Ultra-tightly coupled GPS and inertial navigation system for agile platforms

A machine-implemented method for predicting a carrier frequency of a first GPS satellite signal corresponding to a first GPS satellite in an ultra-tightly coupled navigation system receiving the satellite navigation signal, where the navigation system is disposed on an agile platform and further receives additional GPS satellite navigation signals from a plurality of space vehicles and where the navigation system includes an inertial navigation module producing discrete navigation solution signals at a first rate, and includes a first Kalman Filter (KF) producing discrete KF correction signals at a second rate slower than the first rate, the method comprising:

• filtering a most recently produced one of the discrete navigation solution signals, an ephemeris signal representing the ephemeris of the first GPS satellite, and a most recently produced one of the discrete KF correction signals in a second Kalman filter to provide a prediction of the carrier frequency to a virtual time point that is a half-step ahead of the current time of the navigation system;
• downshifting in frequency according to the predicted carrier frequency a received GPS signal from the first GPS satellite to produce a downshifted received GPS signal;
• correlating the downshifted received GPS signal with a PRN code to produce a correlated signal;
• estimating a range residual for the first GPS satellite based upon the correlated signal to determine an acceleration vector;
• and
• filtering the acceleration vector in the first Kalman filter to produce the discrete correction factors.