This paper describes and demonstrates an assisted GPS technique, termed ''Collective Detection,'' for combining satellite correlograms to enable rapid acquisition and direct positioning. Correctly combining correlation values from multiple satellites reduces the required C/N 0 such that satellite signals, which cannot be acquired individually, can contribute constructively to a position solution. The acquisition search is performed in a position/clock space that directly yields the navigation solution. Results from a hardware simulator and live experiments are presented. The simulations compare combinations of 11 satellites and four satellites at C/N 0 levels of 40 and 20 dB-Hz. The outdoor experiments show horizontal position accuracies on the order of 50 m in open sky conditions and in a narrow courtyard environment using one millisecond of data. Collective detection and positioning is shown to be a promising approach for positioning in weak signal environments.
A new carrier-phase differential global positioning system relative navigation estimator has been developed that extends the use of carrier-phase differential global positioning system techniques to spacecraft formations that operate at geostationary altitudes and above. The estimator achieves rapid convergence to the carrier-phase ambiguities and incorporates a cycle slip detection and recovery algorithm. It solves a linearized problem using leastsquares square-root information processing that does not require spacecraft dynamics models. In this context, integer ambiguities are resolved using an integer least-squares algorithm. The cycle slip algorithm identifies the slip channel by statistical hypothesis testing and estimates the magnitude of the slip. Global positioning system receiverin-the-loop tests with simulated low-Earth orbit data show nearly instantaneous convergence to the correct integer ambiguities and relative position error magnitudes of less than 3 mm. Truth-model simulations are used to simulate geostationary orbits and high-Earth orbit scenarios. The geostationary orbit scenario produces nearly instantaneous convergence to the ambiguities and error magnitudes of less than 0.1 m. The high-Earth orbit case at a radial distance of 17.8 Earth radii converges in minutes with error magnitudes of less than 3 m. Cycle slips, present in the hardwarein-the-loop simulations, are detected and corrected without significant accuracy degradation. Nomenclature c = speed of light in a vacuum c@t = increment to the pseudorange solution clock correction estimate e = extraction vector in the cycle slip detection algorithm f L1 = L1 carrier signal nominal frequency H = measurement sensitivity matrix H = square-root information form of H I = ionosphere error J = least-squares cost function J res = least-squares residual cost function N = time-invariant double-differenced integer ambiguity vector N k = time-varying integer ambiguity vector in the cycle slip recovery algorithm N k = time-varying integer ambiguity vector estimate in the cycle slip detection algorithm N opt = optimal integer ambiguity vector solution P = pseudorange measurement Q = orthonormal transformation matrix R = square-root information matrix R = inverse square root of the measurement error covariance matrix r = pseudorange position vector solution r AB = relative position vector estimate from receiver A to receiver B t A = receiver A time x = position/clock correction state vector x opt = position/clock correction state vector estimate computed using N opt z = linearized measurement vector z= factorized square-root information vector z = square-root information vector z res = square-root information residual vector = initial nominal phase in the receiver n = integer cycle slip estimate n = real-valued cycle slip estimate AB = single-differenced operator defined as A B r = absolute position correction vector r AB = relative position correction vector from receiver A to receiver B t = clock correction t 0 = receiver clock correction computed in th...
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