A direct solution to GPS-type navigation equations. An alternative closed-form solution to the GPS pseudo-range equations.An on-line solution to the aircraft tracking problem with a distributed network of 3D sensors that are imperfectly registered is presented. Errors in the relative positions and orientations of the sensors are modeled and estimated by an extended Kalman filter [EKF], along with the track variables. This optimal solution, tractable for a limited number of targets, is compared through Monte-Carlo simulation with a suboptimal fdter that neglects the sensor systematic errors. The registration errors substantially degrade the accuracy of the aircraft position estimates. The performance of the optimal filter depends on whether the registration errors are to be determined in an absolute or relative setting. When the sensor systematic errors are estimated relative to one of the sensors, the optimal filter performance is excellent.The simulation results are confirmed by a covariance analysis of the optimal filter.

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Ill a multitarget environment, tracking systems must include methods for associating measurements to targets. The complexity of that task is compounded when data from multiple sensors is available. This paper presents a clustering approach to the multitarget multisensor tracking problem. The measurement set is partitioned into equivalence classes ( clusters) and the data association problem is redefined to be one of associating the cluster centers and the tracks, resulting in a significant reduction in the size of the association problem. Track termination and track initiation are part of system design, therefore allowing the designed system to be tested on elaborate multitarget tracking scenarios involving an unknown and changing number of real aircraft trajectories. Methods for evaluating the performance of the tracking system, as well as the clustering algorithms are introduced. An equivalence relation clustering algorithm is derived and compared by Monte-Carlo simulations to the subtractive clustering algorithm. The tracking system is shown to effectively track seven crossing aircraft trajectories of different duration, in the presence of clutter. Track maintenance is performed by extended Kalman filters.