume of the unit,
Figure FDA00040590862200000216
representing nonlinear state estimation value, S k-1 Square root, χ, representing the covariance of the estimation error i,k-1 An initial volume point representing a system state;
s41.2, calculating nonlinear state predicted value
Figure FDA00040590862200000217
Figure FDA0004059086220000031
wherein ,
Figure FDA0004059086220000032
representing the state transfer volume point, +.>
Figure FDA0004059086220000033
Representing the linear state component at time k-1, < ->
Figure FDA0004059086220000034
Represents an uncertainty parameter related to a non-linear state, < ->
Figure FDA0004059086220000035
Representing an input variable associated with a nonlinear state;
s41.3, according to the nonlinear state predicted value in step S41.2
Figure FDA0004059086220000036
Calculating prediction error covariance +.>
Figure FDA0004059086220000037
Figure FDA0004059086220000038
wherein ,Qn Representing process noise
Figure FDA0004059086220000039
Is a variance of (2);
s42, according to the prediction error covariance
Figure FDA00040590862200000310
And nonlinear state predictor +>
Figure FDA00040590862200000311
Calculating a measurement prediction value->
Figure FDA00040590862200000312
And measurement estimation error covariance->
Figure FDA00040590862200000313
The specific method comprises the following steps:
s42.1, generating a predicted volume point χ i,k|k-1 ：
Figure FDA00040590862200000314
wherein ,Sk|k-1 Square root factor, delta, representing estimation error covariance i Representing a unit initial volume point;
s42.2, calculating a measurement predicted value
Figure FDA00040590862200000315
Figure FDA00040590862200000316
wherein ,
Figure FDA00040590862200000317
representing the measurement transfer volume point +.>
Figure FDA00040590862200000318
Representing the linear state component at time k, h k (. Cndot.) represents a measurement transfer matrix associated with a nonlinear state, B k (-) represents a measurement transfer matrix associated with a linear state;
s42.3, according to the measured predicted value
Figure FDA00040590862200000319
Calculating the measurement prediction error covariance +.>
Figure FDA00040590862200000320
Figure FDA00040590862200000321
Wherein R is measurement noise v k Is a variance of (2);
s43, predicting value according to the nonlinear state in the step S41.2
Figure FDA00040590862200000322
And measurement prediction value +.in step S42.2>
Figure FDA00040590862200000323
Calculating predictive cross-covariance +.>
Figure FDA00040590862200000324
Figure FDA00040590862200000325
S44, utilizing predictive cross-covariance
Figure FDA00040590862200000326
And measurement error covariance->
Figure FDA00040590862200000327
Updating the filtering error covariance at time k>
Figure FDA00040590862200000328
And uses the nonlinear state prediction value +>
Figure FDA00040590862200000329
Measurement value y k And measuring the predicted value->
Figure FDA00040590862200000330
Calculating the state value of the nonlinear state of a low-dimensional discretized hybrid model>
Figure FDA00040590862200000331
Figure FDA00040590862200000332
Figure FDA0004059086220000041
wherein ,
Figure FDA0004059086220000042
/>
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