A Particle Filtering Approach to Change Detection for Nonlinear Systems
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A Particle Filtering Approach to Change Detection for Nonlinear Systems Babak Azimi-Sadjadi Electrical, Computer, and Systems Engineering Department, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA Email: [email protected] The Institute for Systems Research, University of Maryland, College Park, MD 20742, USA
P. S. Krishnaprasad The Institute for Systems Research, University of Maryland, College Park, MD 20742, USA Email: [email protected] Received 13 September 2003; Revised 22 March 2004 We present a change detection method for nonlinear stochastic systems based on particle filtering. We assume that the parameters of the system before and after change are known. The statistic for this method is chosen in such a way that it can be calculated recursively while the computational complexity of the method remains constant with respect to time. We present simulation results that show the advantages of this method compared to linearization techniques. Keywords and phrases: nonlinear filtering, generalized likelihood ratio test, CUSUM algorithm, online change detection.
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INTRODUCTION
Page states the change detection problem as follows [1]: “Whenever observations are taken in order it can happen that the whole set of observations can be divided into subsets, each of which can be regarded as a random sample from a common distribution, each subset corresponding to a different parameter value of the distribution. The problems to be considered in this paper are concerned with the identification of the subsamples and the detection of changes in the parameter value.” We refer to a change or an abrupt change as any change in the parameters of the system that happens either instantaneously or much faster than any change that the nominal bandwidth of the system allows. The key difficulty of all change detection methods is that of detecting intrinsic changes that are not necessarily directly observed but are measured together with other types of perturbations [2]. The change detection could be offline or online. In online change detection, we are only interested in detecting the change as quickly as possible (e.g., to minimize the detection delay with fixed mean time between false alarms), and the estimate of the time when the change occurs is not of importance. In offline change detection, we assume that the whole observation sequence is available at once and finding the estimate of the time of change could be one of the goals of the detection method. In this paper, we limit our concern to online detection of abrupt changes. The change detection methods that we consider here can
be classified under the general name of likelihood ratio (LR) methods. Cumulative sum (CUSUM) and generalized LR (GLR) tests are among these methods. CUSUM was first proposed by Page [1]. The most basic CUSUM algorithm assumes that the observation signal is a sequence of stochastic variables which are independent and identically distributed (i.i.d.) with known common probability density function before the change time, and i.i.d. with another kn
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