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Nonlinear observability analysis method with noise correlation

An analysis method and nonlinear technology, applied in the direction of impedance network, adaptive network, electrical components, etc., can solve the problem that the filtering process cannot be continued, and achieve the effect of improving the nonlinear filtering method

Pending Publication Date: 2020-07-03
宁波飞拓电器有限公司
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Problems solved by technology

However, there are still problems with this method: that is, the non-positive definiteness of the matrix will appear with the iteration of the filtering cycle, which will cause the filtering process to fail. To solve this problem, some scholars have studied the square root volumetric Kalman filter. Cholesky decomposition, avoiding filter interruption due to matrix non-positive definiteness
However, at present, few scholars pay attention to noise-related issues, especially in the field of observability. At present, there are only some scholars who analyze noise-related observability based on linear conditions, and there is no noise-related system for nonlinear systems. Scholars have dabbled in
Noise-related problems cannot be simply ignored in the study of nonlinear systems in the context of practical engineering applications

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  • Nonlinear observability analysis method with noise correlation
  • Nonlinear observability analysis method with noise correlation

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[0048] specific implementation

[0049] The present invention proposes a nonlinear observability analysis method based on condition number fusion, and its flow chart is as follows figure 1 shown, including the following steps:

[0050] Step (1) Noise-related nonlinear system decorrelation processing, the given noise-related nonlinear system model is as follows:

[0051]

[0052] where f(x k-1 ) and h(x k ) are the state function and observation function of the nonlinear model respectively, k is a positive integer, x k is the n×1 state vector, z k is an m×1 observation vector. w k-1 , v k are the process noise and observation noise of the nonlinear model, and they are correlated. Assuming that the process noise and the observation noise are correlated, the variance of Gaussian white noise is: Q k , R k , the statistical properties of the noise are:

[0053]

[0054] The decorrelation processing of formula (1) is as follows:

[0055] x k =f(x k-1 )+w k-1 +J k...

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Abstract

The invention relates to a nonlinear observability analysis method with noise correlation, and belongs to the field of nonlinear observability research. The invention provides a nonlinear observability analysis method with noise correlation. Because the observability theory of the nonlinear system is deficient due to the complexity of the nonlinear system, in the existing research of the observability of the nonlinear system, the analysis and research under the condition that the observation noise of the system is related to the process noise are not considered. According to the invention, theexisting nonlinear observability is studied; the situation that process noise is related to observation noise is considered to be added into analysis and calculation of nonlinear observability. According to the method, the observability relation between the noise-related situation and the noise-unrelated situation is compared, the analysis theory of the observability of the nonlinear system is further perfected, the observability is combined with adaptive filtering, and the nonlinear filtering method is improved.

Description

technical field [0001] The invention relates to a nonlinear observability analysis method with noise correlation, which belongs to the field of observability research. Background technique [0002] Nowadays, with the rapid development of economy and technology, most of the control systems in the practical field of modern engineering are nonlinear problems. Traditional Kalman filtering has continuously derived many filtering methods for nonlinear systems under the background of nonlinear environment. There is an EKF processed by first-order Taylor series expansion. This method uses Taylor series expansion to make the nonlinear system approximate to a linear control system, but this method is not feasible for systems with strong nonlinearity. UKF, the unscented Kalman filter, uses UT transformation to approximate the probability density in the point set after transformation. This method does not need to solve the Jacobian matrix for nonlinear systems, and the computational co...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H03H21/00
CPCH03H21/00Y02T90/00
Inventor 杜明唐帅帅葛泉波
Owner 宁波飞拓电器有限公司
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