Estimation of multiple sinusoidal frequencies using truncated least squares methods

To reduce the computational complexity of resolving closely spaced frequencies, three truncated QR methods are proposed: (1) truncated QR without column pivoting (TQR): (2) truncated QR with reordered columns) TQRR); and (3) truncated QR with column pivoting (TQRP). It is demonstrated that many of the benefits of the singular value decomposition based methods are achievable under the truncated QR methods with much lower computational cost. Based on the forward-backward linear prediction model, computer simulations and comparisons are provided for different truncation methods under various SNRs. Comparisons of asymptotic performance for large data samples are also given