Research On Particle Filtering Algorithm And Its Application In Nonlinear Estimation

In the fields of target tracking and positioning,image data processing,communication and control systems,researchers often need to infer other relevant data that are not easily available in the system according to the measurement data,in order to judge and control the operation of the system.This method of obtaining state variables from measurement is a category of parameter estimation in the field of statistics and signal processing.According to the different characteristics of the system and the noise categories mixed in the system or in the measurement process,researchers can select different filtering algorithms to calculate the parameters of the state variables of the system.Regardless of linear or non-linear systems,most filtering algorithms can be classified as recursive Bayesian estimation algorithms based on statistical theory.For linear Gaussian model,the Kalman filtering algorithm is always the optimal solution of the estimation of the state variable parameters.However,most systems are non-linear in reality.The extended Kalman filtering algorithm family linearizes the non-linear system by Taylor series expansion using the structure of Kalman filtering al-gorithm,which lead to a suboptimal solution of the state variable estimation.The high efficiency of the calculation makes the extended Kalman filtering algorithm widely used,but the linearization process of this algorithm to the non-linear system makes it not accurate enough for the system with high non-linearity,and worse yet,higher-order Taylor series expansion needs more computing resources which makes it inefficient.The unscented Kalman filtering algorithm replaces the linearization process of the non-linear system by using the unscented transform,which improves the calculation accuracy of the algorithm.However,the algorithm is only applicable to the system with the noise which follows the Gaussian distribution.The approximation of the system variables is based only on a small number of Sigma points,which limits the improvement of the estimation accuracy of the state variables.The emergence of particle filtering algorithm makes up for the shortcomings of the above two algorithms.Particle filtering algorithm is based on the sequential Monte Carlo framework and is suitable for non-linear non-Gaussian system models.It has better estimation performance for systems with stronger non-linearity.However,the particle filtering algorithm suffer the problem of particle degeneracy and sample impoverishment in the process of recursive calculation.In view of the above-mentioned prob-lems,following work has been done in this dissertation:Firstly,different correlation coefficients have been analyzed.The weights update process of each particle in the sample set of particle filtering algorithm is related to the likelihood function of the cor-responding particles.In order to describe the direct relationship between the calculated measurement values obtained from each particle according to the measurement equation and the system measurement value for a short period of time,this dissertation has introduced and analyzed five different correlation coefficients.This dissertation analyzed the computational performance and time complexity of five different correlation coefficients under different data structures.Secondly,this dissertation has analyzed the resampling algorithm.Resampling algorithm is the key approach to eliminate the particle degradation problem in particle filtering algorithms.However,the traditional resampling algorithm brings the sample impoverishment problem to the sample set.In view of this,this dissertation analyzed different resampling algorithms and introduced the concept of correlation coefficient in the resampling algorithm,based on the idea of kernel function in regularized particle filtering algorithm.This constitutes the proposed particle filtering algorithm based on different correlation coefficients.The particle filtering algorithm proposed in this dissertation is based on the sequential Monte Carlo algorithm structure,and the resampling step in the algorithm is modified.In the process of recursive calculation,the improved resampling algorithm relates the measured values of the system in a certain time period and the likelihood function of each particle in the sample set by several different correlation coefficients.The weights of the particles in the sample set are updated through a characteristic kernel function,which avoids the discarding of the smaller weighted particles in the traditional resampling algorithm and increases the diversity of the sample set.Thirdly,the convergence of the algorithm is proved.In this dissertation,several improved particle filtering algorithms based on different correlation coefficients are proposed.Comparing with other particle filtering algorithms,the proposed algorithm mitigates the problem of particle degeneracy and sample impoverishment.Introduced with the correlation coefficients are some unknown influence of the kernel function in the recursive calculation of the resampling algorithm,which may change the convergence characteristics of the particle filtering algorithm.Therefore,this dissertation establish the mathematical model of the proposed algorithm in probability space,and prove the convergence of the algorithm.Finally,the proposed algorithms are applied to practical simulations.At the end of the disser-tation,three particle filtering algorithms based on correlation coefficient and several algorithms for contrast are applied to the simulation of non-linear system models.The simulations take the system state variables of each model as the research object,and realize the research on the estimation of model parameters.Through the simulation experiments of one-dimensional strong non-linear system model under different noise conditions and 7-dimensional harmonic model under Gaussian noise conditions,it is proved that the proposed algorithm has good accuracy and computational performance for param-eter estimation of different systems.