Minimax rank estimation for subspace tracking

Rank estimation is a classical model order selection problem that arises in a variety of important statistical signal and array processing systems, yet is addressed relatively infrequently in the extant literature. Here we present sample covariance asymptotics stemming from random matrix theory, and bring them to bear on the problem of optimal rank estimation in the context of the standard array observation model with additive white Gaussian noise. The most significant of these results demonstrates the existence of a phase transition threshold, below which eigenvalues and associated eigenvectors of the sample covariance fail to provide any information on population eigenvalues. We then develop a decision-theoretic rank estimation framework that leads to a simple ordered selection rule based on thresholding; in contrast to competing approaches, however, it admits asymptotic minimax optimality and is free of tuning parameters. We analyze the asymptotic performance of our rank selection procedure and conclude with a brief simulation study demonstrating its practical efficacy in the context of subspace tracking.Comment: 10 pages, 4 figures; final versio

Identifying table tennis balls from real match scenes using image processing and artificial intelligence techniques

Table tennis is a fast sport and it is very difficult for a normal human being to manage accurate umpiring, especially in services (serves), which usually take less than a second to complete. The umpire needs to make over 30 observations and makes a judgment before or soon after the service is complete. This is a complex task and the author believes the employment of image processing and artificial intelligence (AI) technologies could aid the umpire to evaluating services more accurately. The aim of this research is to develop an intelligent system which is able to identify and track the location of the ball from live video images and evaluate the service according to the service rules. In this paper, the discussion is focused on the development of techniques for identifying a table tennis ball from match scenes. These techniques formed the basis of the ball detection system. Artificial neural networks (ANN) have been designed and applied to further the accuracy of the detection system. The system has been tested on still images taken at real match scenes and the preliminary results are very promising. Almost all the balls from the images have been correctly identified. The system has been further tested on some video images and the preliminary result is also very encouraging. It shows the system could tolerate the poorer quality of video images. This paper also discusses the idea of employing multiple cameras for improving accuracy. A multi-agent system is proposed because it is known to be able to coordinate and manage the flow of information more effectively