A Linear Extension Method for Multilayer Unscented Kalman Filters with Higher Order Moment Matching

Abstract

The invention discloses a multilayer linear-extension unscented Kalman filter method using higher-order moment matching, belonging to the technical field of nonlinear filtering. The method comprises the following steps: 1, establishing a state equation and a measurement equation of a nonlinear system; 2, determining an initial state value of the system; 3, based on the state estimation and the state equation of the last step, calculating distribution characteristics of random variables of one-step state prediction by using linear-extension unscented transformation; 4, calculating distribution characteristics of random variables after being transformed by the measurement equation, of state prediction by using the linear extension unscented transformation; 5, calculating distribution characteristics of an optimal state by using a Kalman gain in combination with state prediction and actual measurement data; and 6, judging whether the iteration is ended. According to the linear extension method, orthogonally-symmetric samples and a multi-sampling structure are combined by using a proportion modifying idea, and by matching more high-order moments, the approximation accuracy is remarkably improved, the computation complexity is reduced, and the computation efficiency is greatly increased.

Description

technical field [0001] The present invention relates to the field of information fusion technologies such as nonlinear filtering, digital signal processing, and target positioning and tracking, and in particular to a linear extension method (Linear-Extension Unscented Kalman Filter, LUKF ). Background technique [0002] Almost all real-world systems are nonlinear, especially in areas such as aircraft navigation, object tracking, and industrial control. For example: in the process of target positioning and tracking, when the radar is used to observe the air target, the radar can obtain the azimuth angle of the air target relative to itself, but this observation contains noise, and the azimuth observation of the radar in the observation equation is the target position parameter to be estimated Nonlinear functions cannot directly use the linear filtering method to obtain the motion state of the target. It is essentially a nonlinear filtering problem, which is a common problem ...

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Problems solved by technology

[0007] In view of this, the object of the present invention is to provide a linear extension method of a multi-layer unscented Kalman filter of high-order moment matching, which is used to solve the problems of accuracy and computational efficiency of nonlinear filters in practical applications , combined with the existing sampling strategy, using high-order moments and multiple single-row sampling to improve accuracy, and at the same time, using symmetrical sampling and simplified proportional correction methods to reduce computational complexity, thereby achieving synchronous improvements in accuracy and computational efficiency

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