Constrained pole-zero linear prediction: An efficient and near-optimal method for multi-tone frequency estimation

Constrained pole-zero linear prediction (CPZLP) is proposed as a new method for parametric frequency estimation of multiple real sinusoids buried in noise. The method is based on a signal model that consists of a cascade of second-order constrained pole-zero models, thereby exploiting the linear prediction property of sinusoidal signals. The signal model is parametrized directly with the unknown frequencies, which are then estimated using a numerical optimization approach. By independently optimizing each second-order stage in the cascade model, a computationally efficient algorithm is obtained with a complexity that is linear in both the data record length and the number of sinusoids. The linear complexity allows for using relatively long data records, leading to high accuracy even at low signal-to-noise ratios (SNR). Simulation results confirm that the CPZLP algorithm nearly achieves the Cramér-Rao lower bound for SNR as low as 5 dB.