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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.

A Model for Non-Stationary Time Series and its Applications in Filtering and Anomaly Detection