We propose two nonmyopic sensor scheduling algorithms for target tracking applications. We consider a scenario where a bearingonly sensor is constrained to move in a finite number of directions to track a target in a two-dimensional plane. Both algorithms provide the best sensor sequence by minimizing a predicted expected scheduler cost over a finite time-horizon. The first algorithm approximately computes the scheduler costs based on the predicted covariance matrix of the tracker error. The second algorithm uses the unscented transform in conjunction with a particle filter to approximate covariance-based costs or information-theoretic costs. We also propose the use of two branch-and-bound-based optimal pruning algorithms for efficient implementation of the scheduling algorithms. We design the first pruning algorithm by combining branch-and-bound with a breadth-first search and a greedy-search; the second pruning algorithm combines branch-and-bound with a uniform-cost search. Simulation results demonstrate the advantage of nonmyopic scheduling over myopic scheduling and the significant savings in computational and memory resources when using the pruning algorithms.
Abstract-We consider scale-covariant quadratic timefrequency representations (QTFR's) specifically suited for the analysis of signals passing through dispersive systems. These QTFR's satisfy a scale covariance property that is equal to the scale covariance property satisfied by the continuous wavelet transform and a covariance property with respect to generalized time shifts. We derive an existence/representation theorem that shows the exceptional role of time shifts corresponding to group delay functions that are proportional to powers of frequency. This motivates the definition of the power classes (PC's) of QTFR's. The PC's contain the affine QTFR class as a special case, and thus, they extend the affine class. We show that the PC's can be defined axiomatically by the two covariance properties they satisfy, or they can be obtained from the affine class through a warping transformation. We discuss signal transformations related to the PC's, the description of the PC's by kernel functions, desirable properties and kernel constraints, and specific PC members. Furthermore, we consider three important PC subclasses, one of which contains the Bertrand P k distributions. Finally, we comment on the discrete-time implementation of PC QTFR's, and we present simulation results that demonstrate the potential advantage of PC QTFR's.
In this paper, we propose two myopic sensor scheduling algorithms for target tracking scenarios in which there is a tradeoff between tracking performance and sensor-usage costs. Specifically, we consider the problem of activating the lowest cost combination of at most sensors that maintains a desired squared-error accuracy in the target's position estimate. For sensors that provide position information only, we develop a binary (0-1) mixed integer programming formulation for the scheduling problem and solve it using a linear programming relaxation-based branch-and-bound technique. For sensors that provide both position and velocity information, we pose the scheduling problem as a binary convex programming problem and solve it using the outer approximation algorithm. We apply our scheduling procedures in a network of sensors where the sensor-usage costs correspond to network energy consumption. Our simulation results demonstrate that scheduling using binary programming allows us to obtain optimal solutions to scheduling involving up to 50-70 sensors typically in the order of seconds.
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