ESTIMATION OF THE STOCHASTIC MODEL FOR GPS CODE AND PHASE OBSERVABLES

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Abstract
The processing of data gathered with a geodetic measurement technique, like GPS surveying, requires the specification of a mathematical model, consisting of a functional model and a stochastic model. The functional model for GPS surveying is already largely known, but the stochastic model still remains virtually uncharted territory. Hence, in this article a procedure is presented for the estimation of elements of the stochastic model by means of relatively simple formulae. The procedure is used to analyze time series of GPS pseudo-range and carrier phase observations collected at a 1-second interval in a precise relative positioning set up with some state-of-the-art geodetic GPS receiver pairs. It is indicated what effects an adequate stochastic model should comprise. The results show that the variance of the code and phase observables per channel/satellite depends on the elevation angle and that significant mutual correlation exists between C1 and P2 code and between L1 and L2 phase observables. It is therefore concluded that refinements to the stochastic model currently in use are definitely necessary.

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