A new nonlinear filtering algorithm via fourier series

In this paper, a novel nonlinear filtering algorithm is developed based on Fourier series. Since the Fourier series can be used to describe probability density function, it has been used by many researchers for filtering design. However, the original Fourier series based methods require a fixed computation domain, which cannot capture the true dynamic probability density function. The primary contribution of this paper is to design a new Fourier series based nonlinear filtering algorithm which can describe the probability density function at any given domain. Two efficient algorithms are given to adaptively determine the computation domain. The effectiveness of this new filter is evaluated in a benchmark problem and compared with the extended Kalman filter.