A system for determining exact solutions of the pseudorange equations obtained from measurements of location determination (LD) signals received from N LD signal sources by a mobile LD station. The LD signal sources may be part of a GPS, a GLONASS, LEO or any other satellite-based or ground-based LD system, such as Loran. Squares of differences of the pseudorange equations are subtracted from each other to produce N-1 linear relations between the unknown location coordinates x, y and z and the receiver clock offset b. These linear relations are used in one or more squares of pseudorange equations to produce a quadratic equation in b, or in x, y or z. A physically realistic solution b is found and used to determine the remaining unknown coordinates (x,y,z) . No iteration or approximation is required. For N. gtoreq.5, the approach extends to situations where the clock offset varies with time. For N≧5, another approach determines the minimum radius sphere that contains all LD signal antenna locations produced by application of the invention to sets of four LD signals for all permutations of constellations of four LD signal sources. For N. gtoreq.5, another approach uses mean square error minimization to determine the solution set (x,y,z,b). The invention allows use of less complex receiver clocks and allows simpler and faster signal processing to determine the solution set (x,y,z,b).
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