Deep Pattern of Time Series and Its Applications in Estimation, Forecasting, Fault Diagnosis and Target Tracking.

The information contained in a time series is more than what the values themselves are. In this paper, the Time-variant Local Autocorrelated Polynomial model with Kalman filter is proposed to model the underlying dynamics of a time series (or signal) and mine the deep pattern of it, except estimating the instantaneous mean function (also known as trend function), including: (1) identifying and predicting the peak and valley values of a time series; (2) reporting and forecasting the current changing pattern (increasing or decreasing pattern of the trend, and how fast it changes). We will show that it is this deep pattern that allows us to make higher-accuracy estimation and forecasting for a time series, to easily detect the anomalies (faults) of a sensor, and to track a highly-maneuvering target.