Amplitude And Phase Estimation Research Articles

Two-dimensional system identification using amplitude estimation

Stoica, Li and Li, (see IEEE Trans. Signal Processing, vol.48, p.338-52, 2000) introduced an amplitude estimation based scheme for one-dimensional (1-D) system identification that overcomes several drawbacks (e.g., computational complexity, local convergence, and statistical inefficiency when spectrally colored noise is present) suffered by the conventional output error method (OEM). Along the same line, we herein propose a two-dimensional (2-D) system identification scheme that makes use of 2-D amplitude estimation. In particular, we consider the recently introduced 2-D amplitude and phase estimation (APES) amplitude estimator, which has been shown to yield superior performance over its competitors. To benchmark the proposed scheme, we also derive the Cramer-Rao bound (CRB) for the 2-D system identification problem.

High-resolution SAR imaging with angular diversity

We propose to use the APES (amplitude and phase estimation) approach for the spectral estimation of gapped data and synthetic aperture radar (SAR) imaging with angular diversity. A relaxation-based algorithm, referred to as GAPES (Gapped-data APES), is proposed, which includes estimating the spectrum via APES and filling in the gaps via a least squares (LS) fitting. For SAR imaging with angular diversity data fusion, we perform one-dimensional (1-D) windowed fast Fourier transforms (FFTs) in range, use the GAPES algorithm to interpolate the gaps in the aperture for each range, apply 1-D inverse FFTs (IFFTs) and dewindow in range, and finally apply the two-dimensional (2-D) APES algorithm to the interpolated matrix to obtain the 2-D SAR image. Numerical results are presented to demonstrate the effectiveness of the proposed algorithm.

Nonparametric spectral analysis of gapped data via an adaptive filtering approach

We present an algorithm for nonparametric complex spectral analysis of gapped data via an adaptive finite impulse response (FIR) filtering approach, referred to as the gapped-data amplitude and phase estimation (GAPES) algorithm. The incomplete data sequence may contain gaps of various sizes. The GAPES algorithm iterates the following two steps: (1) estimating the adaptive FIR filter and the corresponding complex spectrum via amplitude and phase estimation (APES), a nonparametric adaptive FIR filtering approach, and (2) filling in the gaps via a least-squares APES fitting criterion. The initial condition for the iteration is obtained from the available data segments via APES. Numerical results are presented to demonstrate the effectiveness of the proposed GAPES algorithm.

Adaptive Filter-bank Approach to Restoration and Spectral Analysis of Gapped Data

The main topic of this paper is the nonparametric estimation of complex (both amplitude and phase) spectra from gapped data, as well as the restoration of such data. The focus is on the extension of the APES (amplitude and phase estimation) approach to data sequences with gaps. APES, which is one of the most successful existing nonparametric approaches to the spectral analysis of full data sequences, uses a bank of narrowband adaptive (both frequency and data dependent) filters to estimate the spectrum. A recent interpretation of this approach showed that the filterbank used by APES and the resulting spectrum minimize a least-squares (LS) fitting criterion between the filtered sequence and its spectral decomposition. The extended approach, which is called GAPES for somewhat obvious reasons, capitalizes on the aforementioned interpretation: it minimizes the APES-LS fitting criterion with respect to the missing data as well. This should be a sensible thing to do whenever the full data sequence is stationary, and hence the missing data have the same spectral content as the available data. We use both simulated and real data examples to show that GAPES estimated spectra and interpolated data sequences have excellent accuracy. We also show the performance gain achieved by GAPES over two of the most commonly used approaches for gapped-data spectral analysis, viz., the periodogram and the parametric CLEAN method.

A new derivation of the APES filter

We introduce a novel design criterion for data-dependent narrowband filters that are of interest in temporal or spatial spectral analysis applications. The solution to the design problem considered is shown to coincide with the previously introduced amplitude and phase estimation (APES) filter. The new derivation of APES in this article sheds more light on the properties of APES and provides some intuitive explanation of the performance superiority of the APES filter over the Capon filter.

Using APES for interferometric SAR imaging

We present an adaptive finite impulse response (FIR) filtering approach, which is referred to as the Amplitude and Phase EStimation (APES) algorithm, for interferometric synthetic aperture radar (SAR) imaging. We compare the APES algorithm with other FIR filtering approaches including the Capon and fast Fourier transform (FFT) methods. We show via both numerical and experimental examples that the adaptive FIR filtering approaches such as Capon and APES can yield more accurate spectral estimates with much lower sidelobes and narrower spectral peaks than the FFT method. We show that although the APES algorithm yields somewhat wider spectral peaks than the Capon method, the former gives more accurate overall spectral estimates and SAR images than the latter and the FFT method.

Matched-filter bank interpretation of some spectral estimators

We make use of a matched-filter bank (MAFI) approach to derive spectral estimators for stationary signals with mixed spectra. We show that the Capon spectral estimator as well as the more recently introduced APES (amplitude and phase estimation) method are members of the MAFI class. A seemingly new MAFI-based spectral estimator is shown to reduce to APES as well. The MAFI interpretation of Capon and APES, along with some additional analysis, provides further insights into the properties of and the relationship between these two spectral estimation methods.

Time-varying complex spectral analysis via recursive APES

APES (Amplitude and Phase EStimation) is an adaptive FIR filtering approach introduced recently for complex spectral estimation. For stationary signals, APES can yield more accurate spectral estimates than the widely used Capon and FFT estimators. The authors present a recursive APES algorithm for time-varying spectral analysis, which is computationaly efficient and only involves FFT and simple matrix operations. The recursive APES algorithm is applied to ISAR (inverse synthetic aperture radar) imaging and feature extraction of targets with complex manoeuvring motion. Both numerical and experimental examples are provided to demonstrate the performance of the proposed method.