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The subspace-based technique is used for the estimation of the time of arrival and Doppler shift of a signal of the known waveform. The tool to find required subspaces is a special orthogonal decomposition of received data. It allows concentrate Fisher information about desired parameter in a small number of the first terms of the decomposition. This approach offers a low-dimensional vector of sufficient statistics. It leads to computationally efficient Bayes estimation. Besides, it results in expanding of the SNR range for effective ML-estimating. At last, we can obtain independent time arrival and Doppler shift estimations on the base generalized eigenvectors of the matrix pair.