2,741 research outputs found
Optimal State Estimation with Measurements Corrupted by Laplace Noise
Optimal state estimation for linear discrete-time systems is considered.
Motivated by the literature on differential privacy, the measurements are
assumed to be corrupted by Laplace noise. The optimal least mean square error
estimate of the state is approximated using a randomized method. The method
relies on that the Laplace noise can be rewritten as Gaussian noise scaled by
Rayleigh random variable. The probability of the event that the distance
between the approximation and the best estimate is smaller than a constant is
determined as function of the number of parallel Kalman filters that is used in
the randomized method. This estimator is then compared with the optimal linear
estimator, the maximum a posteriori (MAP) estimate of the state, and the
particle filter
Off-grid Direction of Arrival Estimation Using Sparse Bayesian Inference
Direction of arrival (DOA) estimation is a classical problem in signal
processing with many practical applications. Its research has recently been
advanced owing to the development of methods based on sparse signal
reconstruction. While these methods have shown advantages over conventional
ones, there are still difficulties in practical situations where true DOAs are
not on the discretized sampling grid. To deal with such an off-grid DOA
estimation problem, this paper studies an off-grid model that takes into
account effects of the off-grid DOAs and has a smaller modeling error. An
iterative algorithm is developed based on the off-grid model from a Bayesian
perspective while joint sparsity among different snapshots is exploited by
assuming a Laplace prior for signals at all snapshots. The new approach applies
to both single snapshot and multi-snapshot cases. Numerical simulations show
that the proposed algorithm has improved accuracy in terms of mean squared
estimation error. The algorithm can maintain high estimation accuracy even
under a very coarse sampling grid.Comment: To appear in the IEEE Trans. Signal Processing. This is a revised,
shortened version of version
Outlier robust system identification: a Bayesian kernel-based approach
In this paper, we propose an outlier-robust regularized kernel-based method
for linear system identification. The unknown impulse response is modeled as a
zero-mean Gaussian process whose covariance (kernel) is given by the recently
proposed stable spline kernel, which encodes information on regularity and
exponential stability. To build robustness to outliers, we model the
measurement noise as realizations of independent Laplacian random variables.
The identification problem is cast in a Bayesian framework, and solved by a new
Markov Chain Monte Carlo (MCMC) scheme. In particular, exploiting the
representation of the Laplacian random variables as scale mixtures of
Gaussians, we design a Gibbs sampler which quickly converges to the target
distribution. Numerical simulations show a substantial improvement in the
accuracy of the estimates over state-of-the-art kernel-based methods.Comment: 5 figure
Recovery from Linear Measurements with Complexity-Matching Universal Signal Estimation
We study the compressed sensing (CS) signal estimation problem where an input
signal is measured via a linear matrix multiplication under additive noise.
While this setup usually assumes sparsity or compressibility in the input
signal during recovery, the signal structure that can be leveraged is often not
known a priori. In this paper, we consider universal CS recovery, where the
statistics of a stationary ergodic signal source are estimated simultaneously
with the signal itself. Inspired by Kolmogorov complexity and minimum
description length, we focus on a maximum a posteriori (MAP) estimation
framework that leverages universal priors to match the complexity of the
source. Our framework can also be applied to general linear inverse problems
where more measurements than in CS might be needed. We provide theoretical
results that support the algorithmic feasibility of universal MAP estimation
using a Markov chain Monte Carlo implementation, which is computationally
challenging. We incorporate some techniques to accelerate the algorithm while
providing comparable and in many cases better reconstruction quality than
existing algorithms. Experimental results show the promise of universality in
CS, particularly for low-complexity sources that do not exhibit standard
sparsity or compressibility.Comment: 29 pages, 8 figure
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