CN109543143B - Multi-sensor fusion estimation method of nonlinear deviation system - Google Patents
Multi-sensor fusion estimation method of nonlinear deviation system Download PDFInfo
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Abstract
The invention relates to a multi-sensor fusion estimation method of a nonlinear band deviation system based on a dispersion fusion filtering technology. Aiming at the estimation problem of a nonlinear multi-sensor system with dynamic deviation, the invention adds a dispersion fusion filtering technology and provides a two-stage volume Kalman filtering fusion estimation method. In the decentralized fusion structure, each sensor needs to send its own state estimation information to the fusion center, and at the same time, all filters update the state estimation information in time to obtain a predicted value. And each local filter performs measurement and update on the predicted value to obtain local state estimation information. And processing the state estimation information of all the filters in the fusion center to obtain global state estimation information. The performance of the method is superior to that of a single-sensor two-stage Kalman filtering method.
Description
Technical Field
The invention belongs to the field of filter estimation, and particularly relates to a multi-sensor fusion estimation method with a deviation system based on a dispersion fusion technology.
Background
In reality, nonlinear systems account for a large proportion, and in nonlinear systems, system states or measurements may be affected by dynamic deviations for various reasons. In view of the above, it has become important to perform accurate estimation of the system state. Conventional state estimation methods for non-biased nonlinear systems, such as extended kalman filters, unscented kalman filters, etc., are numerous, while state estimation methods for biased nonlinear systems are not uncommon. It is necessary to find a new estimation method for widely existing band offset systems.
In view of the above, it has become important to perform accurate estimation of the system state. Typically, dynamic bias is linear, and nonlinear systems can be divided into bias-free state systems and bias systems that are not affected by bias. Since the state equation is a nonlinear equation, the unbiased state can be estimated using a nonlinear estimation method (e.g., a volume kalman filter), the bias is partially a linear equation, and the bias can be estimated by a filter that is approximately linear to obtain an estimated value of the bias. Then, the estimation value of the system state is obtained by combining a fusion factor. The calculation amount is obviously reduced due to the separation of matrix operation, and the method is favored by related researchers.
The existing nonlinear two-stage Kalman filter research is mainly based on a single sensor, and the nonlinear two-stage Kalman filter based on multiple sensors is less. Because the data of a single sensor is single, the estimation precision is not high, and a plurality of sensors can be used for estimating the system state, wherein the scattered fusion estimation is a very good estimation method for a nonlinear band deviation system. In this configuration, the total force of the main filter and the partial filter is estimated, and a more accurate estimated value can be obtained.
Disclosure of Invention
For the case of filtering nonlinear systems with multiple sensors, the ways of centralized multi-sensor information fusion (extending the measurement vector) and distributed multi-sensor information fusion that are popular for linear systems are no longer suitable because their accuracy is too poor or the solution process is too complex. Based on a two-stage volume Kalman filter, a dispersion fusion technology is added, and a two-stage volume Kalman fusion estimator is provided. The main filter uses the output information of each local filter, fuses to obtain the global estimated value of the system state, and reasonably feeds back to each local filter. Compared with a two-stage volume Kalman filter of a single sensor, the new method improves the estimation accuracy.
The present invention is largely divided into three parts. The first part is system model establishment; the second part constructs a two-stage volume Kalman filter; in the third part, a two-stage volume Kalman fusion estimator is obtained according to the local filter information.
The invention has the beneficial effects that: the nonlinear band deviation system can be accurately estimated, and compared with a common single-sensor estimation method, the method provided can obtain higher system state estimation accuracy.
Brief description of the drawings
Fig. 1 is a schematic block diagram of the present invention.
Fig. 2 is a detailed process diagram of step 3.
Detailed Description
As shown in fig. 1, the specific implementation steps of the present invention are as follows:
step 1, modeling a system
Taking the nonlinear multi-sensor system with deviation as a model, the statistical characteristics of noise in the system process are known, and the state equation, the deviation equation and the measurement equation of the nonlinear multi-sensor system are described in the following mathematics:
y i,k ＝h i (x k )+D i,k b k +v i,k (3)
wherein k represents a time series; x is x k ，b k And y i,k The system is respectively an n-dimensional state vector, an m-dimensional deviation vector and a p-dimensional observation vector of an ith sensor;and v i,k The system state noise vector, the system deviation noise vector and the measurement noise vector of the ith sensor are respectively; f (x) k ) Is a state transfer function; h is a i (x k ) Is the state observation function of the ith sensor. The process noise, the bias noise and the measurement noise are zero-mean Gaussian white noise sequences: /> v i,k ～N(0,V i,k )。
Step 2, using a single-sensor two-stage volume Kalman filter to respectively obtain an estimated value of a non-deviation state and an estimated value of deviation
The sampling point set (volume point set) of the two-stage volume kalman filter is:
considering fig. 1, estimation information of the unbiased state is obtained:
the residual of the deviation can be expressed as:
the covariance matrix of the bias can be expressed as:
obtaining linear filter deviation state estimation information:
b k+1/k ＝b k/k (17)
due to the presence of state transfer functions and measurement functions, it is necessary to estimate values in a state without deviationAnd predicted valueBased on the above two functions, approximate expressions are given:
thus, the system state can be expressed as:
step 2 is shown in fig. 1.
Step 3, performing dispersion fusion on the N two-stage volume Kalman filters to obtain estimation information of the system state
The dispersion fusion filtering is a good filtering estimation method for the nonlinear band deviation system. In a decentralized fusion architecture, each sensor needs to send its own state and its error covariance matrix to the fusion center. And simultaneously, all filters update time by using the state estimation value and the error covariance matrix at the last moment to obtain a predicted value. Furthermore, each local filter performs measurement and update by using its own predicted value to obtain local state estimation information. And processing by using the state estimation information of all the filters in the fusion center to obtain a global state estimation value and a global error covariance matrix thereof. The i-th unbiased state filter and the main filter find state estimation information:
unbiased state filter:
a main filter:
the ith unbiased state filter performs measurement updates:
wherein Y is i,k+1/k+1 An inverse of the locally estimated covariance matrix for the unbiased state,is the inverse of the local estimate of the unbiased state.
In a decentralized fusion architecture, the fusion center feeds back the global estimate to each local sensor to process the next measurement value, so the vector and matrix of prediction information for each local estimator is the same:
thus, the global estimate is
Wherein Y is g,k+1/k+1 An inverse of the global estimated covariance matrix for the unbiased state,is the inverse of the global estimate of the unbiased state.
Then, the estimation results of the unbiased state filter and the biased filter are combined to obtain estimation information of the system state
Wherein V is i,k+1 Step 3 is shown in FIG. 2 as a fusion factor.
Claims (1)
1. The multi-sensor fusion estimation method of the nonlinear deviation system is characterized by comprising the following steps of:
step 1, modeling a system;
taking the nonlinear multi-sensor system with deviation as a model, the statistical characteristics of noise in the system process are known, and the state equation, the deviation equation and the measurement equation of the nonlinear multi-sensor system are described as follows:
y i,k ＝h i (x k )+D i,k b k +v i,k (3)
wherein k represents time; x is x k ,b k And y i,k The system is respectively an n-dimensional state vector, an m-dimensional deviation vector and a p-dimensional observation vector of an ith sensor;and v i,k The system state noise vector, the system deviation noise vector and the measurement noise vector of the ith sensor are respectively; f (x) k ) Is a state transfer function; h is a i (x k ) A state observation function for the ith sensor; the process noise, the bias noise and the measurement noise are zero-mean Gaussian white noise sequences: /> v i,k ～N(0,V i,k )；
Step 2, using a single-sensor two-stage volume Kalman filter to respectively obtain an estimated value of a non-deviation state and an estimated value of deviation;
the sampling point set of the two-stage volume Kalman filter is as follows:
estimation information of unbiased state:
the residual of the deviation is expressed as:
the covariance matrix of the bias is expressed as:
obtaining linear filter deviation state estimation information:
b k+1/k ＝b k/k (17)
due to the presence of state transfer functions and measurement functions, it is necessary to estimate values in a state without deviationAnd predictive value->Based on this, the function is approximated:
thus, the system state is expressed as:
step 3, performing dispersion fusion on N two-stage volume Kalman filters to obtain estimation information of the system state;
in the decentralized fusion structure, each sensor transmits its own state and its error covariance matrix to the fusion center; simultaneously, all filters update time by using the state estimation value and the error covariance matrix at the last moment to obtain a predicted value; furthermore, each local filter performs measurement and update by using the predicted value of the local filter to obtain local state estimation information; processing the state estimation information of all the filters in the fusion center to obtain a global state estimation value and a global error covariance matrix thereof; the i-th unbiased state filter and the main filter find state estimation information:
unbiased state filter:
a main filter:
the ith unbiased state filter performs measurement updates:
wherein Y is i,k+1/k+1 An inverse of the locally estimated covariance matrix for the unbiased state,office in unbiased stateAn inverse matrix of the partial estimation;
in a decentralized fusion architecture, the fusion center feeds back the global estimate to each local sensor to process the next measurement value, so the vector and matrix of prediction information for each local estimator is the same:
thus, the global estimate is
Wherein Y is g,k+1/k+1 An inverse of the global estimated covariance matrix for the unbiased state,an inverse matrix that is a global estimate of the no bias state;
then, the estimation results of the unbiased state filter and the biased filter are combined to obtain estimation information x of the system state k+1/k+1 ,
Wherein V is i，k+1 Is a fusion factor.
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| CN110490273A (en) * | 2019-09-12 | 2019-11-22 | 河南牧业经济学院 | The multisensor syste fused filtering algorithm that noise variance inaccurately models |
| CN111107070A (en) * | 2019-12-10 | 2020-05-05 | 浙江工业大学 | Target tracking method under DoS attack |
| CN111062359B (en) * | 2019-12-27 | 2023-03-31 | 广东海洋大学深圳研究院 | Two-stage Kalman filtering fusion method based on noise sequential decorrelation |
| CN111756353B (en) * | 2020-06-12 | 2024-04-16 | 杭州电子科技大学 | Nonlinear fusion filtering-based noise optimization method for liquid level instrument |
| CN112489075B (en) * | 2020-12-03 | 2024-02-06 | 杭州电子科技大学 | Sequential inertial multi-sensor fusion filtering method based on characteristic function |
| CN112561834A (en) * | 2020-12-21 | 2021-03-26 | 杭州电子科技大学 | Parallel multi-sensor fusion filtering method based on characteristic function |
| CN112649804A (en) * | 2020-12-21 | 2021-04-13 | 杭州电子科技大学 | Centralized multi-sensor fusion filtering method based on characteristic function |
| CN113011475B (en) * | 2021-01-29 | 2022-12-02 | 深圳信息职业技术学院 | Distributed fusion method considering correlated noise and random parameter matrix |
| CN115022348B (en) * | 2022-05-27 | 2023-04-28 | 江南大学 | Intelligent factory cloud-level architecture data storage method for high-end battery |
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