The probability hypothesis density (PHD) filter is an attractive approach to tracking an unknown and time-varying number of targets in the presence of data association uncertainty, clutter, noise, and detection uncertainty. The PHD filter admits a closed form solution for a linear Gaussian multi-target model. However, this model is not general enough to accommodate maneuvering targets that switch between several models. In this paper, we generalize the notion of linear jump Markov systems to the multiple target case to accommodate births, deaths and switching dynamics. We then derive a closed form solution to the PHD recursion for the proposed linear Gaussian jump Markov multi-target model. Based on this an efficient method for tracking multiple maneuvering targets that switch between a set of linear Gaussian models is developed. An analytic implementation of the PHD filter using statistical linear regression technique is also proposed for targets that switch between a set of nonlinear models. We demonstrate through simulations that the proposed PHD filters are effective in tracking multiple maneuvering targets.

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Recently, a modified homotopy perturbation method with an auxiliary term was proposed for obtaining an analytical approximate solution of a nonlinear equation. The auxiliary term involves a tuning parameter that gives the modified homotopy perturbation method an additional degree-of-freedom to construct the approximate solution. In this paper, we present a systematic approach for choosing the auxiliary parameter and furthermore show that an optimal value of the parameter yields significant improvement in the approximate solution compared to the standard homotopy perturbation method. We consider the nonlinear oscillator with a discontinuity to illustrate the proposed approach.

In a number of application areas such as neural coding there is interest in computing, from real data, the information flows between stochastic processes one of which is a point process. Of particular interest is the calculation of the trajectory (as opposed to marginal) mutual information between an observed point process which is influenced by an underlying but unobserved analog stochastic process i.e. a state. Using particle filtering we develop a model based trajectory mutual information calculation for apparently the first time.

The availability of multivariate point process data in a number of application areas such as neural coding and stochastic finance is generating demand for analysis tools for handling such high-dimensional data. Existing models suffer from the curse of dimensionality problem and are not applicable in the high-dimensional setting. In this paper, we introduce a dynamic index model for the multivariate point process and provide a maximum likelihood estimator which we compute by a non-negative matrix factorization (NMF)-type algorithm. However, the dependence on the point process history in the model implies our algorithm does not fit the traditional NMF framework. The method is illustrated with some data from cortical recordings in cats. 52nd IEEE Conference on Decision and ControlDecember 10-13, 2013. Florence, Italy 978-1-4673-5717-3/13/$31.00 ©2013 IEEE 7028