Discrete time filters for doubly stochastic poisson processes and other exponential noise models
✍ Scribed by Jonathan H. Manton; Vikram Krishnamurthy; Robert J. Elliott
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 189 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0890-6327
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✦ Synopsis
The well-known Kalman ÿlter is the optimal ÿlter for a linear Gaussian state-space model. Furthermore, the Kalman ÿlter is one of the few known ÿnite-dimensional ÿlters. In search of other discrete-time ÿnitedimensional ÿlters, this paper derives ÿlters for general linear exponential state-space models, of which the Kalman ÿlter is a special case. One particularly interesting model for which a ÿnite-dimensional ÿlter is found to exist is a doubly stochastic discrete-time Poisson process whose rate evolves as the square of the state of a linear Gaussian dynamical system. Such a model has wide applications in communications systems and queueing theory. Another ÿlter, also with applications in communications systems, is derived for estimating the arrival times of a Poisson process based on negative exponentially delayed observations.