Particle Filter With Measurement Random Delay And Missing

For the filtering problem of nonlinear dynamic systems,the Bayesian filter provides a theorectically optimal solution.However,this optimal solution involves the computation of complicated high-dimensional integrals,which in general cannot be solved analytically.Particle filter is one of popular ways to approximate these integrals by utilizing the Monte Carlo method.When the number of sampled particles is sufficiently large,particle filter can yield an optimal solution asymptotically.The standard particle filter assumes that the measurements of system are available on-time,but they are more likely to be randomly delayed and missing in practical applications.This phenomenon will impose a great challenge to the state estimation problem of system.In the view of above situation,this paper develops a particle filter with the multi-step measurement random delay and missing.Specifically,by introducing a sequence of independent and identically distributed Bernoulli variables to depict the measurement random delay and missing,a new measurement equation can then be obtained.Based on this new measurement equation,a new measurment likelihood density is obtained,which can indicate the relationship between the actual measurment and the states of system when measurement random delay and missing concur.Finally,an improved particle filter is proposed by modifying the recursive formula of importance weight in the standard particle filter.To testify the effectiveness of the proposed method,the univariate non-stationary growth model is used in this paper.The experimental results show that the proposed method in this paper can tackle the measurement random delay and missing well compared with the standard particle filter.