CN-116522055-B - Parameter self-tuning Kalman filter design method based on expansion state

Abstract

The invention discloses a parameter self-tuning Kalman filter design method based on an expansion state, which is used for reducing estimation errors of a filter when the state estimation is carried out on a nonlinear and track-changing moving target, enhancing the smoothness of a filtering curve and meeting the requirement of higher-precision target tracking. Although the traditional Kalman filtering can realize the optimal estimation under Gaussian noise, the traditional Kalman filtering is only suitable for a linear tracked target state equation, and the state equation is required to be accurate. When it is applied to the field of moving object state estimation, the problem of estimation errors is inevitably caused in the face of tracked objects which cannot be modeled in advance and even have mobility. The invention can be applied to the field of nonlinear even trajectory-variable target tracking by estimating the state equation parameters of the tracked target in real time. The invention breaks through the limitation of the traditional Kalman filtering method, effectively improves the estimation accuracy and the smoothness of the filtering curve of the filter, and optimizes the estimation effect of the filter.

Inventors

• MAO YAO
• SUN MINXING
• SHEN QINGYU
• WANG JUNZHE
• BAO QILIANG

Assignees

• 中国科学院光电技术研究所

Dates

Publication Date

20260512

Application Date

20221201

Claims (4)

1. 1. A parameter self-tuning Kalman filter design method based on an expansion state is characterized in that a state transition matrix of a target tracking Kalman filter is estimated The state transition equation of the target tracking Kalman filter and the estimated state of the designed expanded state Kalman filter are as follows: Wherein, the Representing the estimated state of a classical kalman filter, Representing the position of the tracked object at instant i, Is a state transition matrix that is a state transition matrix, Is a process noise driving matrix and, Is the noise of the process and, Is a parameter that constitutes a state transition matrix, Is the estimated state of the parameter self-tuning Kalman filter; The state transition equation of the new filter is no longer linear, and is estimated by using an unscented Kalman filtering algorithm, and the corresponding state transition equation and observation equation are as follows: Wherein, the 、 The estimated state and the observed value respectively, 、 The state transition equation and the observation equation of the parameter self-tuning Kalman filter are respectively, 、 Process noise and observation noise, respectively; Setting the state as a combination of the current position of the tracked target, the position values at m-1 moments before the current position of the tracked target and the linear addition coefficient values of the position values by using an expansion state method; Linear sum coefficient value Can be set according to the following rules: 。
2. 2. the method for designing a self-tuning Kalman filter based on parameters of an expanded state as claimed in claim 1, wherein the dimension of the estimated state is flexibly selected according to the computing power of the controller and the tracking scene characteristics, but the weight value The number of (2) equals the position value Is a number of (3).
3. 3. The method for designing the parameter self-tuning Kalman filter based on the expansion state of claim 1, wherein the calculation is completed by using an unscented Kalman filtering algorithm, and the method comprises the following specific implementation steps: step (1) of setting parameters Initial value of state estimation value Initial value of state number n and state posterior covariance Covariance of observed noise Process noise covariance Equation of state transition Equation of observation ; Step (2) calculating parameters ; Step (3) UT conversion to obtain 2n+1 Sigma points ; Step (4) calculate 2n+1 Sigma points Respective weights ; Step (5) 2n+1 Sigma spots Respectively making one-step prediction to obtain ; Step (6) of calculating the prior state value Sum state prior covariance ; Step (7) calculate 2n+1 new Sigma points ; Step (8) observation and simulation calculation ; Step (9) according to 2n+1 Point and corresponding weight Predicting observations Sum covariance And ; Step (10) of calculating a Kalman gain matrix ; Step (11) computing posterior state estimation of the system Sum covariance ; Step (12) of calculating an estimated value of the tracked target position ; And (13) returning to the step (3) to perform a new round of filtering calculation.
4. 4. The method for designing the self-tuning Kalman filter based on the parameters of the expansion state according to any one of claims 1 to 3, wherein the self-tuning Kalman filter based on the parameters of the expansion state is used, and the accuracy and the smoothness of an estimation result are improved and the adaptability of the filter is enhanced by estimating the parameters of a state transition matrix of the Kalman filter under the condition that a tracked target cannot model a motion equation in advance or has mobility.

Description

Parameter self-tuning Kalman filter design method based on expansion state Technical Field The invention belongs to the field of target tracking, and particularly relates to a parameter self-tuning Kalman filter design method based on an expansion state, which is mainly used for state estimation and filtering of a variable track maneuvering target which cannot be modeled in advance. The invention effectively expands the state estimation capability of the Kalman filtering algorithm on nonlinear and variable track moving targets, improves the filtering precision and the smoothness of the filtering curve, and optimizes the estimation effect of the filter. Background The method can be applied to the fields of photoelectric tracking, motion capturing, track prediction and the like. In these fields of application, the tracked target is often uncontrolled, which not only results in a related state equation that cannot be established in advance, but also may change during the filtering process in hypersonic aircraft trajectory tracking and prediction based on Singer model (welsh celebration, aerospace control, 2017). The kalman filtering method is widely used "Stochastic theory of minimal realization"(Clary,J.W.Proceedings of the IEEE,IEEE Conference on Decision&Control Including the Symposium onAdaptive Processes.1976)), by virtue of the optimal estimation characteristic and rapidity under gaussian noise, but requires an accurate and linear state equation of a tracked target, so that when the kalman filtering method is applied to tracking a maneuvering target, the filtering effect is significantly deteriorated in Applied optimal estimation (Arthur g.proceedings of IEEE 1974). The extended kalman filter, unscented kalman filter, etc. algorithms generated by the extension of the classical kalman filter algorithm, while enabling the tracking estimation of nonlinear moving objects, also rely on the accurate modeling of tracked objects, kalman filter principle and application (Huang Xiaoping, 2015). Although the conventional robust state estimation method can compensate the uncertainty of the state equation of the tracked target to a certain extent, the uncertainty must be limited "AFramework for State-Space Estimation with Uncertain Models"(Ali H.Sayed.IEEE TRANSACTIONS ONAUTOMATIC CONTROL,2001). an effective estimation method for the uncertain object is to use an extended state observer of an uncertain object class (Han Jing, control and decision, 1995), a method for estimating the disturbance quantity of the state equation by using the extended state is successfully published in 2019 as a model prediction control algorithm based on an extended state kalman filter (Shen Jiong, CN201910614372.6,2019), and the uncertainty is still limited by the determined state equation, so that accurate estimation of the maneuvering target is difficult to realize. With the continuous improvement of the performance requirements of the filter in the fields of photoelectric tracking and the like, how to design a nonlinear filter with self-tuning capability is particularly important when a maneuvering uncontrolled tracked target is faced. There is a need for an improvement over existing kalman filtering methods that will maintain good filtering performance in the face of maneuver targets. Disclosure of Invention Aiming at the problems of filtering and state estimation of a tracked target of uncontrolled and variable track movement, the invention provides a parameter self-tuning Kalman filter based on an expansion state. In order to achieve the aim of the invention, the technical scheme adopted by the invention is that the method for designing the self-tuning Kalman filter based on the parameter of the expansion state is to estimate the state of a nonlinear even track-changing motion target by estimating the parameter of a state transition matrix F KF of the target tracking Kalman filter, wherein the following states are respectively the state transition equation of the target tracking Kalman filter and the estimated state of the designed expansion state Kalman filter: xi＝[pi pi-1 … pi-m+1 c1 c2 … cm]1×2mT Wherein, the Representing the estimated state of a classical kalman filter, p i representing the position of the tracked object at time i, F KF being the state transition matrix, B KF being the process noise driving matrix,Is the process noise, c i is the parameters that make up the state transition matrix, x i is the estimated state of the parameter self-tuning kalman filter. Further, the state transition equation of the new filter is no longer linear, and estimation is needed by using an unscented Kalman filtering algorithm, and the corresponding state transition equation and observation equation are as follows: yi＝h(xi,vi)＝[1 0 … 0]1×2mxi+vi where f (x i,ui)、h(xi,vi) is the state transfer equation and the observation equation of the parameter self-tuning kalman filter, and u i、vi is the process noise and the observation noise, respe