GPS AMBIGUITY RESOLUTION: IMPACT OF TIME CORRELATION, CROSS-CORRELATION AND SATELLITE ELEVATION DEPENDENCE P.J.G. TEUNISSEN Delft Geodetic Computing Centre, Delft University of Technology, Delft, The Netherlands* Summary: In this contribution we discuss the geometry-free GPS single baseline model and show how the least-squares ambiguities are affected by changes in the stochastic model. We particularly pay attention to the effect of time correlation, cross-correlation and satellite elevation dependence. We also differentiate between the impact on the location of the ambiguity search space and the impact on the size and shape of the search space. The analysis is carried out for both the model in which the ionospheric delays are assumed absent, and for the model in which they are assumed present. The former model is applicable to short baselines only. K e y w o r d s : GPS, ambiguity, stochastic model 1. INTRODUCTION Integer ambiguity estimation is a prerequisite for fast, high precision GPS relative positioning. The linear(ized) GPS model of observation equations on which the estimation of the integer ambiguities is based, is generally of the form where y is the vector of "observed minus computed" double-differenced (DD) GPS observables, a is the vector of unknown integer ambiguities, b is the vector that includes all remaining unknown parameters and e is the vector that takes care of the measurement noise and remaining unmodelled effects. Matrices A and B are the appropriate design matrices. In order to solve the above system of equations, the least-squares principle is applied. Since the ambiguities are known to be integral, we are dealing with an integer least-squares problem instead of with a standard least-squares problem. The integer least-squares problem can be solved in three steps. First, an ordinary least-squares solution is computed. Hence, in this step the integer constraints on the ambiguities are discarded. As a result, one obtains the real-valued least-squares solution and corresponding variance matrices This solution is often referred to as the float solution. In the second step, the results of a and Qa of the first step are used to compute the integer least- squares estimates of the ambiguities. The integer least-squares estimate of a denoted as &, and it is the solution of * Address: Thijsseweg 11, 2629 JA Delft, The Netherlands (Fax: +31-15-278 3711; e-mail: lgr@geo.tudelft.nl) Studiageoph. etgeod. 41 (1997), 181-195 © 1997 StudiaGeo s.r.o., Prague 181