An Algorithm for Combined Code and Carrier Phase Based GPS Positioning

The Global Positioning System (GPS) is a satellite based navigation system. GPS satellites transmit signals that allow one to quite accurately estimate the location of GPS receivers. In GPS a typical technique for kinematic position estimation is relative positioning where two receivers are used, one receiver is stationary and its exact position is known, the other is roving and its position is to be estimated. We describe the physical situation and give the mathematical model based on the difference of the measurements at the stationary and roving receivers. The model we consider combines both the code and carrier phase measurements. We then present a recursive least squares approach for position estimation. We take full account of the structure of the problem to make our algorithm efficient, and use orthogonal transformations to ensure numerical reliability of the algorithm. Real data test results suggest our algorithm is effective. An additional benefit of this approach is that the drawbacks of double differencing are avoided. The paper could also serve as a straightforward introduction for numerical analysts to an interesting area of GPS.This revised version was published online in October 2005 with corrections to the Cover Date.