A total estimator of the Hadamard function used for GPS operations

Abstract

Abstract : We describe a method based on the Total deviation approach whereby we improve the confidence of the estimation of the Hadamard deviation that is used primarily in GPS operations. The Hadamard-total deviation described in this paper provides a significant improvement in confidence indicated by an increase of 1.3 to 3.4 times the one degree of freedom of the plain Uadamard deviation at the longest averaging time. The new Hadamard-total deviation is slightly negativdy biased with respect to the usual Uadamard deviation, and T values are restricted to less than or equal to T/3, to be consistent with the usual Uadamard's definition. We give a method of automatically removing bias by a power-law detection scheme. We review the relationship between Kalman fiber parameters and the Hadamard and Allan variances, illustrate the operational problems associated with estimating these parameters, and discuss how the Uadamard-total variance can improve management of present and future GPS satellite clocks.