A Model for Non-Stationary Time Series and its Applications in Filtering and Anomaly Detection
Shixiong Wang, Chongshou Li, Andrew Lim
Abstract
Time series measurements from sensing units (e.g., UWB ranging circuits) always suffer from uncertainties like noises, outliers, dropouts, and/or nonspecific anomalies. In order to extract the true information with high precision from the original corrupted measurements, the signal-model-based signal pre-processing units embedded in sensing circuits are usually employed. However, for a general signal to observe, its signal model cannot be obtained so that the signal-model-based signal processing methods are not applicable. In this article, the time-variant local autocorrelated polynomial (TVLAP) model in the state space is proposed to model the dynamics of a non-stationary stochastic process (i.e., a signal or a time series), through which the model-based signal processing methods could be utilized to denoise, to correct the outliers/dropouts, and/or to identify anomalies contained in the measurements. Besides, the presented method can also be used in change point detection for a time series.