Triple Differencing with Kalman Filtering: Making It Work

Since global positioning system (GPS) measurements are ranges (code) and biased ranges (carrier), it seems natural to model them as ranges and determine the biases. This is particularly compelling since the double-difference range biases turn out to be integers. At some level there is also an elegance, perhaps therefore a naturalness, to modeling the carrier measurements as time differences of double differences. While something is lost something else is gained. Here we apply the proven delayed-state Kalman filter to processing carrier phase measurements as triple differences. In practice we process these triple differences along with double-difference code measurements. We also treat the measurement error as, mostly, Gauss-Markov states to be determined. Many of the details are discussed and experimental results are included. These demonstrate that excellent performance can be obtained if the Kalman filter modeling is done carefully. © 2000 John Wiley & Sons, Inc.