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Likelihood function decomposition is a technique to coordinate deployed fields of multiple diverse heterogeneous sensors and for the automated processing of large volumes of multisensor data. It is an innovative new concept that is potentially useful in many of the kinds of nonlinear problems that arise in sensor fields used for detection, classification, and localization. Algorithms derived via the...
The well-known Shepp-Vardi algorithm (1982) for positron emission tomography (PET) is used to estimate the intensity function of the emissions of short-lived radioisotopes absorbed by the brain or other tissues. In the PET application, radioisotope emissions are modeled as a nonhomogeneous Poisson point process. The Shepp-Vardi algorithm produces the maximum a posteriori (MAP) estimate of the intensity...
A variety of authors have incorporated multiple target motion models into the probabilistic multi-hypothesis tracking (PMHT) algorithm using a discrete Markov chain to model the motion model switching process. However, in these papers the observed data likelihood function is not written down for this model, nor is it evaluated because all possible model assignment sequences must be considered over...
The multitarget intensity filter is derived from a Bayesian first principles approach using a Poisson point process approximation at one step. The prior multitarget model is assumed to be a Poisson point process. The Bayes multitarget posterior probability density function is first defined on the Poisson event space, and then reformulated in terms of the intensity functions that characterize all Poisson...
A multisensor multitarget intensity filter is derived for N sensors. The multitarget process is assumed to be a Poisson point process, as are the sensor measurement sets. The sensor data are pooled, but sensor labels are retained. The likelihood function of the pooled data is obtained via the Poisson point process models. The Bayes information updated point process is not Poisson, but it is shown...
Probabilistic multi-hypothesis tracking (PMHT) is an algorithm for tracking multiple targets when measurement-to- target assignments are unknown and must be jointly estimated with the target tracks. Multi-frame assignment PMHT (MF- PMHT) is an algorithm designed to mitigate some performance problems associated with PMHT. In MF-PMHT, the PMHT algorithm is applied to multi-frame sequences in the last...
An alternating directions method is presented for joint maximum a posteriori estimation of target track and sensor field using bistatic range data. The algorithm cycles over two sub-algorithms: one improves the target state estimate conditioned on sensor field state, and the other improves the sensor field state estimate conditioned on target state. Nonlinearities in the sub-algorithms are mitigated...
Multistatic active target and sensor field tracking in GPS-denied scenarios requires the computation of joint maximum a posteriori estimates of target and sensor field tracks. An alternating directions algorithm, based on a new integral decomposition of the likelihood function of a bistatic range measurement, cycles over two distinct subalgorithms: The first improves the target estimate by estimating...
Multistatic active target tracking in GPS-denied scenarios is complicated by the fact that the emitter and receiver locations are unknown and must be estimated jointly with the target track. Maximum a posteriori algorithms for solving this joint estimation problem are complicated by the nonlinearities in the likelihood function of the bistatic range measurement. A new integral representation of this...
A three-layer feedforward neural network (NN) that implements the optimum Neyman-Pearson (N-P) classifier is described. This NN is useful whenever it is appropriate to characterize (1) input classes as multivariate random variables, and (2) input data vectors as realizations of one of the multivariate random variables. The purpose of the NN is thus simply to compute the conditional likelihoods necessary...
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