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Maximum cross-correlation entropy Kalman filtering method based on random weighting criterion

A criterion, the largest technology, applied in the field of signal processing, can solve the problem of the degradation of estimation performance, and achieve the effect of increasing the correlation entropy, improving the accuracy and the effectiveness of the estimation, and improving the accuracy.

Pending Publication Date: 2022-03-22
LUOYANG INST OF SCI & TECH
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Problems solved by technology

However, the use of Gaussian and filtering requires that the probability density distribution of the noise is known, which is difficult to achieve in engineering practice: the Huber technique will lead to a decrease in estimation performance because its influence function will not drop after the influence parameter γ exceeds 1.345; while the student t Filtering can only be used when the system noise covariance and measurement noise covariance are small

Method used

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  • Maximum cross-correlation entropy Kalman filtering method based on random weighting criterion
  • Maximum cross-correlation entropy Kalman filtering method based on random weighting criterion
  • Maximum cross-correlation entropy Kalman filtering method based on random weighting criterion

Examples

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Comparison scheme
Effect test

Embodiment 1

[0099] Consider a general linear system model:

[0100]

[0101]

[0102] Where θ = π / 18, and the system noise is Gaussian noise Q i (k-1) ~ n (0, 2) (i = 1, 2), the amount of measuring noise is a mixed Gaussian noise R (K) to 0.9N (0, 1) + 0.1 N (0,100).

[0103] According to the maximum correlation entropy Kalman filtering method based on the random weighted criterion, the state initial value is taken Error covariance matrix P (0 | 0) = DIAG (100,100). The nuclear width σ of the Gaussian nuclear function is set to 0.1, 0.5, 1, 2, 3, 5, 8, 10, compared to the KF algorithm and MCKF (σ = 2), respectively. figure 2 , 3 Two state x 1 , X 2 Probability density function under different filtering algorithms. The simulation results of the maximum correlation entropy Karman filtering method based on random weight weighted criteria are shown in the curve RWMCKF. It can be seen that more conventional KF and MCKF, the performance advantage is obvious: the KF algorithm is biased in the...

Embodiment 2

[0106] Replacing the simulation model is a one-dimensional line sex accelerated motion, the system model and measurement model are as follows:

[0107]

[0108]

[0109] Among them, Δt = 0.1s, and the system noise and quantitative noise are nonlinear mixed Gaussian noise:

[0110] Qi 1 (k-1) ~ 0.9N (0,0.01) + 0.1n (0, 1)

[0111] Qi 2 (k-1) ~ 0.9N (0,0.01) + 0.1n (0, 1)

[0112] Qi 3(k-1) ~ 0.9N (0,0.01) + 0.1n (0, 1)

[0113] R (k) ~ 0.8 N (0, 0.01) + 0.2N (0,100).

[0114] According to the maximum correlation entropy Kalman filtering method based on the random weighted criterion, the filtering algorithm is first initialized. State initial value and covariance at the beginning value are set to x (0) = [001] T , P (0 | 0) = DIAG (0.01, 0.01, 0.01). The nuclear width σ of the Gaussian nuclear function is set to 2 (which is relatively optimum in Example 1), and the mean square error under KF, MCKF (σ = 2) and RWMCKF (σ = 2) algorithm can be obtained. surface:

[0115] Table I KF...

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Abstract

The invention provides a maximum cross-correlation entropy Kalman filtering method based on a random weighting criterion. Comprising the following steps: constructing a linear system equation and a measurement equation, selecting a proper kernel width, initializing a system state and a covariance, updating one-step prediction of the state and the covariance according to the system equation, and re-initializing a state value at an initial iteration moment of a fixed point, the method comprises the following steps: performing system model deformation according to an initial system and a measurement equation, calculating an error after deformation and a kernel function of the error, obtaining two diagonal matrixes according to a random weighting criterion and the kernel function, and correcting a one-step prediction covariance and a measurement error by the two diagonal matrixes so as to correct a gain matrix; according to the method, for the non-Gaussian heavy tail impact noise problem of a linear model, the performance better than that of Kalman filtering and maximum cross-correlation entropy Kalman filtering can be obtained, the method can be widely applied to the situation that the noise of a linear system is non-Gaussian, and the filtering estimation precision under the non-Gaussian noise situation is improved.

Description

Technical field [0001] The present invention belongs to the field of signal processing. Background technique [0002] Status estimation is an important issue in signal processing. The Karman filtering method is one of the important methods of resolving the status estimation problem under the Gaussian noise of the linear system, which makes full use of the status model of the system and observation data, so that the state estimate is minimized by solving the problem, thus obtaining the system Optimal estimate. However, due to system model or quantity, the noise is contaminated, which often occurs the case of heavy-end non-Gaussian noise, which can cause the Calman filtering algorithm to decrease or even diverge, so it is necessary to target a filtering algorithm for non-Gaussian noise. [0003] The filtering algorithm that is currently appearing for the measurement noise is: Gaussian and filtering, Huber technology-based M estimated filtering and STUDENT'S method T-filtered. Howev...

Claims

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Application Information

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IPC IPC(8): H03H17/02
CPCH03H17/0257
Inventor 赵雪华兰曼卫一卿王冰冰王素芳秦玉琨
Owner LUOYANG INST OF SCI & TECH
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