THE LAMBDA-METHOD FOR FAST GPS SURVEYING P.J.G. Teunissen, P.J. de Jonge and C.C.J.M. Tiberius Delft Geodetic Computing Centre (LGR) Faculty of Geodetic Engineering Delft University of Technology Thijsseweg 11, NL-2629 JA Delft E-mail: lgr@geo.tudelft.nl The Netherlands Abstract: Fast and high precision relative GPS positioning based on short observation time span data is possible, when reliable estimates of the integer double difference ambiguities can be determined in an efficient manner. In the present contribution it will be shown how this can be achieved by means of the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA). The method was introduced in [Teunissen, 1993] and consists of two steps: (a) a decorrelation of the double difference ambiguities; and (b) a sequential conditional least-squares based search. The decorrelation is based on an integer approximation of the conditional least-squares transformation. Through the decorrelation, the spectrum of sequential conditional ambiguity variances is flattened and lowered, and a dramatic improvement in ambiguity precision is reached. Both the theoretical and practical intricacies of the method will be reviewed. 1. Introduction The GPS double difference carrier phase measurements are ambiguous by an unknown integer number of cycles. The a priori knowledge of the integerness of the ambiguities can be used to strengthen the baseline solution. This is in particular of relevance for applications where use is made of short observation time spans. The principle of least-squares is used to determine the most likely integer estimates of the ambiguities. Due to the integer nature of the ambiguities, no direct method exists for the computation of these most likely integer estimates. Hence, use has to be made of a discrete search process. Although one can construct rather straightforward search procedures for the correct determination of the integer ambiguity estimates, difficulties will be encountered when one requires that the search procedures are to be efficient, in terms of computational speed, as well. This is particularly true when short observation time spans are used. In the literature, many important contributions have been made in the area of GPS integer ambiguity estimation. Starting from rather simple but time consuming rounding schemes, the methods have evolved into complex and efficient search algorithms. Examples are the methods and refinements, which have been proposed in [Blewitt, 1989], [Euler and Landau, 1992], [Frei, 1991], [Hatch, 1991] and [Wübbena, 1991]. Nevertheless, it has been our experience that still some room of improvement, in terms of efficiency and general applicability, is possible. It is our believe, that these requirements are satisfied by the least-squares ambiguity decorrelation adjustment. The basic principles of the method, together with some typical results, will therefore be presented in this contribution. 2. Integer least-squares estimation The nonlinear observation equation for the difference between the simultaneous phase measurements of a receiver j of the signals transmitted by two different satellites, k and l, and the simultaneous measurements of a second receiver i of the same signals, reads The unknown parameters in this equation are: (a) , the linear combination of the four geometric distances between (1) Φ kl ij (t) ρ kl ij I kl ij T kl ij δm kl ij λN kl ij kl ij ρ kl ij Presented at the International Symposium "GPS Technology Applications" Bucharest, Romania, September 26-29, 1995.