We develop a new frequency-domain dynamic response method to model integrated Inertial Navigation System (INS) and Global Positioning System (GPS) architectures and provide an accurate impulse-response-based INS-only navigation solution when GPS signals are denied (GPS outages). The input to such a dynamic system is the INS-only solution and the output is the INS/GPS integration solution; both are used to derive the transfer function of the dynamic system using Least Squares Frequency Transform (LSFT). The discrete Inverse Least Squares Frequency Transform (ILSFT) of the transfer function is applied to estimate the impulse response of the INS/GPS system in the time domain. It is shown that the long-term motion dynamics of a DQI-100 IMU/Trimble BD950 integrated system are recovered by 72%, 42%, 75%, and 40% for north and east velocities, and north and east positions respectively, when compared with the INS-only solution (prediction mode of the INS/GPS filter). A comparison between our impulse response model and the current state-of-the-art time-domain feed-forward neural network shows that the proposed frequency-dependent INS/GPS response model is superior to the neural network model by about 26% for 2D velocities and positions during GPS outages.
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