Track fusion between sensors at separate locations depends on the ability to estimate sensor biases to produce a single integrated picture. Approximating the nonlinear nature of the coordinate system with linear offsets is insufficient for tracking across the full volume of the sensors. In this research, a method to compute biases in sensor coordinates is expanded from the intial two dimensional approach to three dimensions. In addition, tracks are associated and fused together in a Track-Oriented Multiple Hypothesis Tracker, leveraging an Adaptive Semi-Greedy Search algorithm to effectively observe the track pattern across each sensor to compute these biases. The best hypothesis is reported as the current state, with high quality hypotheses kept from frame to frame at depth$N$. The performance of the bias estimation is assessed against the root mean squared error (RMSE) and normalized estimation error squard (NEES) for both the biases as well as the produced system tracks. A complex scenario with closely-spaced objects and maneuvering targets was selected to provide robust testing of the existing algorithm, demonstrating that it is effective beyond the initial simple scenario it was evaluated against.

When performing track correlation and fusion in conjunction with bias estimation for sensor registration, the pattern match bias estimation is usually performed by modeling the biases as additive constants to the tracks in Cartesian space. Since sensor biases actually occur in sensor polar or spherical coordinates, the bias model of adding constants to the tracks can only be applied to a group of somewhat closely-spaced tracks before the linear assumption of the biases in Cartesian coordinates breaks down. A methodology to estimate sensor biases in the native coordinate frame in which they occur is presented, along with simulation results that illustrate its performance. Modeling the biases in sensor coordinates allow for tracks throughout the field of view to be used for sensor bias estimation, producing better sensor registration and track picture. In this research, sensor tracks are transmitted to a fusion center, where track correlation, bias estimation, and fusion are performed. Murty’s K-best hypotheses algorithm is utilized to generated the top K hypotheses for track-to-track correlation. Each hypothesis produces an estimate of the sensor biases. The correlation hypotheses are corrected for their sensor bias estimates and new correlation scores are computed, and the biascorrected correlation hypotheses are ranked to find the best. The best hypothesis is selected as the most recent system track picture. The system tracks produced by the best hypothesis are correlated against the previous system track picture to maintain system track number continuity. The performance of the bias estimation is assessed against the root mean squared error (RMSE) and normalized estimation error squared (NEES) errors of the estimated biases versus the true biases. A scenario with four tracks and two sensors is used to demonstrate the observability of these biases. The results show that the biases as applied to the remote sensor are observable and mitigated, allowing for a more accurate track picture.

Asymptotic approximations to the partition function of Gaussian random fields are derived. Textures are characterized via Gaussian random fields induced by stochastic difference equations determined by finitely supported, stationary, linear difference operators, adjusted to be nonstationary at the boundaries. It is shown that as the scale of the underlying shape increases, the log-normalizer converges to the integral of the log-spectrum of the operator inducing the random field. Fitting the covariance of the fields amounts to fitting the parameters of the spectrum of the differential operator-induced random field model. Matrix analysis techniques are proposed for handling textures with variable orientation. Examples of texture parameters estimated from training data via asymptotic maximum-likelihood are shown. Isotropic models involving powers of the Laplacian and directional models involving partial derivative mixtures are explored. Parameters are estimated for mitochondria and actin-myocin complexes in electron micrographs and clutter in forward-looking infrared images. Deformable template models are used to infer the shape of mitochondria in electron micrographs, with the asymptotic approximation allowing easy recomputation of the partition function as inference proceeds.