nal-Mean Estimation Via Jump-Diffusion ses in Multiple Target Tracking/Recognition
M. I. Miller, Anuj Srivastava, Ulf Grenander · 1995
A new algorithm is presented for generating the conditional mean estimates of functions of target positions, ori- entations and type in recognition, and tracking of an unknown number of targets and target types. Taking a Bayesian approach, a posterior measure is defined on the trackindtarget parameter space by combining a narrowband sensor array manifold model with a high resolution imaging model, and a prior based on airplane dynamics. The Newtonian force equations governing rigid body dynamics are utilized to form the prior density on airplane motion. The conditional mean estimates are generated using a random sampling algorithm based on jump-dimion processes (l) for empirically generating MMSE estimates of functions of these random target positions, orientations, and type under the posterior measure. Results are presented on target tracking and identification from an implementation of the algorithm on a networked Silicon Graphics workstation and DECmppMasPar parallel machine. I. INTRODUCTION AROMIT DAAL03-92-G-0115, ONR N00014-91-J-1021, ARL MDA972- inference or hypothesis space becomes a search across count- able disconnected unions of these Cartesian product groups, with the model order and model type the variables to be infemd. We take a Bayesian approach, i.e., we define a prior distribution supported on this countable union of spaces, from which the posterior distribution is constructed. The parametric representation of the target scene is selected to correspond to conditional expectations under this posterior. As we are particularly interested in noncooperative mov- ing targets, the algorithms are made robust to motion by incorporation of knowledge about motion dynamics into the prior dis~bution. The Newtonian force equations, a system of differential equations governing the motion of targets, are used to induce the prior. These differential equations are parameterized by the target and its orientation motion described by rotations in the 3-D torus group. It is the introduction of these Newtonian force equations that makes tracking and recognition inseparable, since the equations of motion are explicitly parameterized by the sequence of air- plane orientations. This provides the significant link between tracking algorithms based on data from narrowband sensors arrays in which the target is unresolved in the data (effectively a point), and high resolution information perhaps provided by a second sensor preserving the orientation information from which target recognition is performed. In part, it is this fundamental link that has motivated us to solve the trackinghecognition problem in a single consistent estimation framework in which the inference proceeds via the fusion of