Publications

Abstract not provided.

Abstract not provided.

This report describes least squares solution methods and linearized estimates of solution errors caused by data errors. These methods are applied to event locating systems which use time-of-arrival (TOA) data. Analyses are presented for algorithms that use the TOA data in a ''direct'' manner and for algorithms utilizing Time-of-arrival Squared (TSQ) methods. Location and error estimation results were applied to a ''typical'' satellite TOA detecting system. Using Monte Carlo methods, it was found that the linearized location error estimates were valid for random data errors with relatively large variances and relatively poor event/sensor geometries. In addition to least squares methods, which use an L{sub 2} norm, methods were described for L{sub 1} and L{sub {infinity}} norms. In general, these latter norms offered little improvement over least squares methods. Reduction of the location error variances can be effected by using information in addition to the TOA data themselves by adding judiciously chosen ''conditioning'' equation(s) to the least squares system. However, the added information can adversely affect the mean errors. Also, conditioned systems may offer location solutions where nonconditioned scenarios may not be solvable. Solution methods and linearized error estimates are given for ''conditioned'' systems. It was found that for significant data errors, the linearized estimates were also close to the Monte Carlo results.