High moment matching based unscented kalman filter polynomial method

Abstract

The invention discloses a high moment matching based unscented kalman filter polynomial method and belongs to the non-linear filter technology field. The high moment matching based unscented kalman filter polynomial method comprises the following steps of establishing a state equation and a measuring equation of a non-linear system; confirming original state random distribution characters which comprise a mean value, a covariance and a high moment of an original state, a noise distribution character and an original measuring value; calculating distribution characters of a random variable of a one-step state prediction through multi-layer unscented transformation based on state estimation and the state equation at the last moment; calculating distribution characters of measurement of the state prediction through the MUT (Multi-layer Unscented Transformation) based on the state prediction and the measuring equation in the step three; calculating distribution characters of an optimal state through kalman gain with the state prediction and measuring data fused and completing one-step estimation tasks of the non-linear system. The high moment matching based unscented kalman filter polynomial method is used for solving the accuracy and calculation stability problems of the non-linear filter during practical application process and improves the accuracy through the high moment and the multiple symmetric sampling and in combination with the existing sampling strategy.

Description

technical field [0001] The invention belongs to the technical fields of information fusion such as nonlinear filtering, digital signal processing, and target positioning and tracking, and relates to a polynomial method of an unscented Kalman filter based on high-order moment matching. Background technique [0002] At present, in the fields of aircraft navigation, target tracking and industrial control. Almost all real-world systems are nonlinear. 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 in the...

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Problems solved by technology

[0004] Compared with the unscented Kalman filter, the EKF has the following three disadvantages: (1) When the high-order terms of the nonlinear function Taylor expansion cannot be ignored, linearization will cause a large error in the system, and even the filter Difficult to be stable; (2) In many practical problems, it is difficult to obtain the Jacobian matrix of nonlinear functions, or even does not exist; (3) EKF needs to be derived, so it is necessary to clearly understand the specific form of nonlinear functions, and black boxes cannot be achieved package, making it difficult to modularize application

[0006] At present, the UKF used in the field of target tracking is the second-order UKF method. For Gaussian nonlinear systems, the estimation accuracy of the second-order UKF can only reach the cubic Taylor expansion of the nonlinear function, which has limited accuracy and poor stability. In applications, there is an urgent need for a sampling strategy that takes into account accuracy, stability, and computational efficiency

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