Estimation theory

About: Estimation theory is a research topic. Over the lifetime, 35334 publications have been published within this topic receiving 1037566 citations.

Adaptive additive modeling with continuous parameter trajectories

Abstract: This paper investigates the estimation of time varying amplitude and phase trajectories of sinusoidal signal components. The new algorithm adaptively optimizes the parameters of a smoothly connected piecewise polynomial trajectory model. A mathematical analysis is presented that relates the user-selected meta parameters of the trajectory model (polynomial order, segment size, and smoothness at the junctions) to the analysis properties of the adaptive algorithm. It reveals new insights into the relationships between the meta parameters and the resulting time/frequency resolution of the estimate. Moreover, it is shown that for efficient optimization, the phase trajectory needs to be represented in a specific form. A new approach to address the bias/variance tradeoff of the polynomial phase trajectory model by means of regularization is presented and a complete adaptive analysis/synthesis system for sinusoidal sound components is proposed. The adaptive analysis system is investigated by means of simple tracking experiments to demonstrate the effect of the smoothness constraints and compare the results with a standard short-time Fourier transformation (STFT) base frequency estimation technique and known Cramer-Rao bounds. The potential of the adaptive strategy for the modeling of sinusoidal transients is discussed and it is shown that it achieves similar transient quality as a previously proposed method, however, with considerably lower model error. Two examples for modeling real-world signals are discussed

Processing radio frequency ultrasound images: a robust method for local spectral features estimation by a spatially constrained parametric approach

Abstract: Spectral estimation is a major component in studies aiming at characterizing biological tissues through the analysis of backscattered radio frequency (RF) ultrasonic signals and images. However, conventional spectral estimation techniques yield a well-known trade-off between spatial resolution and variance. The backscattered signals are stochastic by nature, so short-term local analysis results in a high variance of the estimates, which cannot efficiently be reduced through conventional spatial averaging. We address this issue by describing a spectral estimation technique that reduces the variance of the estimates (by smoothing the local estimates in spectrally homogeneous regions) while preserving spectral discontinuities (i.e., the smoothing is not performed across regions with different spectral contents). The proposed approach is set in a Bayesian framework and is based on local autoregressive (AR) estimation, constrained by smoothness priors. These smoothness priors are introduced through a Markov random field in which the associated potential functions are nonquadratic, allowing thereby to preserve discontinuity. The method is validated on simulated RF images and tested on echocardiographic images acquired in vivo. The results are compared to the estimates provided by the conventional Burg technique. These results clearly demonstrate the ability of the proposed approach to improve spectral estimation in terms of variance reduction and discontinuity detection.

Detection and Estimation for Communication and Radar Systems

Abstract: 1. Introduction and motivation to detection and estimation 2. Review of probability and random processes 3. Statistical hypothesis testing theory 4. Detection of deterministic binary signals in Gaussian noises 5. M-ary detection and classification of deterministic signals 6. Non-coherent detection 7. Parameter estimation 8. Analytical and simulation methods for system performance analysis and design.