An Examination of Some Signi cant Approaches to Statistical Deconvolution

We examine statistical approaches to two significant areas of deconvolution - Blind Deconvolution (BD) and Robust Deconvolution (RD) for stochastic stationary signals. For BD, we review some major classical and new methods in a unified framework of nonGaussian signals. The first class of algorithms we look at falls into the class of Minimum Entropy Deconvolution (MED) algorithms. We discuss the similarities between them despite differences in origins and motivations. We give new theoretical results concerning the behaviour and generality of these algorithms and give evidence of scenarios where they may fail. In some cases, we present new modifications to the algorithms to overcome these shortfalls. Following our discussion on the MED algorithms, we next look at a recently proposed BD algorithm based on the correntropy function, a function defined as a combination of the autocorrelation and the entropy functiosn. We examine its BD performance when compared with MED algorithms. We find that the BD carried out via correntropy-matching cannot be straightforwardly interpreted as simultaneous moment-matching due to the breakdown of the correntropy expansion in terms of moments. Other issues such as maximum/minimum phase ambiguity and computational complexity suggest that careful attention is required before establishing the correntropy algorithm as a superior alternative to the existing BD techniques. For the problem of RD, we give a categorisation of different kinds of uncertainties encountered in estimation and discuss techniques required to solve each individual case. Primarily, we tackle the overlooked cases of robustification of deconvolution filters based on estimated blurring response or estimated signal spectrum. We do this by utilising existing methods derived from criteria such as minimax MSE with imposed uncertainty bands and penalised MSE. In particular, we revisit the Modified Wiener Filter (MWF) which offers simplicity and flexibility in giving improved RDs to the standard plug-in Wiener Filter (WF)

Generalized Multi-kernel Maximum Correntropy Kalman Filter for Disturbance Estimation

Disturbance observers have been attracting continuing research efforts and are widely used in many applications. Among them, the Kalman filter-based disturbance observer is an attractive one since it estimates both the state and the disturbance simultaneously, and is optimal for a linear system with Gaussian noises. Unfortunately, The noise in the disturbance channel typically exhibits a heavy-tailed distribution because the nominal disturbance dynamics usually do not align with the practical ones. To handle this issue, we propose a generalized multi-kernel maximum correntropy Kalman filter for disturbance estimation, which is less conservative by adopting different kernel bandwidths for different channels and exhibits excellent performance both with and without external disturbance. The convergence of the fixed point iteration and the complexity of the proposed algorithm are given. Simulations on a robotic manipulator reveal that the proposed algorithm is very efficient in disturbance estimation with moderate algorithm complexity.Comment: in IEEE Transactions on Automatic Control (2023

Testing adaptive market efficiency in the presence of non-Gaussian uncertainties

One of the central debates in finance concerns the Efficient Market Hypothesis (EMH)—wherein markets are assumed to be efficient in the absolute sense. However, the possibility of time-varying weak-form market efficiency has received increasing attention in recent years. Under the Adaptive Market Hypothesis (AMH) it is postulated that market efficiency is dynamic, which advocates using models with non-constant coefficients. The concept of evolving efficiency has yielded a Test for Evolving Efficiency (TEE) and following that, a Generalised Test for Evolving Efficiency (GTEE) – both with an associated Kalman filtering (KF) technique. Unfortunately, these methods assume that the inherent stochastic processes are Gaussian despite widespread evidence that many real financial time series are nonGaussian. Unlike the classical KF, modern filters such as the maximum correntropy Kalman filters (MCC-KF) have been shown to be less sensitive to non-Gaussian uncertainties. These filters utilise a similarity measure known as correntropy– which incorporates higher order information than the mean square criterion that is utilised in the classical KF. As a result, they have been shown to improve filter robustness against outliers or impulsive noises. In this paper, the South African and American stock markets are tested for adaptive market efficiency using both the standard KF and the MCC-KF. A simulation study shows that the MCC-KF is a more robust estimator of adaptive efficiency but it less accurately estimates unknown system parameters. The South African stock market is found to be inefficient prior to August 2004 but achieves efficiency thereafter. Testing the S&P500 does not provide evidence of inefficiency in the American stock markets. The GTEE, implemented with the MCC-KF, is selected as the bestperforming test for the S&P500

Investigation of the performance of multi-input multi-output detectors based on deep learning in non-Gaussian environments

The next generation of wireless cellular communication networks must be energy efficient, extremely reliable, and have low latency, leading to the necessity of using algorithms based on deep neural networks (DNN) which have better bit error rate (BER) or symbol error rate (SER) performance than traditional complex multi-antenna or multi-input multi-output (MIMO) detectors. This paper examines deep neural networks and deep iterative detectors such as OAMP-Net based on information theory criteria such as maximum correntropy criterion (MCC) for the implementation of MIMO detectors in non-Gaussian environments, and the results illustrate that the proposed method has better BER or SER performance

Robust Sensor Fusion for Indoor Wireless Localization

Location knowledge in indoor environment using Indoor Positioning Systems (IPS) has become very useful and popular in recent years. Indoor wireless localization suffers from severe multi-path fading and non-line-of-sight conditions. This paper presents a novel indoor localization framework based on sensor fusion of Zigbee Wireless Sensor Networks (WSN) using Received Signal Strength (RSS). The unknown position is equipped with two or more mobile nodes. The range between two mobile nodes is fixed as priori. The attitude (roll, pitch, and yaw) of the mobile node are measured by inertial sensors (ISs). Then the angle and the range between any two nodes can be obtained, and thus the path between the two nodes can be modeled as a curve. Through an efficient cooperation between two or more mobile nodes, this framework effectively exploits the RSS techniques. This constraint help improve the positioning accuracy. Theoretical analysis on localization distortion and Monte Carlo simulations shows that the proposed cooperative strategy of multiple nodes with extended Kalman filter (EKF) achieves significantly higher positioning accuracy than the existing systems, especially in heavily obstructed scenarios