*Earth Planets Space,* Vol. 52 (No. 10), pp. 807-812, 2000

*LETTER*

## A search space optimization technique for improving ambiguity resolution and computational efficiency

Donghyun Kim and Richard B. Langley

Geodetic Research Laboratory, Department of Geodesy and Geomatics Engineering, University of New Brunswick, Fredericton, N.B., Canada

(Received January 5, 2000; Revised June 24, 2000; Accepted July 9, 2000)

**Abstract: **
An Optimal Method for Estimating GPS Ambiguities (OMEGA) that enables very high performance and computational efficiency has been developed and demonstrated. This method employs two search space reduction processes--a scaling and a screening process--that are related to the search space transformation and the ambiguity candidate filtering in multi-search levels. To obtain the highest efficiency, an optimization procedure, which determines the parameters to minimize the number of candidates under given conditions, is implemented in closed-form before the search-verification step. The method is essentially based on the least-squares-approach originally proposed by Hatch but uses a modified and more efficient process. Two improved algorithms are introduced in this paper. First, an alternative algorithm for the spectral decomposition, which reduces the dimension of the residuals vector to its degrees of freedom, is given in closed form. This algorithm is implemented in the computational step of the quadratic form of the residuals in order to increase computational efficiency. Second, an efficient error model for the threshold of the filter equation that is used to derive the search space scaling process is given. This error model shows two advantages: 1) it bounds noise signals of the filter equation; 2) it gives efficient thresholds so that the scaling effects for the search space can be increased.

Corresponding author E-mail: kim@unb.ca

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