The LAMBDA method for integer ambiguity estimation: implementation aspects

High precision relative GPS positioning is based on the very precise carrier phase measurements. In order to achieve high precision results within a short observation time span, the integer nature of the ambiguities has to be exploited. In this report the full procedure for parameter estimation based on the model of double di erence GPS observations is reviewed, but the emphasis will be on the integer estimation of the GPS double di erence ambiguities. The LAMBDAmethod will be used for the integer estimation. LAMBDA stands for Least-squares AMBiguity Decorrelation Adjustment. By means of the Z-transformation, the ambiguities are decorrelated prior to the integer estimation. The integer minimization problem is then attacked by a discrete search over an ellipsoidal region, the ambiguity search ellipsoid. The shape and orientation of the ellipsoid are governed by the variance covariance matrix of the ambiguities. The decorrelation realizes an ellipsoid that is very much sphere-like. It can be searched through very e ciently. The size of the ellipsoid can be controlled prior to the search using the volume function. The volume gives an indication of the number of candidates contained in the ellipsoid. A request for only a few candidates can be made, and this enables a straightforward implementation of the search. A limited number of candidates will be output of which one is the integer least-squares estimate for the vector of ambiguities. The LAMBDA method provides, based on the oat ambiguities and their variance covariance matrix, the integer least-squares estimate for the ambiguities. Therewith, the xed solution can be computed. By the decorrelation, the integer estimation can be carried out very fast and e ciently. The total procedure typically takes 30 ms or less on a 486-66 MHz PC for a baseline with 12 ambiguities. The method has been introduced in [1]. Preliminary fast positioning results using the LAMBDAmethod are given in [8], [9] and [10]. In this report, the implementation aspects of the method are discussed. A detailed description of the method is given, as well as the algorithms in the stylized Matlab notation of [7]. v