Abstract
The Gaussian mixture filter can solve the non-Gaussian problem of target tracking in complex environment by the multimode approximation method, but the weights of the Gaussian component of the conventional Gaussian mixture filter are only updated with the arrival of the measurement value in the measurement update stage. When the nonlinear degree of the system is high or the measurement value is missing, the weight of the Gauss component remains unchanged, and the probability density function of the system state cannot be accurately approximated. To solve this problem, this paper proposes an algorithm to update adaptive weights for the Gaussian components of a Gaussian mixture cubature Kalman filter (CKF) in the time update stage. The proposed method approximates the non-Gaussian noise by splitting the system state, process noise, and observation noise into several Gaussian components and updates the weight of the Gaussian components in the time update stage. The method contributes to obtaining a better approximation of the posterior probability density function, which is constrained by the substantial uncertainty associated with the measurements or ambiguity in the model. The estimation accuracy of the proposed algorithm was analyzed using a Taylor expansion. A series of extensive trials was performed to assess the estimation precision corresponding to various algorithms. The results based on the data pertaining to the lake trial of an unmanned underwater vehicle (UUV) demonstrated the superiority of the proposed algorithm in terms of its better accuracy and stability compared to those of conventional tracking algorithms, along with the associated reasonable computational time that could satisfy real-time tracking requirements.
Highlights
Nonlinear filtering is widely applied in the fields of target tracking, localization, navigation, signal processing, communication, and automatic control
Based on the stochastic state space mode, the core task of nonlinear filtering involves the computation of the probability density function (PDF)
Is paper proposes an adaptive weight update scheme of the Gaussian components for the Gaussian mixture filter in the time update stage. is method contributes to obtaining a better approximation of the posterior probability density function, which is constrained by large uncertainty in the measurements or ambiguity in the model. e Gaussian mixture filter is improved through combination with the cubature Kalman filter (CKF). e Gaussian components are predicted and updated using a CKF with the results merged and weighted. e estimation accuracy of the proposed algorithm is analyzed using a Taylor expansion
Summary
Nonlinear filtering is widely applied in the fields of target tracking, localization, navigation, signal processing, communication, and automatic control. For highly nonlinear passive tracking systems, an improved Gaussian mixture filter algorithm has been proposed in the literature [22], and the limited Gaussian mixture model has been used to approximate the posterior density of the state and process noises and measurement noises. In all these methods, while propagating the uncertainty through a nonlinear system, the weights of the Gaussian components are not regular and are updated only in the measurement update stage. Note that the weights ωsk|k− 1(i) do not change during the propagation from (7), which is acceptable if the system has a precise model. e reason that the weight remains constant is that the covariance is assumed to be sufficiently small. is aspect is a problem when the system model has a large uncertainty and the measurements are not frequently available
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