Time-variant harmonic model, modulated sliding discrete Fourier transform, and Kalman filter-based time-frequency domain fusion for fast self-calibration of the installation errors of rotational inertial navigation systems

Extensive effort has been exerted to calibrate the installation errors of rotational inertial navigation systems without additional equipment under the condition of low signal-to-noise ratio (SNR). Thus, all traditional frequency or time domain methods have failed to calibrate the installation errors rapidly and independently in dynamic conditions. We propose a novel rapid parameter self-calibration method that can fuse the complementary advantages of frequency and time domain methods to solve the aforementioned challenge. First, a modulated time-variant harmonic model of the installation errors is built to overcome the limitation of the traditional constant harmonic model. Second, a modulated sliding discrete Fourier transform (mSDFT) is utilized to estimate the harmonic coefficients of the frequency domain model. Finally, the Kalman filter (KF) based on the modulated time-variant harmonic model is used to calibrate the installation errors under the low SNR condition. Simulation and turntable test results show that the proposed method estimates the installation errors rapidly and accurately under the low SNR condition. The sea test result shows that the convergence time reaches 5,254 s with an estimation accuracy of 10 arcsec. The results obtained by proposed method are far better than those obtained by other existing typical filters. Experimental results indicate that the fusion of the time-variant harmonic model, mSDFT, and KF can incorporate the benefits of time and frequency domain methods and overcome their individual drawbacks.