Kaushik Mahata

Direction-of-Arrival Estimation Using a Mixed

A set of vectors is called jointly sparse when its elements share a common sparsity pattern. We demonstrate how the direction-of-arrival (DOA) estimation problem can be cast as the problem of recovering a joint-sparse representation. We consider both narrowband and broadband scenarios. We propose to minimize a mixed ℓ2,0 norm approximation to deal with the joint-sparse recovery problem. Our algorithm can resolve closely spaced and highly correlated sources using a small number of noisy snapshots. Furthermore, the number of sources need not be known a priori. In addition, our algorithm can handle more sources than other state-of-the-art algorithms. For the broadband DOA estimation problem, our algorithm allows relaxing the half-wavelength spacing restriction, which leads to a significant improvement in the resolution limit.

\ell _{2,0}

The paper gives all overview of various methods for identifying dynamic errors-in-variables systems. Several approaches are classified by how the original information in time-series data of the noisy input and output measurements is condensed before further processing. For some methods, such as instrumental variable estimators, the information is condensed into a nonsymmetric covariance matrix as a first step before further processing. In a second class of methods, where a symmetric covariance matrix is used instead, the Frisch scheme and other bias-compensation approaches appear. When dealing with the estimation problem in the frequency domain, a milder data reduction typically takes place by first computing spectral estimators of the noisy input-output data. Finally, it is also possible to apply maximum likelihood and prediction error approaches using the original time-domain data in a direct fashion. This alternative will often require quite high computational complexity but yield good statistical efficiency. The paper is also presenting various properties of parameter estimators for the errors-in-variables problem, and a few conjectures are included, as well as some perspectives and experiences by the authors.

Norm Approximation

l0 norm based algorithms have numerous potential applications where a sparse signal is recovered from a small number of measurements. The direct l0 norm optimization problem is NP-hard. In this paper we work with the the smoothed l0(SL0) approximation algorithm for sparse representation. We give an upper bound on the run-time estimation error. This upper bound is tighter than the previously known bound. Subsequently, we develop a reliable stopping criterion. This criterion is helpful in avoiding the problems due to the underlying discontinuities of the l0 cost function. Furthermore, we propose an alternative optimization strategy, which results in a Newton like algorithm.

Perspectives on errors-in-variables estimation for dynamic systems

A novel direct approach for identifying continuous-time linear dynamic errors-in-variables models is presented in this paper. The effects of the noise on the state-variable filter outputs are analyzed. Subsequently, a few algorithms to obtain consistent continuous-time parameter estimates in the errors-in-variables framework are derived. It is also possible to design search-free algorithms within our framework. The algorithms can be used for non-uniformly sampled data. The asymptotic distributions of the estimates are derived. The performances of the proposed algorithms are illustrated with some numerical simulation examples.

An Improved Smoothed

We address the problem of finding a set of sparse signals that have nonzero coefficients in the same locations from a set of their compressed measurements. A mixed lscr2,0 norm optimization approach is considered. A cost function appropriate to the joint-sparse problem is developed, and an algorithm is derived. Compared to other convex relaxation based techniques, the results obtained by the proposed method show a clear improvement in both noiseless and noisy environments.

\ell^0

Many practical system identification problems can be formulated as linear regression problems. The parameter estimates can be computed using instrumental variables (IV) or total least squares (TLS) estimators, both of which have moderate computational complexity. In this work, explicit expressions for the asymptotic covariance matrix of the TLS estimates is derived and is shown to be same as that of the IV method. The accuracy of the parameter estimates for an errors-in-variables model using the above methods has been treated in particular, as standard analysis does not apply. The results obtained from the numerical simulations show that the practical behaviour of the estimators is well predicted by the theoretical results. We provide an explanation why for finite samples, the IV approach is found to be somewhat more robust than the TLS approach. On the other hand, the TLS approach has lower computational load than the IV method.

Approximation Algorithm for Sparse Representation

Parametric estimation of the dynamic errors-in-variables models is considered in this paper. In particular, a bias compensation approach is examined in a generalized framework. Sufficient conditions for uniqueness of the identified model are presented. Subsequently, a statistical accuracy analysis of the estimation algorithm is carried out. The asymptotic covariance matrix of the system parameter estimates depends on a user chosen filter and a certain weighting matrix. It is shown how these can be tuned to boost the estimation performance. The numerical simulation results suggest that the covariance matrix of the estimated parameter vector is very close to the Cramer-Rao lower bound for the estimation problem.

Identification of continuous-time errors-in-variables models

ℓ⁰ norm based signal recovery is attractive in compressed sensing as it can facilitate exact recovery of sparse signal with very high probability. Unfortunately, direct ℓ⁰ norm minimization problem is NP-hard. This paper describes an approximate ℓ⁰ norm algorithm for sparse representation which preserves most of the advantages of ℓ⁰ norm. The algorithm shows attractive convergence properties, and provides remarkable performance improvement in noisy environment compared to other popular algorithms. The sparse representation algorithm presented is capable of very fast signal recovery, thereby reducing retrieval latency when handling

A Robust Algorithm for Joint-Sparse Recovery

Subspace-based estimation of multiple real-valued sine wave frequencies is considered in this paper. A novel data covariance model is proposed. In the proposed model, the dimension of the signal subspace equals the number of frequencies present in the data, which is half of the signal subspace dimension for the conventional model. Consequently, an ESPRIT-like algorithm using the proposed data model is presented. The proposed algorithm is then extended for the case of complex-valued sine waves. Performance analysis of the proposed algorithms are also carried out. The algorithms are tested in numerical simulations. When compared with ESPRIT, the newly proposed algorithm results in a significant reduction in computational burden without any compromise in the accuracy.

On instrumental variable and total least squares approaches for identification of noisy systems

In this paper we propose a parametric and a non-parametric identification algorithm for dynamic errors-in-variables model. We show that the two-dimensional process composed of the input-output data admits a finite order ARMA representation. The non-parametric method uses the ARMA structure to compute a consistent estimate of the joint spectrum of the input and the output. A Frisch scheme is then employed to extract an estimate of the joint spectrum of the noise free input-output data, which in turn is used to estimate the transfer function of the system. The parametric method exploits the ARMA structure to give estimates of the system parameters. The performances of the algorithms are illustrated using the results obtained from a numerical simulation study.