Joint Tracking of Manoeuvring Targets and Classification of Their Manoeuvrability
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Joint Tracking of Manoeuvring Targets and Classification of Their Manoeuvrability Simon Maskell QinetiQ Ltd, St. Andrews Road, Malvern, Worcestershire WR14 3PS, UK Email: [email protected] Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK Received 30 May 2003; Revised 23 January 2004 Semi-Markov models are a generalisation of Markov models that explicitly model the state-dependent sojourn time distribution, the time for which the system remains in a given state. Markov models result in an exponentially distributed sojourn time, while semi-Markov models make it possible to define the distribution explicitly. Such models can be used to describe the behaviour of manoeuvring targets, and particle filtering can then facilitate tracking. An architecture is proposed that enables particle filters to be both robust and efficient when conducting joint tracking and classification. It is demonstrated that this approach can be used to classify targets on the basis of their manoeuvrability. Keywords and phrases: tracking, classification, manoeuvring targets, particle filtering.
1.
INTRODUCTION
When tracking a manoeuvring target, one needs models that can cater for each of the different regimes that can govern the target’s evolution. The transitions between these regimes are often (either explicitly or implicitly) taken to evolve according to a Markov model. At each time epoch there is a probability of being in one discrete state given that the system was in another discrete state. Such Markov switching models result in an exponentially distributed sojourn time, the time for which the system remains in a given discrete state. SemiMarkov models (also known as renewal processes [1]) are a generalisation of Markov models that explicitly model the (discrete-state-dependent) distribution over sojourn time. At each time epoch there is a probability of being in one discrete state given that the system was in another discrete state and how long it has been in that discrete state. Such models offer the potential to better describe the behaviour of manoeuvring targets. However, it is believed that the full potential of semiMarkov models has not yet been realised. In [2], sojourns were restricted to end at discrete epochs and filtered mode probabilities were used to deduce the parameters of the timevarying Markov process, equivalent to the semi-Markov process. In [3], the sojourns were taken to be gamma-distributed with integer-shape parameters such that the gamma variate could be expressed as a sum of exponential variates; the semi-Markov model could then be expressed as a (potentially highly dimensional) Markov model. This paper
proposes an approach that does not rely on the sojourn time distribution being of a given form, and so is capable of capitalising on all available model fidelity regarding this distribution. The author asserts that the restrictions of the aforementioned approaches currently limit the use of semi-Markov models in tracking systems and that the improved modelling (and so estimation) a
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