# Risk Sensitive Filtering with Poisson Process Observations

## Abstract

In this paper we consider risk sensitive filtering for Poisson process observations. Risk sensitive filtering is a type of robust filtering which offers performance benefits in the presence of uncertainties. We derive a risk sensitive filter for a stochastic system where the signal variable has dynamics described by a diffusion equation and determines the rate function for an observation process. The filtering equations are stochastic integral equations. Computer simulations are presented to demonstrate the performance gain for the risk sensitive filter compared with the risk neutral filter.

- Authors:

- Defence Science and Technology Organisation, PO Box 1500, Salisbury, South Australia 5108 (Australia), E-mail: Paul.Malcolm@dsto.defence.gov.au
- Department of Engineering, Faculty of Engineering and Information Technology, Australian National University, Canberra, ACT 0200 (Australia), E-mail: Matthew.James@anu.edu.au
- Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, T6G 2E1 (Canada), E-mail: R.Elliott@ualberta.ca

- Publication Date:

- OSTI Identifier:
- 21064271

- Resource Type:
- Journal Article

- Journal Name:
- Applied Mathematics and Optimization

- Additional Journal Information:
- Journal Volume: 41; Journal Issue: 3; Other Information: DOI: 10.1007/s002459910020; Copyright (c) 2000 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 2000 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; DIFFUSION EQUATIONS; FUNCTIONS; HAZARDS; INTEGRAL EQUATIONS; POISSON EQUATION; STOCHASTIC PROCESSES

### Citation Formats

```
Malcolm, W. P., James, M. R., and Elliott, R. J.
```*Risk Sensitive Filtering with Poisson Process Observations*. United States: N. p., 2000.
Web. doi:10.1007/S002459910020.

```
Malcolm, W. P., James, M. R., & Elliott, R. J.
```*Risk Sensitive Filtering with Poisson Process Observations*. United States. doi:10.1007/S002459910020.

```
Malcolm, W. P., James, M. R., and Elliott, R. J. Mon .
"Risk Sensitive Filtering with Poisson Process Observations". United States. doi:10.1007/S002459910020.
```

```
@article{osti_21064271,
```

title = {Risk Sensitive Filtering with Poisson Process Observations},

author = {Malcolm, W. P. and James, M. R. and Elliott, R. J.},

abstractNote = {In this paper we consider risk sensitive filtering for Poisson process observations. Risk sensitive filtering is a type of robust filtering which offers performance benefits in the presence of uncertainties. We derive a risk sensitive filter for a stochastic system where the signal variable has dynamics described by a diffusion equation and determines the rate function for an observation process. The filtering equations are stochastic integral equations. Computer simulations are presented to demonstrate the performance gain for the risk sensitive filter compared with the risk neutral filter.},

doi = {10.1007/S002459910020},

journal = {Applied Mathematics and Optimization},

issn = {0095-4616},

number = 3,

volume = 41,

place = {United States},

year = {2000},

month = {5}

}

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