The Efficient Particle Filter With Out-of-sequence Measurements

In multi-sensor systems,due to the differences of sensors or the lags of network,the time stamps of measurements obtained by the sensors are often inconsistent with the actual time sequence of the measurements arriving at the fusion center,causing the “earlier measurements” can arrive at the fusion/estimation center after the “later measurements”.This Phenomenon is referred to as “Out-of-sequence Measurements Problem”.Further,due to the complexity of state evolution and measurement transitions,there are widespread cases of nonlinearity and non-Gaussian in real systems.In the above nonlinear and non-Gaussian dynamical system under out-of-sequence measurement(OOSM),the traditional Bayesian filtering is difficult to obtain the analytic solution,therefore,the numerical approximation method is needed to realize the Bayesian recursion.Particle filter(PF),utilizing a large number of weighted samples to approximate the posterior density function(PDF),can give an efficient and high-precision implementation of Bayesian filtering.However,the traditional sequential importance sampling-resampling(SIR)based particle filter(SIR-PF)faces with the particle impoverishment and only utilizes the single sampling density property.In the OOSM environment,designing a satisfactory proposal density is difficult with considering the possibility of the coexistence of the measurements with different time stamps and the multi-model PDF.Motivated by the above consideration,a deterministic mixture multiple importance sampling(DMMIS)method is introduced in this thesis.this method rectifies the particle impoverishment and improves the estimation accuracy by increasing the diversity of samples.The main work of this thesis is as follows.Firstly,For the recursive filtering problem of nonlinear systems under OOSM,firstly,a multiple importance sampling-based particle filtering(DMMIS-PF)algorithm is proposed.By utilizing DMMIS,we design a DMMIS-PF under in-sequence measurement,then considering the OOSM problem,a DMMIS-PF under OOSM is proposed.Furthermore,a numerical realization method is given,where the particles are drawn from a batch of proposal distributions regarding as one mixture and the weight is updated by treating the entire mixture as a global proposal.In the simulation scenario of in-sequence measurement,several DMMIS-PFs and SIR-PFs based on the same implementation method are compared in a target tracking scenario using a constant velocity model with multimode process noise with in-sequence measurements.The simulation results show that the proposed DMMIS-PF algorithm has better estimation performance.In the simulation scenario of single-step and multi-step lagged OOSMs,the target is modeled as random walk model.The proposed algorithm is compared with the SIR-PF.The numerical results shows that the proposed algorithm has better estimation accuracy.Secondly,For the estimation of Markovian switching systems,considering the OOSM problem,a multiple model particle filter algorithm based on multiple importance sampling(IMM-DMMIS-PF)is proposed.In the framework of multi-mode,a multiple model particle filter based on multiple importance sampling is proposed considering the normal measurement.Then,combining the RTS smooth methods,a multiple model particle filter based on MIS is proposed considering the OOSM problem,which overcomes the problem in designing the importance sampling function due to the posterior probability multimodality caused by the coupling of model switching and measurement delay.In the simulation scenario of multi-model target tracking modeled by jump Markov process,the proposed algorithm is compared with the multi-model BPF and the multi-model quadrature particle filter.The simulation results shows that the proposed algorithm has better performance.In the simulation scenario of the OOSM,the proposed algorithm is compared with the multimodel bootstrap particle filtering algorithm in the random walk scenario modeled by jump Markov process.The simulation results show that the proposed algorithm has better estimation accuracy.