Estimation problem has been one of the most important aspects in signal processing. For linear systems with Gaussian noises, the estimation problem is relatively easy to perform. However, there are no exact filtering solutions for nonlinear stochastic processes in general.

In recent years, nonlinear filters based on probability density function (PDF) have received increasing attention in control system as well as signal processing field, due to the fact that the PDF captures all the statistical characteristics of a random variable. There are generally two kinds of criteria that can be used in PDF filtering: PDF shaping and entropy minimization. However, a shortcoming of the PDF filter may be that in most cases it can only guarantee local optimum.

So LIU Yu, WANG Hong, Senior Member of IEEE and HOU Chaohuan, Fellow of IEEE design a novel filter for nonlinear and non-Gaussian systems, with properly chosen parameters and by incorporating unscented Kalman filter (UKF) and PDF filter. Wherein, the UKF is a typical method of Kalman family to perform nonlinear filtering problems. It computes the conditional mean and variance accurately up to the third order approximation for Gaussian noises, whereas it does not perform well under either long-tail or multi-modal noises.

Of this design, the UKF is used to give a preliminary estimation of the state, while the PDF filter makes the Renyi’s entropy of the innovation as small as possible. An additional RBF-network is added to the UKF innovation term to compensate for the non-Gaussianity of the whole system. Besides, parameters of the RBF-network are updated using minimum entropy criterion at each time step.

It has been shown that the proposed algorithm has a high accuracy in estimation because entropy can characterize all the randomness of the residual while UKF only cares for the mean and the covariance. It has been proved that with properly chosen bandwidth, the minimum entropy problem of the innovation is convex. Therefore, the proposed adaptive nonlinear filter will be globally convergent and the misadjustment will be proportional to the step size. The effectiveness of the proposed method is shown by simulation.

This research was supported in part by Natural Science Foundation of China under grants 61290323 and 61134006. Also, this research was supported by Director Foundation of Institute of Acoustics, Chinese Academy of Sciences under grant Y154221511.

The research result was released online http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6570499 and on Signal Processing, IEEE Transactions on (Volume: PP, Issue: 99).

Contact:

LIU Yu

Institute of Acoustics, Chinese Academy of Sciences

liuyu2010@mail.ioa.ac.cn