Robert B. Washburn

A new relaxation algorithm and passive sensor data association

The static problem of associating measurements at a given time from three angle-only sensors in the presence of clutter, missed detections, and an unknown number of targets is addressed. The measurement-target association problem is formulated as one of maximizing the joint likelihood function of the measurement partition. Mathematically, this formulation leads to a generalization of the 3-D assignment (matching) problem, which is known to be NP hard. The solution to the optimization problem developed is a Lagrangian relaxation technique that successively solves a series of generalized two-dimensional (2-D) assignment problems. The algorithm is illustrated by several application examples. >

ASYMPTOTIC AGREEMENT AMONG COMMUNICATING DECISIONMAKERS.

This paper studies asymptotic agreement among communicating decision-makers in terms of the evolution of a dynamical system defined on the lattice of information o-algebras. This approach focuses on the concept of decisions based on common knowledge introduced earlier by Aumann, but it extends the investigation to general decision rules. We obtain conditions for asymptotic agreement in cases of direct, indirect, and random communications. We also present several examples to illustrate disagreement when the agreement conditions are not satisfied

Performance Analysis for Hybrid State Estimation Problems

Hybrid state estimation problems are statistical estimation problems in which both continuous-valued and discrete-valued states and parameters occur. The hybrid state model provides both a natural formulation for many types of surveillance and tracking problems and a powerful framework for deriving theoretically optimal and practical suboptimal tracking algorithms. This paper describes research in developing tools for evaluating the performance of optimal and suboptimal hybrid state estimation problems.

Rate distortion lower bound for a special class of nonliear estimation problems

This paper studies a rate distortion lower bound of the mean square error for a special class of non-linear estimation problems which have measurements that can be expressed as a memoryless nonlinear function of a Gaussian distributed state plus Gaussian distributed measurement noise. This bound is computable in closed form for a large class of nonlinearities and it is asymptotically tighter than Cramer-Rao type bounds in the limit of low signal-to-noise ratio. Practical computability and tightness of the bound are discussed, and several illustrative examples are given, including the cubic sensor problem.

Rate distortion lower bound for a special class of nonlinear estimation problems

Abstract A rate distortion lower bound of minimum mean square error is presented for a special class of discrete time nonlinear filtering problems which have measurements that can be expressed as a memoryless nonlinear function of a Gaussian distributed space process with additive Gaussian noise. The lower bound is exactly and practically computable for a large class of nonlinearities and is proved to be asymtotically tighter than Cramer-Rao type bounds in the limit of low signal-to-noise ratio.