Abstract:
The Kalman filtering represents a time-domain filtering method based on dynamic models. Its frequency-domain implementation emerges as a key technique for airborne gravity data processing. In light of this, this study explored and designed a frequency-domain-based Kalman smoothing filter based on the Kalman filter model established previously by the authors through approximation using a low-order Taylor series expansion. First, using the Taylor series formula, the impacts of signal amplitude, signal frequency, data sampling rate, and model dimension on model errors were analyzed. The frequency response function H(\texte^\textj\omega ) of the Kalman smoothing filter under steady-state conditions was then derived using the general Kalman smoothing filtering algorithm. Subsequently, based on the cutoff frequency f_c and amplitude-frequency response parameter \left| H(f_c)\right| of the smoothing filter, a method was proposed to determine the statistical parameters of systematic and measurement noise. This method aims to estimate the variances of the systematic and measurement noise series. Measured data from a certain area were processed using the filter proposed in this study and the scheme for solving gravity anomalies. The results were compared with those derived using the GT-1A system software, yielding an average mean square error (MSE) of 0.47 mGal.