A Maximum Principle for Optimal Control of Discrete-Time Stochastic Systems With Multiplicative Noise


The most Probability Probabilistic Multi-Hypothesis Tracker (ML-PMHT) will be used as a robust multisensor, low-observable, multitarget active tracker. It is a non-Bayesian algorithm that uses a generalized chance ratio take a look at (GLRT) to differentiate between muddle and targets. We have a tendency to use a new methodology, initially developed to get the likelihood density function (pdf) of the utmost point in the ML-PMHT log-chance ratio (LLR) due to muddle, to currently develop a pdf for the most price of the ML-PMHT LLR caused by a target. With expressions for the pdfs of the maximum points caused by each muddle (developed in an exceedingly companion article) and a target, we have a tendency to will, for a given set of tracking parameters (signal-to-noise ratio, search volume, target measurement likelihood of detection, etc.), develop ML-PMHT "tracker operating characteristic" curves, like receiver operating characteristic curves for a detector. Since ML-PMHT will be considered an optimal algorithm in the way that, as long as the target and the surroundings match the algorithm's assumptions, all the knowledge from all the available measurements will be used, and no approximations are necessary to urge the algorithm to function, the analysis presented in this paper offers for the primary time part of the answer to the elemental question: Can a particular target be tracked?

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