Non-recursive estimation using a batch filter based on particle filtering

In this paper, a non-recursive estimation algorithm using a batch filter based on particle filtering is developed and demonstrated for a one-dimensional nonlinear example. Algorithms of a batch filter based on unscented transformation are also briefly reviewed. To verify the performance of the presented batch filter based on particle filtering, numerical simulations and accuracy assessments are conducted, and the results are compared with those of batch filter based on unscented transformation under various nonlinear and non-Gaussian environments. The root mean square value of differences between observed states and computed states after convergence is used to check the precision of the filtering process. The estimated initial state value and its difference from the true initial state value are used to verify the state accuracy of the nonlinear estimation. The large initial state error is used for the nonlinear environment, and five types of simulated measurement noise are used for the non-Gaussian environments. Under conditions of large initial state error or large non-Gaussian measurement noise, the non-recursive estimation algorithm developed in this paper yields more robust and accurate estimation results than the batch filter based on unscented transformation. In addition, sensitivity analysis of estimation parameters is performed for effective nonlinear estimation, and this shows that the developed non-recursive estimation algorithm does not require the heavy scaling parameter tuning which is required for batch filter based on unscented transformation. For the consideration of computational burden, the complexity analysis is also performed. Therefore, we conclude that the non-recursive batch filter based on particle filtering is effectively applicable to batch estimation problems under nonlinear and non-Gaussian environments.