Singh, SS and Whiteley, N and Godsill, SJ (2011) *Approximate likelihood estimation of static parameters in multi-target models.* In: Bayesian Time Series Models. UNSPECIFIED, pp. 225-244.

## Abstract

© Cambridge University Press 2011. Target-tracking problems involve the online estimation of the state vector of an object under surveillance, called a target, that is changing over time. The state of the target at time n, denoted Xn, is a vector in E1⊂ and contains its kinematic characteristics, e.g. the target’s position and velocity. Typically only noise-corrupted measurements of the state of the object under surveillance are available. Specifically, the observation at time n, denoted Yn, is a vector in E2⊂ and is a noisy measurement of the target’s state as acquired by a sensor, e.g. radar. The statistical model most commonly used for the sequence of random variables {(Xn, Yn+1)}n≥0is the hidden Markov model (HMM): The superscript θ on these densities (as well as on all densities introduced subsequently), denotes the dependency of the model on a vector of parameters θ. We will assume a parameterisation such that θ ∈ Θ ⊂ ℝnθ. When the target first appears in the surveillance region, its initial state is distributed according to the probability density µθon E1. The change in its state vector from time n - 1 to n is determined by the Markov transition density fθ(·|xn-1). Furthermore, the observation generated at time n is a function of the target’s state at time n and noise, or equivalently generated according to the probability density gθ(·|xn) on E2, and is conditionally independent of previously generated observations and state values.

Item Type: | Book Section |
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Subjects: | UNSPECIFIED |

Divisions: | Div F > Signal Processing and Communications |

Depositing User: | Cron Job |

Date Deposited: | 17 Jul 2017 19:42 |

Last Modified: | 07 Mar 2019 14:57 |

DOI: | 10.1017/CBO9780511984679.012 |