An inertial (“INS”) / 
GPS receiver includes an INS sub-
system which incorporates, into a modified 
Kalman filter, GPS observables and / or other observables that span previous and current times. The INS filter utilizes the observables to update position information relating to both the current and the previous times, and to propagate the current position, velocity and attitude related information. The GPS 
observable may be 
delta phase measurements, and the other observables may be, for example, wheel pick-offs (or counts of wheel revolutions) that are used to calculate along track differences, and so forth. The inclusion of the measurements in the filter together with the current and the previous position related information essentially eliminates the effect of 
system dynamics from the 
system model. A position difference can thus be formed that is directly 
observable by the 
phase difference or along track difference measured between the previous and 
current time epochs. Further, the 
delta phase measurements can be incorporated in the INS filter without having to maintain GPS carrier 
ambiguity states. The INS sub-system and the GPS sub-system share GPS and INS position and 
covariance information. The 
receiver time tags the INS and any other non-
GPS measurement data with GPS time, and then uses the INS and GPS filters to produce INS and GPS position information that is synchronized in time. The GPS / INS 
receiver utilizes GPS position and associated 
covariance information and the GPS and / or other observables in the updating of the INS filter. The INS filter, in turn, provides updated 
system error information that is used to propagate inertial current position, velocity and attitude information. Further, the 
receiver utilizes the inertial position, velocity and 
covariance information in the GPS filters to speed up GPS 
satellite signal re-acquisition and associated 
ambiguity resolution operations