Abstract: A system is disclosed for computing least cost paths under hard constraints such as turn angle constraints. In an explicit embodiment, a transformation is performed on a graph representation of an optimization problem to generate a transformed graph incorporating the hard constraint in the edges of the transformed graph. Unconstrained optimization is then performed on the transformed graph using an implementation of Dijkstra's algorithm. The structure of the transformed graph lends itself to searching for an optimal solution using data structures of the vertices of the original graph. In an implicit embodiment, the searching is performed using the data structures but without explicitly generating the transformed graph. The enhanced performance of the invention is sufficient to allow for dynamic re-routing of vehicles in uncertain or changing environments.

Abstract: We describe 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. First 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. Empirical testing for variously distributed data in both three and eight dimensions indicate that the scaling is significantly reduced from N2, where N is the size of the data set.

Abstract: A method and apparatus are described for fusing a plurality of signals, corresponding to mean and covariance estimates, into a single signal when the given signal estimates are correlated to an unknown degree. The core components of the method and apparatus are (1) capability to express the means and covariances of the set of signals in inverse form in a common coordinate frame and (2) capability to form a signal determined by a convex combination of the means and covariances, so expressed. The set of estimates to be fused may comprise previously fused estimates as well as measurements of a physical system. The signal derived from the fused result can be transmitted and used to physically respond to the measured state of the system of interest.

Abstract: A system and a method for estimating the mean and covariance resulting from the application of a given nonlinear function or transformation when applied to a given mean and covariance derived from measurements of a physical system or process. The method comprises selecting a set of points having an arbitrary mean different from the given mean, but with covariance about the given mean equal to that of the given covariance; applying the given nonlinear function to each element of the selected set of points; computing an estimate of the mean of the nonlinearly transformed given mean and covariance; and computing the covariance of the nonlinearly transformed set of points about the estimated mean. The system and method provide an efficient procedure for accurately incorporating nonlinear models of quantities of interest in tracking systems, control mechanisms, and many other related signal processing systems.

Abstract: A system and a method for estimating the expected value and covariance of a nonlinear function of a random variable includes the steps of measuring the random variable, generating a discrete distribution of a first set of values for the random variable about the measured value for the random variable which have a predetermined covariance, calculating a second set of values by applying the nonlinear function to the first set of values, and determining the mean and the covariance of the nonlinear function of the measured value based upon the second set of values. The system and the method provide a tractable procedure for accurately estimating the mean and the covariance of a nonlinear function of one or more random variables, which has applications in tracking, process control, and system modelling.

Abstract: A method for efficiently determining correlations between tracks and objects in a multi-target tracking system comprises defining a current track measurement estimate for each track, and building a measurement tree from the track measurement estimates. The estimates may be either point or volume measurement estimates. After defining the measurement tree, a measurement defining a volume measurement is taken of one of the objects. The measurement is correlated to one or more tracks by searching the measurement tree. The tree is searched by determining, at each node of the tree, if the volume measurement intersects the particular track point or volume measurement estimate associated with the particular node. Additionally, a search volume is associated with each node, such that the decision to search further paths emanating from a particular node is made by determining if the volume measurement intersects the associated search volume.

Abstract: A method and apparatus for reducing the calculations necessary to track a mber of targets. The invention trades off the magnitude of search radius in parameter space against the number of extra copies made of the track data structure in a manner that inherently saves computation as the number of targets becomes large.

Abstract: A method and apparatus for generating a track data set corresponding to a plurality of objects. A system employing the invention receives reports, e.g. radar echoes, from the plurality of objects over a time interval, partitions the time interval into subintervals or time bins, and sorts the returns into the time bins. In each bin, the reports are very close to one another in time, so that, in correlating the reports in each bin to the tracks, one can use the reports to form the necessary search tree, rather than using the tracks. Doing so increases efficiency if the number of reports per time interval significantly exceeds the number of tracks.