The subspace-based technique is used for the estimation of the time of arrival and Doppler shift of a signal of known waveform. The tool to find required subspaces is a special orthogonal decomposition of received data. It allows one to concentrate Fisher information on the desired parameter in just a few of the first terms of the decomposition. This approach offers a low-dimensional vector of sufficient statistics. It leads to computationally efficient Bayesian estimation. Besides, it results in expansion of the signal-to-noise ratio (SNR) range for effective maximum likelihood (ML) estimation. Finally, we can obtain independent time arrival and Doppler shift estimations based on generalized eigenvectors.
