With the advent of the digital computer, time series analysis has gained wide attention and is being applied to many fields of science. This paper reviews many traditional and recent techniques for time series analysis and change detection, including spectral and wavelet analyses with their advantages and weaknesses. First, Fourier and least-squares-based spectral analysis methods and spectral leakage attenuation methods are reviewed. Second, several time-frequency decomposition methods are described in detail. Third, several change or breakpoints detection methods are briefly reviewed. Finally, some of the applications of the methods in various fields, such as geodesy, geophysics, remote sensing, astronomy, hydrology, finance, and medicine, are listed in a table. The main focus of this paper is reviewing the most recent methods for analyzing non-stationary time series that may not be sampled at equally spaced time intervals without the need for any interpolation prior to the analysis. Understanding the methods presented herein is worthwhile to further develop and apply them for unraveling our universe.

In this paper, we examine the effect of changing the temperature points on MEMS-based inertial sensor random error. We collect static data under different temperature points using a MEMS-based inertial sensor mounted inside a thermal chamber. Rigorous stochastic models, namely Autoregressive-based Gauss-Markov (AR-based GM) models are developed to describe the random error behaviour. The proposed AR-based GM model is initially applied to short stationary inertial data to develop the stochastic model parameters (correlation times). It is shown that the stochastic model parameters of a MEMS-based inertial unit, namely the ADIS16364, are temperature dependent. In addition, field kinematic test data collected at about 17 °C are used to test the performance of the stochastic models at different temperature points in the filtering stage using Unscented Kalman Filter (UKF). It is shown that the stochastic model developed at 20 °C provides a more accurate inertial navigation solution than the ones obtained from the stochastic models developed at −40 °C, −20 °C, 0 °C, +40 °C, and +60 °C. The temperature dependence of the stochastic model is significant and should be considered at all times to obtain optimal navigation solution for MEMS-based INS/GPS integration.