Kullback-Leibler divergence -based improved particle filter

In this paper, we develop an improved particle filtering algorithm for nonlinear states estimation. In case of standard particle filter, the latest observation is not considered for the evaluation of the weights of the particles as the importance function is taken to be equal to the prior density function. This choice of importance sampling function simplifies the computation but can cause filtering divergence. In cases where the likelihood function is too narrow as compared to the prior function, very few particles will have significant weights. Hence a better proposal distribution that takes the latest observation into account is desired. The proposed algorithm consists of a particle filter based on minimizing the Kullback-Leibler divergence distance to generate the optimal importance proposal distribution. The proposed algorithm allows the particle filter to incorporate the latest observations into a prior updating scheme using the estimator of the posterior distribution that matches the true posterior more closely. In the comparative study, the state variables are estimated from noisy measurements of these variables, and the various estimation techniques are compared by computing the estimation root mean square error with respect to the noise-free data. The simulation results show that the proposed algorithm, outperforms the standard particle filter, the unscented Kalman filter, and the extended Kalman filter algorithms.