Abstract: A GPS system and method for real-time determination of integer ambiguities in a global positioning system (GPS) receiver and, more specifically, to a GPS system and method for determining integer ambiguities of a GPS solution using a Kalman filter with double difference integer ambiguities as additional states to estimate the ambiguities until they are estimated to within a sufficiently tight variance around their error estimates. Thereafter, all the candidate integer ambiguity values are searched in the range domain, e.g., along the double difference lines-of-sight for each satellite, until one is selected; if the after-the-fit residuals for the selected integers are below a certain threshold, then the selected integers are accepted as the integer ambiguities. If not, another set of candidate integer values are selected and analyzed.