Capturing a Change in the Covariance Structure of a Multivariate Process

This research is inspired from monitoring the process covariance structure of q attributes where samples are independent, having been collected from a multivariate normal distribution with known mean vector and unknown covariance matrix. The focus is on two matrix random variables, constructed from different Wishart ratios, that describe the process for the two consecutive time periods before and immediately after the change in the covariance structure took place. The product moments of these constructed random variables are highlighted and set the scene for a proposed measure to enable the practitioner to calculate the run-length probability to detect a shift immediately after a change in the covariance matrix occurs. Our results open a new approach and provides insight for detecting the change in the parameter structure as soon as possible once the underlying process, described by a multivariate normal process, encounters a permanent/sustained upward or downward shift.

High-Dimensional Conditional Covariance Matrices Estimation Using a Factor-GARCH Model

Estimation of a conditional covariance matrix is an interesting and important research topic in statistics and econometrics. However, modelling ultra-high dimensional dynamic (conditional) covariance structures is known to suffer from the curse of dimensionality or the problem of singularity. To partially solve this problem, this paper establishes a model by combining the ideas of a factor model and a symmetric GARCH model to describe the dynamics of a high-dimensional conditional covariance matrix. Quasi maximum likelihood estimation (QMLE) and least square estimation (LSE) methods are used to estimate the parameters in the model, and the plug-in method is introduced to obtain the estimation of conditional covariance matrix. Asymptotic properties are established for the proposed method, and simulation studies are given to demonstrate its performance. A financial application is presented to support the methodology.

Covariance matrix transformation method in all-earth integrated navigation considering coordinate frame conversion

In the exploration of polar region, navigation is one of the most important issues to be resolved. To avoid the limitations of single navigation coordinate frame, the navigation systems usually use different navigation coordinate frames in polar and nonpolar region, such as the north-oriented geographic frame and the grid frame. However, the error states and covariance matrix are related with the definition of navigation coordinate frame, since the coordinate frame conversion will cause the integrated navigation Kalman filter overshoot and error discontinuity. To solve this problem, the transformation relationship of error states defined in different frames is deduced, whereby the covariance matrix transformation relationship is also analyzed. On this basis, covariance transformation-based the open-loop and the closed-loop Kalman filter integrated navigation algorithms are proposed. The effectiveness of algorithms is verified by flight tests with rotational strapdown inertial navigation system (RSINS)/global navigation satellite system (GNSS) integrated navigation system.

Signal Model and Parameter Estimation for Colocated Mimo Radar

In this paper, we consider the signal model and parameter estimation for multiple-input multiple-output (MIMO) radar with colocated antennas on stationary platforms. Considering internal clutter motion, a closed form of the covariance matrix of the clutter signal is derived. Based on the proposed closed form and low rank property of the clutter covariance matrix and by using the singular value decomposition, we have proposed a subspace model for the clutter signal. Following the proposed signal model, we have provided maximum likelihood (ML) estimation for its unknown parameters. Finally, the application of the proposed ML estimation in space time adaptive processing (STAP) is investigated in simulation results. Our ML estimation needs no secondary training data and it can be used in scenarios with nonhomogeneous clutter in range.