Method for filtering non-Gaussian linear stochastic system based on negentropy

Abstract

A method for filtering a non-Gaussian linear stochastic system based on the negentropy comprises the steps that firstly, a filter is designed according to a common linear stochastic system; secondly, due to the fact that an error equation is a non-Gaussian stochastic process, an indicator function is selected as a linear combination of a covariance matrix and the negentropy of an evaluated error, and the probability statistic characteristic of the evaluated error is represented as complete as possible; secondly, a probability density function of the evaluated error is worked out according to the characteristic of a characteristic function, and therefore a negentropy expression of the evaluated error is obtained; finally, a filter gain of the filter is solved and the indicator function is minimized. According to the method, the linear stochastic system state influenced by non-Gaussian noise can be estimated and the method can be applied to the fields of inertial navigation, a guiding system, target tracking, signal processing and the like.

Description

technical field [0001] The invention relates to a non-Gaussian linear random system filtering method based on negative entropy, especially a filtering method for random input probability density functions with strong non-Gaussian characteristics such as asymmetry and multiple peaks, which can be used for inertial Navigation, guidance system, target tracking, signal processing and other fields. Background technique [0002] In recent years, with the development of aerospace technology, the requirements for the autonomy and rapid response capability of aircraft have become higher and higher, which means that many complex estimation tasks must be solved quickly and effectively. Filtering theory is the key technology to solve these problems. Which filtering method to use, to estimate the system state from the perspective of optimal probability and statistics, based on the existing hardware conditions, is of great significance to improve the accuracy of aircraft control and navi...

AI Technical Summary

Problems solved by technology

However, because it is difficult to obtain the optimal sampling distribution in practice, the accuracy of the Monte Carlo filtering algorithm is not high and the algorithm is complex, computationally intensive, and poor in real-time performance.

To sum up, the existing filtering methods either assume that random noise obeys a Gaussian distribution or require a large number of samples. Such processing methods mainly have the following disadvantages: For systems affected by non-Gaussian noise, a lot of information is contained in high-order statistical properties Inside, the variance can no longer fully characterize its probabilistic and statistical properties

The Kalman filtering method is based on the minimum variance of the estimation error, which will inevitably reduce the accuracy; the Monte Carlo filtering algorithm requires a large number of sampling samples to obtain better results, but due to various constraints in the actual system, it is difficult to obtain optimal sampling samples, and does not take full advantage of the noise statistics

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