Accurate and Simple Estimator for Lossy Wave Equation

Abstract

Abstract-In this letter, parameter estimation of a uniformly sampled signal that satisfies the lossy wave equation in Gaussian noise is investigated. By exploiting the linear prediction property of the noise-free signal, a maximum likelihood estimator for the parameters is first developed. Relaxation is then applied to yield a simple and accurate algorithm. It is shown that the estimation performance of the proposed method attains Cramér-Rao lower bound.

Accurate Parameter Estimation for Wave Equation

“…When the wave equation is applied to a channel waveguide, the propagation direction is confined to one-dimension (1-D), say, z, the guided field measured along the propagation direction z can be described by reducing (3) …”

“…Although the NLS estimator can attain the maximum likelihood (ML) performance under white Gaussian noise environment, it is hard to implement in practice as its objective function is multi-modal. Recently, So et al [3] have devised an iterative quadratic maximum likelihood (IQML) [4][5][6] algorithm for the 1-D wave equation in white Gaussian noise by making use of the linear prediction (LP) property [7,8] in U (z). Apart from more computationally attractive, it is demonstrated in [3] that the IQML scheme can provide optimum accuracy even with a smaller threshold signal-to-noise ratio (SNR) than that of the NLS estimator.…”

“…Recently, So et al [3] have devised an iterative quadratic maximum likelihood (IQML) [4][5][6] algorithm for the 1-D wave equation in white Gaussian noise by making use of the linear prediction (LP) property [7,8] in U (z). Apart from more computationally attractive, it is demonstrated in [3] that the IQML scheme can provide optimum accuracy even with a smaller threshold signal-to-noise ratio (SNR) than that of the NLS estimator. However, both [2,3] only address the simplest scenario of M = 1 in (4) which corresponds to the 1-D single-mode waveguide.…”

“…Apart from more computationally attractive, it is demonstrated in [3] that the IQML scheme can provide optimum accuracy even with a smaller threshold signal-to-noise ratio (SNR) than that of the NLS estimator. However, both [2,3] only address the simplest scenario of M = 1 in (4) which corresponds to the 1-D single-mode waveguide. For M > 1, the waveguide is multi-mode and a generalized treatment is required, which will be discussed in detail in this work.…”

“…In Section 2, we develop an IQML-based parameter estimator for the wave equation of (4) in the presence of white Gaussian noise, which can be considered as an extension of [3]. The basic idea is to solve for {k z,m } in an iterative manner first and then estimate {A m } and {B m } according to linear least squares (LLS).…”