Filtering and control performance bounds with implications on asymptotic separation
Automatica (Journal of IFAC)
Suboptimal nonlinear filtering of the rate of an observed point process
Mathematical and Computer Modelling: An International Journal
Recursive estimation of a discrete-time Markov chain
Mathematical and Computer Modelling: An International Journal
Automatica (Journal of IFAC)
| Hi-index | 754.84 |
Equations are derived that describe the time evolution of the posterior statistics of a general Markov process that modulates the intensity function of an observed inhomogeneous Poisson counting process. The basic equation is a stochastic differential equation for the conditional characteristic function of the Markov process. A separation theorem is established for the detection of a Poisson process having a stochastic intensity function. Specifically, it is shown that the causal minimum-mean-square-error estimate of the stochastic intensity is incorporated in the optimum Reiffen-Sherman detector in the same way as if it were known. Specialized results are obtained when a set of random variables modulate the intensity. These include equations for maximum a posteriori probability estimates of the variables and some accuracy equations based on the Cramér-Rao inequality. Procedures for approximating exact estimates of the Markov process are given. A comparison by simulation of exact and approximate estimates indicates that the approximations suggested can work well even under low count rate conditions.