Efficient gating in data association with multivariate Gaussian distributed states

An efficient algorithm for evaluating the (weighted bipartite graph of) associations between two sets of data with Gaussian error, e.g., between a set of measured state vectors and a set of estimated state vectors, is described. A general method is developed for determining, from the covariance matrix, minimal d-dimensional error ellipsoids for the state vectors which always overlap when a gating criterion is satisfied. Circumscribing boxes, or d-ranges, for the data ellipsoids are then found and whenever they overlap the association probability is computed. For efficiently determining the intersections of the d-ranges, a multidimensional search tree method is used to reduce the overall scaling of the evaluation of associations. Very few associations that lie outside the predetermined error threshold or gate are evaluated. The search method developed is a fixed Mahalanobis distance search. Empirical tests for variously distributed data in both three and eight dimensions indicate that the scaling is significantly reduced. Computational loads for many large-scale data association tasks can therefore be significantly reduced by this or related methods