Conventional Least-squares Estimator Research Articles

Maximum-A-Posteriori Estimation of Retinal Oxygen Tension Based on Photon Counting Statistics.

The regularization of retinal oxygen tension estimation was previously proposed with an assumption that phosphorescence intensity images are corrupted by additive Gaussian noise. Based on this assumption, a regularized least-squares estimate has been shown to be better than a conventional least-squares estimation. However, this assumption is inconsistent with the acquisition process of phosphorescence intensity images acquired using an intensified charge-coupled device camera. Almost the entire acquisition process is governed by the natural aspects of photons. Therefore, a method based on photon counting statistics is more appropriate. In this study, we propose a regularized oxygen tension estimation method based on photon counting statistics and a phosphorescence lifetime imaging model.

High-dimensional multivariate autoregressive model estimation of human electrophysiological data using fMRI priors

Multivariate autoregressive (MVAR) model estimation enables assessment of causal interactions in brain networks. However, accurately estimating MVAR models for high-dimensional electrophysiological recordings is challenging due to the extensive data requirements. Hence, the applicability of MVAR models for study of brain behavior over hundreds of recording sites has been very limited. Prior work has focused on different strategies for selecting a subset of important MVAR coefficients in the model to reduce the data requirements of conventional least-squares estimation algorithms. Here we propose incorporating prior information, such as resting state functional connectivity derived from functional magnetic resonance imaging, into MVAR model estimation using a weighted group least absolute shrinkage and selection operator (LASSO) regularization strategy. The proposed approach is shown to reduce data requirements by a factor of two relative to the recently proposed group LASSO method of Endemann et al (Neuroimage 254:119057, 2022) while resulting in models that are both more parsimonious and more accurate. The effectiveness of the method is demonstrated using simulation studies of physiologically realistic MVAR models derived from intracranial electroencephalography (iEEG) data. The robustness of the approach to deviations between the conditions under which the prior information and iEEG data is obtained is illustrated using models from data collected in different sleep stages. This approach allows accurate effective connectivity analyses over short time scales, facilitating investigations of causal interactions in the brain underlying perception and cognition during rapid transitions in behavioral state.

Improved infrasound array processing with robust estimators

SUMMARY Infrasound array data are commonly used to detect and characterize infrasonic signals from a variety of natural and anthropogenic sources. Here we examine the effectiveness of robust regression estimators (L1-norm regression, M-estimators and least trimmed squares) for infrasound array processing, and compare them against standard array processing algorithms (least-squares estimation, frequency–wavenumber analysis and progressive multi-channel correlation) using a combination of real and synthetic data. Of particular interest is how each algorithm performs when one of the array elements produces data outliers. Synthetic tests on elements containing a clock error, constant values or only pink noise are performed, and we analyse the relative ability of the estimators to recover plane wave parameters. The L1-norm regression, M-estimate, frequency–wavenumber analysis and least trimmed squares estimates provided superior results than conventional least-squares estimation. Evaluation of least trimmed squares weights consistently identified the element with the simulated error, providing additional information on array performance. Least trimmed squares processing consistently identified an element with reversed polarity for Alaska Volcano Observatory array ADKI. International Monitoring System stations IS57 and IS55 were likewise processed. Data from an element of IS57, which had lower cross-correlation values than the remaining elements, were consistently identified as having outliers in array processing. An element with a timing error was identified in the analysis of IS55 data. These results suggest robust regression methods, in particular least trimmed squares, improve upon standard methods and should be used more widely, as they can provide robust array processing results and insight into array performance. Further, robust regression methods are not limited to infrasound array processing applications, and it is likely that they would also be effective for seismic array data.

MIMO channel estimation in correlated fading environments

This paper presents two analytic correlated multiple-input multiple-output (MIMO) block fading channel models and their time-variant extensions that encompass the popular Kronecker model and the more general Weichselberger model as special cases. Both static and time-variant models offer compact representations of spatial- and/or time-correlated channels. When the transmit antenna array is such that the associated MIMO channel has a small angle spread (AS), which occurs quite often in a cellular downlink, our models admit reduced-rank channel representations. They also provide compact channel state information (CSI) descriptions which are needed in feedback systems and in many post channel estimation applications. The latter has the important implication of reduced feedback channel bandwidth requirement and lower post-processing complexity. Based on one of the proposed channel models we present novel iterative algorithms for estimating static and time-variant MIMO channels. The proposed models make it natural to decompose each iteration of our algorithms into two successive stages that are responsible for estimating the correlation coefficients and the signal direction, respectively. Using popular industry-approved standard channel models, we verify through simulations that our algorithms yield good MSE performance which, in many practical cases, is better than that achievable by a conventional least-square estimator. The mean-squared error (MSE) performance of our estimators are analyzed and the resulting predictions are consistent with those estimated by simulations.

Robust approaches to remote calibration of a transmitting array

We consider the problem of estimating the gains and phases of the RF channels of a M-element transmitting array, based on a calibration procedure where M orthogonal signals are sent through M orthogonal beams and received on a single antenna. The received data vector obeys a linear model of the type y = A Fg + n where A is an unknown complex scalar accounting for propagation loss and g is the vector of unknown complex gains. In order to improve the performance of the least-squares (LS) estimator at low signal to noise ratio (SNR), we propose to exploit knowledge of the nominal value of g , viz g ¯ . Towards this end, two approaches are presented. First, a Bayesian approach is advocated where A and g are considered as random variables, with a non-informative prior distribution for A and a Gaussian prior distribution for g . The posterior distributions of the unknown random variables are derived and a Gibbs sampling strategy is presented that enables one to generate samples distributed according to these posterior distributions, leading to the minimum mean-square error (MMSE) estimator. A second approach consists in solving a constrained least-squares problem in which h = A g is constrained to be close to a scaled version of g ¯ . This second approach yields a closed-form solution, which amounts to a linear combination of g ¯ and the LS estimator. Numerical simulations show that the two new estimators significantly outperform the conventional LS estimator, especially at low SNR.

Multi-objective parameter estimation via minimal correlation criterion

The paper deals with the problem of parameter estimation using two different sources of information, namely a time series with dynamic data and steady-state data. The new estimator is based on a two-step procedure: first a multi-objective optimization is performed, leading to a set of Pareto-optimal vectors of parameter estimates and, second, a single model is chosen based on the free-run simulation error which is required to be minimally correlated with the model output. The procedure is general in nature and can be applied to any model representation, but for the sake of simplicity, the new procedure is illustrated using NARX polynomial models for which closed formulae for generating the Pareto-set are readily available. Monte Carlo simulation studies suggest that the new estimator, which does not assume any particular noise model, is fairly unbiased even when the conventional least-squares estimator is biased.

Training-based and semiblind channel estimation for MIMO systems with maximum ratio transmission

This paper is a comparative study of training-based and semiblind multiple-input multiple-output (MIMO) flat-fading channel estimation schemes when the transmitter employs maximum ratio transmission (MRT). We present two competing schemes for estimating the transmit and receive beamforming vectors of the channel matrix: a training-based conventional least-squares estimation (CLSE) scheme and a closed-form semiblind (CFSB) scheme that employs training followed by information-bearing spectrally white data symbols. Employing matrix perturbation theory, we develop expressions for the mean-square error (MSE) in the beamforming vector, the average received signal-to-noise ratio (SNR) and the symbol error rate (SER) performance of both the semiblind and the conventional schemes. Finally, we describe a weighted linear combiner of the CFSB and CLSE estimates for additional improvement in performance. The analytical results are verified through Monte Carlo simulations

Robust mean-squared error estimation in the presence of model uncertainties

We consider the problem of estimating an unknown parameter vector x in a linear model that may be subject to uncertainties, where the vector x is known to satisfy a weighted norm constraint. We first assume that the model is known exactly and seek the linear estimator that minimizes the worst-case mean-squared error (MSE) across all possible values of x. We show that for an arbitrary choice of weighting, the optimal minimax MSE estimator can be formulated as a solution to a semidefinite programming problem (SDP), which can be solved very efficiently. We then develop a closed form expression for the minimax MSE estimator for a broad class of weighting matrices and show that it coincides with the shrunken estimator of Mayer and Willke, with a specific choice of shrinkage factor that explicitly takes the prior information into account. Next, we consider the case in which the model matrix is subject to uncertainties and seek the robust linear estimator that minimizes the worst-case MSE across all possible values of x and all possible values of the model matrix. As we show, the robust minimax MSE estimator can also be formulated as a solution to an SDP. Finally, we demonstrate through several examples that the minimax MSE estimator can significantly increase the performance over the conventional least-squares estimator, and when the model matrix is subject to uncertainties, the robust minimax MSE estimator can lead to a considerable improvement in performance over the minimax MSE estimator.

Linear Minimax Regret Estimation of Deterministic Parameters with Bounded Data Uncertainties

We develop a new linear estimator for estimating an unknown parameter vector x in a linear model in the presence of bounded data uncertainties. The estimator is designed to minimize the worst-case regret over all bounded data vectors, namely, the worst-case difference between the mean-squared error (MSE) attainable using a linear estimator that does not know the true parameters x and the optimal MSE attained using a linear estimator that knows x. We demonstrate through several examples that the minimax regret estimator can significantly increase the performance over the conventional least-squares estimator, as well as several other least-squares alternatives.

An unbiased and computationally efficient LS estimation method for identifying parameters of 2D noncausal SAR models

An unbiased and computationally efficient modified least squares (LS) estimation method for identifying parameters of two-dimensional noncausal simultaneous autoregressive models is presented. Some intuitive and mathematical proof of the unbiasedness of the method are given, and a recursive in-order fast algorithm to implement it is introduced. Computer simulation results are given to sustain the theoretical analysis. Both the theoretical analysis and the computer simulation show that the method possesses much higher estimation accuracy and lower computational complexity than the conventional LS estimation method. Compared to the approximate maximum-likelihood method of Kashyap and Chellappa (1983), the scheme is much faster, has the same estimation accuracy, and is parallelizable. >