Research On Particle Filter Algorithm And Its Application

The state estimation of nonlinear systems has caught the focus of many researchers, and becomes a hot research field with great theoritical value and application field. Over the last some years, particle filter which can be used to estimate the state of nonlinear systems has been developed. It has been widely applied in many fields such as statistical signal processing, economics, biostatistics, communications, target tracking, fault diagnosis, satellitic navigation, sonar orientation and so on.Nowadays, a lot of problems about particle filter algorithm have been in need of solution. These problems include the choice of importance probability density function, particle degeneracy, particle impoverishment, convergence, improving the accuracy and speed of particle filter, the hardware representation of particle filter, developing widely application field of particle filter and so on. In this paper the smoothing method is associated with particle filter to estimate accurately the state of nonlinear systems. At the same time our research is focused on the resampling of particles to improve the effect of particle degeneracy. Based on the particle filter, the fault detection of nonlinear systems and the single station passive target tracking with bearing-only measurement are researched to develop the application field of the particle filter. The main contributions of this dissertation are as follows:Firstly, a state estimation algorithm of nonlinear systems is proposed with the similarity between the observation path of particles and the observation path of system state. In this algorithm the weight of the particle is modified with the above similarity to increase the weight of the particle which is close to the system state. This proposed algorithm consists of the filtering for the current state and the smoothing for the previous state. Using the algorithm the state estimation accuracy of nonlinear systems is improved. When the system noise and observation noise are Gaussian, the RMSE and the error variance of the this proposed algorithm are better than SIR, APF, RPF, GPF, and GSPF in a typical example about the state estimation of a nonlinear system. When the system noise and observation noise are heavy-tail,χ2(2), t(2) or F(2,20), the RMSE of the this proposed algorithm is better than SIR, APF, RPF, GPF, and GSPF and the variance of the error of the this proposed algorithm is samller. Its time complexity is low without resampling. The results of the simulation demonstrate that the time complexity of the proposed algorithm is lower than SIR, APF, and APF and almost same with GPF.Secondly, the real-time performance of the proposed algorithm will be degraded due to the presence of the smoothing operation for more accurate state estimates. In this paper an improved algorithm is proposed, which has rasmpling based on the similarity between the observation paths without the smoothing operation. When the variance of the system Gaussian noise is bigger than the observation Gaussian noise, the RMSE of the this improved algorithm is better than SIR, APF, RPF, and GPF in a typical example about the state estimation of a nonlinear system and the variance of the error of the this improved algorithm is almost same with them. When the variance of the system Gaussian noise is samller than the observation Gaussian noise, the RMSE of the improved algorithm is almost same with them.Thirdly, those known particle filters will be inapplicable when all weights of used particles are zero due to the severe particle degeneracy. In this paper an idea is proposed to solve the problem. The idea is that the executive process is choiced according to all likelihood values of used particles. The reliability of SIR, APF, RPF, GPF, and the proposed algorithm in this paper is improved with the idea. The results of the simulation are presented to demonstrate the availability of all above improved algorithm.Fourthly, in this paper a fault detection approach based on SIR state estimation and smoothed residual is proposed for fault detection of nonlinear systems. In this approach the estimate value of the state of the nonlinear system is estimated firstly using SIR. Then the difference between these ideal observation of the estimate value and those observation of the state of the system is smoothed. The fault detection is done according to these smoothed difference. When the variance of the system noise is samller than the observation noise, the results of the simulation are presented to demonstrate the improved performance of the proposed algorithm over the fault detection approach based on SIR likelihood for fault detection. Finally, the particle filter with the resampling based on the similarity of observation paths is used for an example of single station passive target tracking with bearing-only measurement. The results of the simulation are presented to demonstrate the improved accuracy of the proposed algorithm over SIR, APF, and GPF.