Research On Filtering Algorithm Based On Gauss Sum

Gauss sum filtering theory is mainly used for processing the situations that system noise is non-Gauss distribution and posterior probability density of the nonlinear system model can not be approximated by using the distribution of the single Gauss, now it is widely used in the fields of aerospace, electronic information and target tracking etc. According to different system conditions, the scholars have presented different Gauss sum filtering algorithms: Gauss Sum Kalman Filtering algorithm for linear systems, Gauss Sum Extended Kalman Filtering algorithm for dealing with weak nonlinear system, Gauss Sum Particle Filter algorithm for solving strong nonlinear system. But the existing research results exist two problems: On the one hand is due to defects in the algorithm itself, the filter effect is not good, on the other hand is filtering problem under certain conditions is also no corresponding algorithm could handle it. So the research makes the further improvement and research based on the existing algorithms, put forward the Gauss sum filtering algorithms there is higher filtering accuracy and could handle other different system conditions.Contents of the research completes includes:(1)Gaussian Sum Incremental Kalman Filter under poor observation conditionDue to the influence of environment and equipment, system error unknown often with the process of filtering, incremental Kalman filter under poor observation condition can eliminate unknown measurement system errors and very good on the state tracking.However, when the system process noise and measurement noise are subject to nonGaussian distributions, the algorithm cannot be used directly. Addressing this problem, we present a Gaussian sum incremental Kalman filter under poor observation condition though combining with the Gaussian sum filtering algorithm. In the algorithm, the initial state,process noise and measurement noise are approximated by the form of Gaussian sum. Then each Gaussian item is used to predict and update according to the incremental Kalman filter theory. Finally, state value is approximated by using the form of accumulated sum.Simulation results show, in systems with non-Gaussian noise distribution, the proposed algorithm can eliminate the measurement system successfully, and can improve the accuracy and reliability effectively.(2) Gaussian Sum Derivative Free Iterated Extended Kalman FilterWhen the system is a strong nonlinear Gauss distribution system, and the nonlinear function of the measurement equation is complex, the solution of the Jacobian matrix is difficult, we can use Derivative Free Iterated Extended Kalman filtering algorithm for state estimation, but when the system is a strong nonlinear and non-Gauss distribution, the algorithm is no longer suitable. Addressing this problem, we present a Gaussian SumDerivative Free Iterated Extended Kalman filtering algorithm. The algorithm uses Gauss sum filter theory to deal with the non-Gauss distribution, while using the secant method,namely the secant line between two points instead of solving Jacobian matrix, avoiding the problem that solving the Jacobian matrix is difficult. Simulation experiment show that: the algorithm can improve the precision of Kalman filter, and can track the target effectively.(3) Gaussian Sum Kalman Filter with colored noisesIt is assumed that the process noise and measurement noise are Gaussian white noises with zero mean in the standard Kalman filter. However, there are often colored noises with non-Gaussian distribution in applications. At this time, the standard Kalman filter does not work. Addressing at this problem, the paper proposed a Gaussian sum Kalman filter with colored noises. First, the colored noises are whited by the state augmentation and measurement augmentation. Second, according to the idea of the Gaussian sum filter, nonGaussian distribution is approximated by using the summation of multiple Gaussian items,and the state is estimated accurately. The experimental results show that the proposed algorithm can eliminate the influence of the colored noises effectively and enhance the filtering accuracy.