Compressed matched filter for non-Gaussian noise

We consider estimation of a deterministic unknown parameter vector in a linear model with non-Gaussian noise. In the Gaussian case, dimensionality reduction via a linear matched filter provides a simple low dimensional sufficient statistic which can be easily communicated and/or stored for future inference. Such a statistic is usually unknown in the general non-Gaussian case. Instead, we propose a hybrid matched filter coupled with a randomized compressed sensing procedure, which together create a low dimensional statistic. We also derive a complementary algorithm for robust reconstruction given this statistic. Our recovery method is based on the fast iterative shrinkage and thresholding algorithm which is used for outlier rejection given the compressed data. We demonstrate the advantages of the proposed framework using synthetic simulations

Finite sample performance of linear least squares estimators under sub-Gaussian martingale difference noise

Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required. Surprisingly, bounding the probability of large errors with finitely many samples has been left open, especially when dealing with correlated noise with unknown covariance. In this paper we analyze the finite sample performance of the linear least squares estimator under sub-Gaussian martingale difference noise. In order to analyze this important question we used concentration of measure bounds. When applying these bounds we obtained tight bounds on the tail of the estimator's distribution. We show the fast exponential convergence of the number of samples required to ensure a given accuracy with high probability. We provide probability tail bounds on the estimation error's norm. Our analysis method is simple and uses simple $L_{\infty}$ type bounds on the estimation error. The tightness of the bounds is tested through simulation. The proposed bounds make it possible to predict the number of samples required for least squares estimation even when least squares is sub-optimal and used for computational simplicity. The finite sample analysis of least squares models with this general noise model is novel

Error-constrained filtering for a class of nonlinear time-varying delay systems with non-gaussian noises

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this technical note, the quadratic error-constrained filtering problem is formulated and investigated for discrete time-varying nonlinear systems with state delays and non-Gaussian noises. Both the Lipschitz-like and ellipsoid-bounded nonlinearities are considered. The non-Gaussian noises are assumed to be unknown, bounded, and confined to specified ellipsoidal sets. The aim of the addressed filtering problem is to develop a recursive algorithm based on the semi-definite programme method such that, for the admissible time-delays, nonlinear parameters and external bounded noise disturbances, the quadratic estimation error is not more than a certain optimized upper bound at every time step. The filter parameters are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programme method. A simulation example is exploited to illustrate the effectiveness of the proposed design procedures.This work was supported in part by the Leverhulme Trust of the U.K., the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National Natural Science Foundation of China under Grant 61028008 and Grant 61074016, the Shanghai Natural Science Foundation of China under Grant 10ZR1421200, and the Alexander von Humboldt Foundation of Germany. Recommended by Associate Editor E. Fabre

An optimisation approach to robust estimation of mulitcomponent polynomial phase signals in non-Gaussian noise

In this paper, we address the problem of estimating the parameters of multicomponent polynomial phase signals in impulsive noise which arises in many practical situations. In the presence of this non-standard noise, existing techniques perform can poorly. We propose a nonlinear M-estimation approach to improve the existing techniques. The phase parameters are obtained by solving a nonlinear optimisation problem. A procedure is proposed to find the global minimum at low computational cost. Simulation examples show the proposed method performs better than existing method

A new robust Kalman filter-based subspace tracking algorithm in an impulsive noise environment

The conventional projection approximation subspace tracking (PAST) algorithm is based on the recursive least-squares algorithm, and its performance will degrade considerably when the subspace rapidly changes and the additive noise is impulsive. This brief proposes a new robust Kalman filter-based subspace tracking algorithm to overcome these two limitations of the PAST algorithm. It is based on a new extension of the adaptive Kalman filter with variable number of measurements (KFVNM) for tracking fast-varying subspace. Furthermore, M-estimation is incorporated into this KFVNM algorithm to combat the adverse effects of impulsive noise. Simulation results show that the robust KFVNM-based subspace tracking algorithm has a better performance than the PAST algorithm for tracking fast-varying subspace and in an impulsive noise environment. © 2010 IEEE.published_or_final_versio

A nonlinear M-estimation approach to robust asynchronous multiuser detection in Non-gaussian noise

A nonlinear M-estimation approach is proposed to solve the multiuser detection problem in asynchronous code-division multiple-access (CDMA) systems where the ambient noise is impulsive and the delays are not known. We treat the unknown delays as nuisance parameters and the transmitted symbols as parameters of interest. We also analyze the asymptotic performance of the proposed estimator and propose suboptimal but computationally efficient procedures for solving the nonlinear optimization function. Simulation results show considerable improvements over the conventional approaches