Kalman filtered Compressed Sensing

Vaswani, Namrata

doi:10.1109/icip.2008.4711899

Cited by 265 publications

(286 citation statements)

References 10 publications

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“…A sparsity-aware recursive estimator of un-modeled signal variations is developed in [2]. Relative to [2] and [10], the novelty of the present paper is a sparsity-aware fixed-interval smoother.…”

Section: Introductionmentioning

confidence: 99%

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Lasso-Kalman smoother for tracking sparse signals

Angelosante

Roumeliotis

Giannakis

2009

2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers

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Abstract-Fixed-interval smoothing of time-varying vector processes is an estimation approach with well-documented merits for tracking applications. The optimal performance in the linear Gauss-Markov model is achieved by the Kalman smoother (KS), which also admits an efficient recursive implementation. The present paper deals with vector processes for which it is known a priori that many of their entries equal to zero. In this context, the process to be tracked is sparse, and the performance of sparsityagnostic KS schemes degrades considerably. On the other hand, it is shown here that a sparsity-aware KS exhibits complexity which grows exponentially in the vector dimension. To obtain a tractable alternative, the KS cost is regularized with the sparsity-promoting ℓ1 norm of the vector process -a relaxation also used in linear regression problems to obtain the leastabsolute shrinkage and selection operator (Lasso). The Lasso (L)KS derived in this work is not only capable of tracking sparse time-varying vector processes, but can also afford an efficient recursive implementation based on the alternating direction method of multipliers (ADMoM). Finally, a weighted (W)-LKS is also introduced to cope with the bias of the LKS, and simulations are provided to validate the performance of the novel algorithms.

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Section: Introductionmentioning

confidence: 99%

“…Exploiting sparsity to track time-varying signals has been considered in [10], where a sparsity-aware Kalman filter is proposed to track abrupt changes in the support of dynamic magnetic resonance imaging (MRI) signals. A sparsity-aware recursive estimator of un-modeled signal variations is developed in [2].…”

Section: Introductionmentioning

confidence: 99%

Lasso-Kalman smoother for tracking sparse signals

Angelosante

Roumeliotis

Giannakis

2009

2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers

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“…One algorithm is to incorporate Kalman signal evolution model to compressive sensing framework [10]. By utilizing the known signal evolution model as a prior, the algorithm improves the performance of DOA estimation.…”

Section: Introductionmentioning

confidence: 99%

“…There are also some DOA estimation algorithms in compressive sensing framework to deal with DOA dynamic changing [10,11].…”

Section: Introductionmentioning

confidence: 99%

HIGH-DYNAMIC DOA ESTIMATION BASED ON WEIGHTED L<sub>1</sub> MINIMIZATION

Wang¹,

Wu²

2013

PIER C

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Abstract-In high dynamic environment, due to the rapid relative movement between receiver and transmitter, the DOA (Direction of Arrival) of signals will change even between two consecutive snapshots. Thus, covariance-based DOA estimation algorithms are ineffective. Compressive sensing algorithms, as a kind of novel DOA estimation algorithms, are still effective with only one snapshot. At the same time, it is noted that the DOA changing is limited by relative moving speed and distance between receiver and transmitter. In this paper, a DOA tracking algorithm based on weighted L 1 minimization is proposed which utilizing the DOA changing scope between two consecutive snapshots as a prior to improve the tracking performance. Different from other multiple snapshots compressive sensing algorithms which assumed fixed DOA among multiple consecutive snapshots, the proposed algorithm takes into account the DOA changing among different snapshots. The simulation results demonstrate the advantages of the proposed algorithm.

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“…A greedy RLS algorithm designed for finding sparse solutions to linear systems has been presented in [20], and it has been demonstrated that it has better performance than the standard RLS algorithm for estimating sparse time-varying FIR channels. A compressed sensing (CS)-based Kalman filter has been developed in [21] for estimating signals with time varying sparsity pattern. 1 In this paper, we first derive the reweighted l 1 -norm penalized LMS algorithm which is based on modifying the LMS error (objective) function by adding the l 1 -norm penalty term and also introducing a reweighting of the CIR coefficients.…”

Section: Introductionmentioning

confidence: 99%

Reweighted l1-norm penalized LMS for sparse channel estimation and its analysis

Taheri

Vorobyov

2014

Signal Processing

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A new reweighted l 1 -norm penalized least mean square (LMS) algorithm for sparse channel estimation is proposed and studied in this paper. Since standard LMS algorithm does not take into account the sparsity information about the channel impulse response (CIR), sparsity-aware modifications of the LMS algorithm aim at outperforming the standard LMS by introducing a penalty term to the standard LMS cost function which forces the solution to be sparse. Our reweighted l 1 -norm penalized LMS algorithm introduces in addition a reweighting of the CIR coefficient estimates to promote a sparse solution even more and approximate l 0 -pseudo-norm closer. We provide in depth quantitative analysis of the reweighted l 1 -norm penalized LMS algorithm. An expression for the excess mean square error (MSE) of the algorithm is also derived which suggests that under the right conditions, the reweighted l 1 -norm penalized LMS algorithm outperforms the standard LMS, which is expected. However, our quantitative analysis also answers the question of what is the maximum sparsity level in the channel for which the reweighted l 1 -norm penalized LMS algorithm is better than the standard LMS. Simulation results showing the better performance of the reweighted l 1 -norm penalized LMS algorithm compared to other existing LMS-type algorithms are given.

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Kalman filtered Compressed Sensing

Cited by 265 publications

References 10 publications

Lasso-Kalman smoother for tracking sparse signals

Lasso-Kalman smoother for tracking sparse signals

HIGH-DYNAMIC DOA ESTIMATION BASED ON WEIGHTED L<sub>1</sub> MINIMIZATION

Reweighted l1-norm penalized LMS for sparse channel estimation and its analysis

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