Abstract
Parameter estimation of time-varying non-Gaussian autoregressive processes can be a highly nonlinear problem. The problem gets even more difficult if the functional form of the time variation of the process parameters is unknown. In this paper, we address parameter estimation of such processes by particle filtering, where posterior densities are approximated by sets of samples (particles) and particle weights. These sets are updated as new measurements become available using the principle of sequential importance sampling. From the samples and their weights we can compute a wide variety of estimates of the unknowns. In absence of exact modeling of the time variation of the process parameters, we exploit the concept of forgetting factors so that recent measurements affect current estimates more than older measurements. We investigate the performance of the proposed approach on autoregressive processes whose parameters change abruptly at unknown instants and with driving noises, which are Gaussian mixtures or Laplacian processes.
Highlights
In on-line signal processing, a typical objective is to process incoming data sequentially in time and extract information from them
We address parameter estimation of such processes by particle filtering, where posterior densities are approximated by sets of samples and particle weights
We investigate the performance of the proposed approach on autoregressive processes whose parameters change abruptly at unknown instants and with driving noises, which are Gaussian mixtures or Laplacian processes
Summary
In on-line signal processing, a typical objective is to process incoming data sequentially in time and extract information from them. Many alternative approaches to overcome the deficiencies of the extended Kalman filter have been tried including Gaussian sum filters [15], approximations of the first two moments of densities [16], evaluations of required densities over grids [17], and the unscented Kalman filter [18] Another approach to tracking time-varying signals is particle filtering [19]. One advantage of particle filters over other methods is that they can be applied to almost any type of problem where signal variations are present This includes models with high nonlinearities and with noises that are not necessarily Gaussian. We address the problem of tracking the parameters of a non-Gaussian autoregressive (AR) process whose parameters vary with time. In [32, 33], particle filters are applied to estimation of time-varying AR models, but the driving noises there are Gaussian processes.
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