Dave Zachariah

Weighted SPICE: A unifying approach for hyperparameter-free sparse estimation☆

Abstract In this paper we present the SPICE approach for sparse parameter estimation in a framework that unifies it with other hyperparameter-free methods, namely LIKES, SLIM and IAA. 1 Specifically, we show how the latter methods can be interpreted as variants of an adaptively reweighted SPICE method. Furthermore, we establish a connection between SPICE and the l 1 -penalized LAD estimator as well as the square-root LASSO method. We evaluate the four methods mentioned above in a generic sparse regression problem and in an array processing application.

Cooperative Decentralized Localization Using Scheduled Wireless Transmissions

In this letter we develop a solution for decentralized localization of transceiving nodes in wireless networks. By exploiting a common transmission schedule, this is achieved without any additional communication and dispels the need for synchronized nodes. We derive the Cramer-Rao bounds for the solution and formulate two practical estimators for localization. Finally, the solution and estimators are tested in numerical experiments.

Joint Ranging and Clock Parameter Estimation by Wireless Round Trip Time Measurements

In this paper, we develop a new technique for estimating fine clock errors and range between two nodes simultaneously by two-way time-of-arrival measurements using impulse-radio ultrawideband signals. Estimators for clock parameters and the range are proposed, which are robust with respect to outliers. They are analyzed numerically and by means of experimental measurement campaigns. The technique and derived estimators achieve accuracies below 1 Hz for frequency estimation, below 1 ns for phase estimation, and 20 cm for range estimation, at a 4-m distance using 100-MHz clocks at both nodes. Therefore, we show that the proposed joint approach is practical and can simultaneously provide clock synchronization and positioning in an experimental system.

Schedule-based sequential localization in asynchronous wireless networks

In this paper, we consider the schedule-based network localization concept, which does not require synchronization among nodes and does not involve communication overhead. The concept makes use of a common transmission sequence, which enables each node to perform self-localization and to localize the entire network, based on noisy propagation-time measurements. We formulate the schedule-based localization problem as an estimation problem in a Bayesian framework. This provides robustness with respect to uncertainty in such system parameters as anchor locations and timing devices. Moreover, we derive a sequential approximate maximum a posteriori (AMAP) estimator. The estimator is fully decentralized and copes with varying noise levels. By studying the fundamental constraints given by the considered measurement model, we provide a system design methodology which enables a scalable solution. Finally, we evaluate the performance of the proposed AMAP estimator by numerical simulations emulating an impulse-radio ultra-wideband (IR-UWB) wireless network.

Online Hyperparameter-Free Sparse Estimation Method

In this paper, we derive an online estimator for sparse parameter vectors which, unlike the LASSO approach, does not require the tuning of any hyperparameters. The algorithm is based on a covariance matching approach and is equivalent to a weighted version of the square-root LASSO. The computational complexity of the estimator is of the same order as that of the online versions of regularized least-squares (RLS) and LASSO. We provide a numerical comparison with feasible and infeasible implementations of the LASSO and RLS to illustrate the advantage of the proposed online hyperparameter-free estimator.

Self-Localization of Asynchronous Wireless Nodes With Parameter Uncertainties

We investigate a wireless network localization scenario in which the need for synchronized nodes is avoided. It consists of a set of fixed anchor nodes transmitting according to a given sequence and a self-localizing receiver node. The setup can accommodate additional nodes with unknown positions participating in the sequence. We propose a localization method which is robust with respect to uncertainty of the anchor positions and other system parameters. Further, we investigate the Cramér-Rao bound for the considered problem and show through numerical simulations that the proposed method attains the bound.

A multicomponent T2 relaxometry algorithm for myelin water imaging of the brain

Models based on a sum of damped exponentials occur in many applications, particularly in multicomponent T2 relaxometry. The problem of estimating the relaxation parameters and the corresponding amplitudes is known to be difficult, especially as the number of components increases. In this article, the commonly used non‐negative least squares spectrum approach is compared to a recently published estimation algorithm abbreviated as Exponential Analysis via System Identification using Steiglitz–McBride.

Minimum sidelobe beampattern design for MIMO radar systems: A robust approach

In this paper, we propose a robust transmit beampattern design for multiple-input multiple-output (MIMO) radar systems. The objective considered here is minimization of the beampattern sidelobes, subject to constraints on the transmit power where the waveform co-variance matrix is the optimization variable. Motivated by the fact that the steering vectors are subject to uncertainties in practice, we propose a worst-case robust beampattern design where the uncertainties are parameterized by a deterministic set. We show that the resulting non-convex maximin problem can be translated into a convex problem. We numerically illustrate that the steering vector uncertainty yields a severe degradation in the array performance, i.e., the transmit beampattern. Also, we show that the proposed robust design improves the transmit beampattern by reducing the worst case sidelobe peak levels.

Scalable and Passive Wireless Network Clock Synchronization in LOS Environments

Clock synchronization is ubiquitous in wireless systems for communication, sensing, and control. In this paper, we design a scalable system in which an indefinite number of passively receiving wireless units can synchronize to a single master clock at the level of discrete clock ticks. Accurate synchronization requires an estimate of the node positions to compensate the time-of-flight transmission delay in line-of-sight environments. If such information is available, the framework developed here takes position uncertainties into account. In the absence of such information, as in indoor scenarios, we propose an auxiliary localization mechanism. Furthermore, we derive the Cramer–Rao bounds for the system, which show that it enables synchronization accuracy at sub-nanosecond levels. Finally, we develop and evaluate an online estimation method, which is statistically efficient.

Recursive Identification Method for Piecewise ARX Models: A Sparse Estimation Approach

This paper deals with the identification of nonlinear systems using piecewise linear models. By means of a sparse over-parameterization, this challenging problem is turned into a convex optimization problem. The proposed method uses a likelihood-based methodology which adaptively penalizes model complexity and directly leads to a recursive implementation. In this sparse estimation approach, the tuning of user parameters is avoided, and the computational complexity is kept linear in the number of data samples. Numerical examples with both simulated and experimental data are presented and the results are compared with previously published methods.