Extended Kalman filtering problem in wildlife telemetry
Sugathadasa, Manjula Samanmalee
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The problem of accurately locating the position of an animal using noisy directional data is treated here from the viewpoint of extended Kalman filtering methodology. The physical model considered consists of an animal moving randomly in a confined area and the location of it is tracked using several fixed measuring devices, each of which is nominally capable measuring the angular location of the animal from its own location. These angular measurements are inaccurate due to random noise. The system is modelled mathematically as follows. Time is assumed to move in discrete steps which coincide with moments at which measurements are taken. During a given time step, the movement of the animal is described by a linear difference equation driven by random noise, and the inaccuracies of the measuring devices are modelled as additive noise with zero mean and known covariance. The extended Kalman filtering problem for this system is formulated, and theoretical analysis is carried out. It is shown that if the animal movement is suitably confined, then the covariance of estimation errors satisfy a stable dynamical system. In particular, bounds on the magnitude of the covariance of estimation errors are derived. It is also shown that there is an associated extended Kalman filtering problem with stable filter and covariance dynamics. Extensive simulation experiments are carried out to compare the performance of Kalman filtering strategies with well established triangulation methods.