A Nonlinear Smoothing Algorithm for Chaotic and Non-Chaotic Time Series

A new NARMA based smoothing algorithm is introduced for chaotic and non-chaotic time series. The new algorithm employs a cross validation method to determine the smoother structure, requires very little user interaction and can be combined with wavelet thresholding to further enhance the noise reduction. Numerical examples are included to illustrate the application of the new algorithm

Linear and nonlinear trending and prediction for AVHRR time series data

The variability of AVHRR calibration coefficient in time was analyzed using algorithms of linear and non-linear time series analysis. Specifically we have used the spline trend modeling, autoregressive process analysis, incremental neural network learning algorithm and redundancy functional testing. The analysis performed on available AVHRR data sets revealed that (1) the calibration data have nonlinear dependencies, (2) the calibration data depend strongly on the target temperature, (3) both calibration coefficients and the temperature time series can be modeled, in the first approximation, as autonomous dynamical systems, (4) the high frequency residuals of the analyzed data sets can be best modeled as an autoregressive process of the 10th degree. We have dealt with a nonlinear identification problem and the problem of noise filtering (data smoothing). The system identification and filtering are significant problems for AVHRR data sets. The algorithms outlined in this study can be used for the future EOS missions. Prediction and smoothing algorithms for time series of calibration data provide a functional characterization of the data. Those algorithms can be particularly useful when calibration data are incomplete or sparse

Identification of nonlinear lateral flow immunoassay state-space models via particle filter approach

This is the post-print of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, the particle filtering approach is used, together with the kernel smoothing method, to identify the state-space model for the lateral flow immunoassay through available but short time-series measurement. The lateral flow immunoassay model is viewed as a nonlinear dynamic stochastic model consisting of the equations for the biochemical reaction system as well as the measurement output. The renowned extended Kalman filter is chosen as the importance density of the particle filter for the purpose of modeling the nonlinear lateral flow immunoassay. By using the developed particle filter, both the states and parameters of the nonlinear state-space model can be identified simultaneously. The identified model is of fundamental significance for the development of lateral flow immunoassay quantification. It is shown that the proposed particle filtering approach works well for modeling the lateral flow immunoassay.This work was supported in part by the International Science and Technology Cooperation Project of China under Grant 2009DFA32050, Natural Science Foundation of China under Grants 61104041, International Science and Technology Cooperation Project of Fujian Province of China under Grant 2009I0016

Particle Learning and Smoothing

Particle learning (PL) provides state filtering, sequential parameter learning and smoothing in a general class of state space models. Our approach extends existing particle methods by incorporating the estimation of static parameters via a fully-adapted filter that utilizes conditional sufficient statistics for parameters and/or states as particles. State smoothing in the presence of parameter uncertainty is also solved as a by-product of PL. In a number of examples, we show that PL outperforms existing particle filtering alternatives and proves to be a competitor to MCMC.Comment: Published in at http://dx.doi.org/10.1214/10-STS325 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Filtering and Smoothing with Score-Driven Models

We propose a methodology for filtering, smoothing and assessing parameter and filtering uncertainty in misspecified score-driven models. Our technique is based on a general representation of the well-known Kalman filter and smoother recursions for linear Gaussian models in terms of the score of the conditional log-likelihood. We prove that, when data are generated by a nonlinear non-Gaussian state-space model, the proposed methodology results from a first-order expansion of the true observation density around the optimal filter. The error made by such approximation is assessed analytically. As shown in extensive Monte Carlo analyses, our methodology performs very similarly to exact simulation-based methods, while remaining computationally extremely simple. We illustrate empirically the advantages in employing score-driven models as misspecified filters rather than purely predictive processes.Comment: 33 pages, 5 figures, 6 table

Optimization viewpoint on Kalman smoothing, with applications to robust and sparse estimation

In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least squares problem, highlight special structure, and show that the classic filtering and smoothing algorithms are equivalent to a particular algorithm for solving this problem. Once this equivalence is established, we present extensions of Kalman smoothing to systems with nonlinear process and measurement models, systems with linear and nonlinear inequality constraints, systems with outliers in the measurements or sudden changes in the state, and systems where the sparsity of the state sequence must be accounted for. All extensions preserve the computational efficiency of the classic algorithms, and most of the extensions are illustrated with numerical examples, which are part of an open source Kalman smoothing Matlab/Octave package.Comment: 46 pages, 11 figure