OMP-type Algorithm with Structured Sparsity Patterns for Multipath Radar Signals

A transmitted, unknown radar signal is observed at the receiver through more than one path in additive noise. The aim is to recover the waveform of the intercepted signal and to simultaneously estimate the direction of arrival (DOA). We propose an approach exploiting the parsimonious time-frequency representation of the signal by applying a new OMP-type algorithm for structured sparsity patterns. An important issue is the scalability of the proposed algorithm since high-dimensional models shall be used for radar signals. Monte-Carlo simulations for modulated signals illustrate the good performance of the method even for low signal-to-noise ratios and a gain of 20 dB for the DOA estimation compared to some elementary method

Cram\'er-Rao Bounds for Polynomial Signal Estimation using Sensors with AR(1) Drift

We seek to characterize the estimation performance of a sensor network where the individual sensors exhibit the phenomenon of drift, i.e., a gradual change of the bias. Though estimation in the presence of random errors has been extensively studied in the literature, the loss of estimation performance due to systematic errors like drift have rarely been looked into. In this paper, we derive closed-form Fisher Information matrix and subsequently Cram\'er-Rao bounds (upto reasonable approximation) for the estimation accuracy of drift-corrupted signals. We assume a polynomial time-series as the representative signal and an autoregressive process model for the drift. When the Markov parameter for drift \rho<1, we show that the first-order effect of drift is asymptotically equivalent to scaling the measurement noise by an appropriate factor. For \rho=1, i.e., when the drift is non-stationary, we show that the constant part of a signal can only be estimated inconsistently (non-zero asymptotic variance). Practical usage of the results are demonstrated through the analysis of 1) networks with multiple sensors and 2) bandwidth limited networks communicating only quantized observations.Comment: 14 pages, 6 figures, This paper will appear in the Oct/Nov 2012 issue of IEEE Transactions on Signal Processin

Spatial Whitening Framework for Distributed Estimation

Designing resource allocation strategies for power constrained sensor network in the presence of correlated data often gives rise to intractable problem formulations. In such situations, applying well-known strategies derived from conditional-independence assumption may turn out to be fairly suboptimal. In this paper, we address this issue by proposing an adjacency-based spatial whitening scheme, where each sensor exchanges its observation with their neighbors prior to encoding their own private information and transmitting it to the fusion center. We comment on the computational limitations for obtaining the optimal whitening transformation, and propose an iterative optimization scheme to achieve the same for large networks. We demonstrate the efficacy of the whitening framework by considering the example of bit-allocation for distributed estimation.Comment: 4 pages, 2 figures, this paper has been presented at CAMSAP 2011; Proc. 4th Intl. Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2011), San Juan, Puerto Rico, Dec 13-16, 201

Parameter Estimation from Time-Series Data with Correlated Errors: A Wavelet-Based Method and its Application to Transit Light Curves

We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has a power spectral density varying as $1/f^\gamma$. We present an accurate and fast [O(N)] algorithm for parameter estimation based on computing the likelihood in a wavelet basis. The method is illustrated and tested using simulated time-series photometry of exoplanetary transits, with particular attention to estimating the midtransit time. We compare our method to two other methods that have been used in the literature, the time-averaging method and the residual-permutation method. For noise processes that obey our assumptions, the algorithm presented here gives more accurate results for midtransit times and truer estimates of their uncertainties.Comment: Accepted in ApJ. Illustrative code may be found at http://www.mit.edu/~carterja/code/ . 17 page

Foreground component separation with generalised ILC

The 'Internal Linear Combination' (ILC) component separation method has been extensively used to extract a single component, the CMB, from the WMAP multifrequency data. We generalise the ILC approach for separating other millimetre astrophysical emissions. We construct in particular a multidimensional ILC filter, which can be used, for instance, to estimate the diffuse emission of a complex component originating from multiple correlated emissions, such as the total emission of the Galactic interstellar medium. The performance of such generalised ILC methods, implemented on a needlet frame, is tested on simulations of Planck mission observations, for which we successfully reconstruct a low noise estimate of emission from astrophysical foregrounds with vanishing CMB and SZ contamination.Comment: 11 pages, 6 figures (2 figures added), 1 reference added, introduction expanded, V2: version accepted by MNRA

On Distributed Linear Estimation With Observation Model Uncertainties

We consider distributed estimation of a Gaussian source in a heterogenous bandwidth constrained sensor network, where the source is corrupted by independent multiplicative and additive observation noises, with incomplete statistical knowledge of the multiplicative noise. For multi-bit quantizers, we derive the closed-form mean-square-error (MSE) expression for the linear minimum MSE (LMMSE) estimator at the FC. For both error-free and erroneous communication channels, we propose several rate allocation methods named as longest root to leaf path, greedy and integer relaxation to (i) minimize the MSE given a network bandwidth constraint, and (ii) minimize the required network bandwidth given a target MSE. We also derive the Bayesian Cramer-Rao lower bound (CRLB) and compare the MSE performance of our proposed methods against the CRLB. Our results corroborate that, for low power multiplicative observation noises and adequate network bandwidth, the gaps between the MSE of our proposed methods and the CRLB are negligible, while the performance of other methods like individual rate allocation and uniform is not satisfactory