An Efficient Method of Doppler Parameter Estimation in the Time–Frequency Domain for a Moving Object From TerraSAR-X Data

A method measuring Doppler parameters by joint time-frequency analysis is presented. Two-dimensional velocity retrieval can be achieved by estimation of the Doppler center frequency and Doppler frequency rate for the range and azimuth velocity components, respectively. The Doppler spectrum along a Doppler phase history line in the time-frequency domain was reconstructed and projected onto the frequency and time dimensions. The peak of the frequency axis projected spectrum corresponds to the Doppler center frequency, while that of the time axis indicates an azimuth time of closest approach. The Doppler frequency rate is obtained by measuring the slope of the Doppler spectrum in the time-frequency domain. Simulation using TerraSAR-X and Envisat ASAR parameters indicated that the velocity errors were less than 1 m/s or 5% for moving objects with a velocity higher than 3 m/s. While the measurement of Doppler center frequency was reliable over the entire velocity range, errors in Doppler frequency rate became large if the velocity was slower than 3 m/s (or 10.8 km/h). Range migration correction plays a key role for the precision of Doppler parameter estimation. An experiment using TerraSAR-X and truck-mounted corner reflectors validated the measurement accuracy of the approach. The absolute and percent errors of the range velocity (49.6 km/h) were 1.4 km/h and 2.8%, respectively, and the azimuth velocity (23.8 km/h) measurement was comparatively accurate, with a percent error of 1.8% under an assumption of zero acceleration. To apply the method to single-look complex data, the full Doppler bandwidth must be preserved.