Simplified Noise Modeling of GPS Measurements for a Fast and Reliable Cycle Ambiguity Resolution

The relationship between the observable noise model and the satellite elevation angle can be modeled quite well by an exponential function.[Jin, 1996] Noise size and dependence on the elevation angle are, however, different for each observation and receiver type. Therefore, the coefficient determination of this model is an issue, and various methods including PR-CP, single difference, and time difference have been suggested. The limitations of them are difficulty to model the carrier phase noise and to eliminate bias. To overcome these disadvantages for using Jin's model, we suggest zero baseline double difference (DD) and noise sorting algorithm. Data DD technique in zero baseline is useful to eliminate all the troublesome GPS biases, and the remaining error is the sum of GPS measurement noises from two satellites. These DD residuals for hours should be sorted by the combination of satellite elevation angles, and then variance value of the residual for each combination can be estimated. Using these values, we construct an over-determined linear equation whose solution is a set of noise variance for each satellite elevation angle. With 24hr Trimble 4000ssi data, we easily worked out the coefficients of the noise model not only for pseudorange but also for carrier phase. We estimated the standard deviation of the measurement DD using our model, and plotted 1 and 3 sigma lines for every epoch to verify the representation of the residual error. 63.3% of pseudorange residual and 65.9% of phase error did not exceed the 1 sigma lines. Additionally, 99.2% and 99.5% of them lied within 3sigma line. These figures prove that the Gaussian property of measurement noise, and that the suggested model by our algorithm corresponds to the observable noise information.