This chapter describes a novel approach for target tracking using distribution based Kalman filtering. The approach utilizes the probabilistic hypothesis density (PHD) filter. The PHD filter is a continuous time, nonlinear filter. It computes the posterior probability distribution of the states and the state estimates. The evaluation of the posterior probabilities is done using a finite set of samples. Each sample is a set of coordinates which belong to the target hypothesis. The probability density function is approximated using a Gaussian distribution. The noise covariance is also assumed to be known and constant.
The approaches described in this chapter involve the solution of a nonlinear set of equations that are often solved by iteration. The approach described here involves solving a linear programming problem under the assumption of linear Gaussian dynamics. We assume that the state vectors are defined over the whole state space. The cost function is the sum of the mean square errors, which is calculated locally. A single measurement is associated with each target. The measurement noise is assumed to be known and constant. The measurement sigma points are defined by the sonar acoustical parameters, and the observation space is defined by the set of cells in which the target is assumed to be detected at each time step.
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One of the drawbacks to this approach was that we needed to recompile every time we made even a small change to the code. This slowed everything else we were doing down and because we couldn't always have someone waiting for the application to finish building. 827ec27edc