Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
1972 | 10.1109/TIT.1972.1054756 | Information Theory, IEEE Transactions |
Keywords | Field | DocType |
Filtering,Markov processes,Parameter estimation,Poisson processes,Signal detection | Applied mathematics,Discrete mathematics,Mathematical optimization,Markov process,Counting process,Markov property,Point process,Continuous-time stochastic process,Stochastic differential equation,Time reversibility,Mathematics,Markov renewal process | Journal |
Volume | Issue | ISSN |
18 | 1 | 0018-9448 |
Citations | PageRank | References |
55 | 28.43 | 3 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Snyder, Donald L. | 1 | 363 | 175.26 |