Subspace Leakage Suppression for Joint Parameter Estimation of Quality Factors and Time Delays in Dispersive Media
Linear prediction methods, based on a Hankel data matrix, suffer from subspace leakage and degraded resolution when applied to data models that do not result in a mode matrix with Vandermonde structure, such as the constant-Q model. In the absence of noise, the Vandermonde structure ensures the equivalence between the number of backscattered signals and the rank of the data matrix. This paper first identifies the origin of subspace leakage residing in subspace-based and linear prediction methods when applied to data of the constant-Q model. Second, it proposes a frequency-distortion technique, based on the extension theorems, for suppressing the leakage and preserving the time resolution performance of these methods. The effectiveness of the distortion technique is then demonstrated on GPR simulated data by extending the damped MUSIC algorithm to the joint parameter estimation of the constant-Q model.
Linear prediction methods, based on a Hankel data matrix, suffer from subspace leakage and degraded resolution when applied to data models that do not result in a mode matrix with Vandermonde structure, such as the constant-Q model. In the absence of noise, the Vandermonde structure ensures the equivalence between the number of backscattered signals and the rank of the data matrix. This paper first identifies the origin of subspace leakage residing in subspace-based and linear prediction methods when applied to data of the constant-Q model. Second, it proposes a frequency-distortion technique, based on the extension theorems, for suppressing the leakage and preserving the time resolution performance of these methods. The effectiveness of the distortion technique is then demonstrated on GPR simulated data by extending the damped MUSIC algorithm to the joint parameter estimation of the constant-Q model.