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Approximate likelihood estimation of static parameters in multi-target models

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.

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© 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 X n , is a vector in E 1 ⊂ 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 Y n , is a vector in E 2 ⊂ 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 {(X n , Y n+1 )} n≥0 is 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 ⊂ ℝ nθ . When the target first appears in the surveillance region, its initial state is distributed according to the probability density µ θ on E 1 . The change in its state vector from time n - 1 to n is determined by the Markov transition density f θ (·|x n-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 g θ (·|x n ) on E 2 , and is conditionally independent of previously generated observations and state values.

Item Type: Book Section
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:42
Last Modified: 14 Sep 2017 01:27
DOI: 10.1017/CBO9780511984679.012