Analysis of incremental augmented affine projection algorithm for distributed estimation of complex-valued signals

This paper considers the problem of distributed estimation in an incremental network when the measurements taken by the node follow a widely linear model. The proposed algorithm which we refer to it as incremental augmented affine projection algorithm (incAAPA) utilizes the full second order statistical information in the complex domain. Moreover, it exploits spatio-temporal diversity to improve the estimation performance. We derive steady-state performance metric of the incAAPA in terms of the mean-square deviation (MSD). We further derive sufficient conditions to ensure mean-square convergence. Our analysis illustrate that the proposed algorithm is able to process both second order circular (proper) and noncircular (improper) signals. The validity of the theoretical results and the good performance of the proposed algorithm are demonstrated by several computer simulations

Distributed Affine Projection Algorithm Over Acoustically Coupled Sensor Networks

[EN] In this paper, we present a distributed affine projection (AP) algorithm for an acoustic sensor network where the nodes are acoustically coupled. Every acoustic node is composed of a microphone, a processor, and an actuator to control the sound field. This type of networks can use distributed adaptive algorithms to deal with the active noise control (ANC) problem in a cooperative manner, providing more flexible and scalable ANC systems. In this regard, we introduce here a distributed version of the multichannel filtered-x AP algorithm over an acoustic sensor network that it is called distributed filtered-x AP (DFxAP) algorithm. The analysis of the mean and the mean-square deviation performance of the algorithm at each node is given for a network with a ring topology and without constraints in the communication layer. The theoretical results are validated through several simulations. Moreover, simulations show that the proposed DFxAP outperforms the previously reported distributed multiple error filtered-x least mean square algorithm.This work was supported in part by EU together with Spanish Government under Grant TEC2015-67387-C4-1-R (MINECO/FEDER), and in part by Generalitat Valenciana under PROMETEOII/2014/003.Ferrer Contreras, M.; Gonzalez, A.; Diego Antón, MD.; Piñero, G. (2017). Distributed Affine Projection Algorithm Over Acoustically Coupled Sensor Networks. IEEE Transactions on Signal Processing. 65(24):6423-6434. https://doi.org/10.1109/TSP.2017.2742987S64236434652

Autocalibration with the Minimum Number of Cameras with Known Pixel Shape

In 3D reconstruction, the recovery of the calibration parameters of the cameras is paramount since it provides metric information about the observed scene, e.g., measures of angles and ratios of distances. Autocalibration enables the estimation of the camera parameters without using a calibration device, but by enforcing simple constraints on the camera parameters. In the absence of information about the internal camera parameters such as the focal length and the principal point, the knowledge of the camera pixel shape is usually the only available constraint. Given a projective reconstruction of a rigid scene, we address the problem of the autocalibration of a minimal set of cameras with known pixel shape and otherwise arbitrarily varying intrinsic and extrinsic parameters. We propose an algorithm that only requires 5 cameras (the theoretical minimum), thus halving the number of cameras required by previous algorithms based on the same constraint. To this purpose, we introduce as our basic geometric tool the six-line conic variety (SLCV), consisting in the set of planes intersecting six given lines of 3D space in points of a conic. We show that the set of solutions of the Euclidean upgrading problem for three cameras with known pixel shape can be parameterized in a computationally efficient way. This parameterization is then used to solve autocalibration from five or more cameras, reducing the three-dimensional search space to a two-dimensional one. We provide experiments with real images showing the good performance of the technique.Comment: 19 pages, 14 figures, 7 tables, J. Math. Imaging Vi

An affine combination of two LMS adaptive filters - Transient mean-square analysis

This paper studies the statistical behavior of an affine combination of the outputs of two LMS adaptive filters that simultaneously adapt using the same white Gaussian inputs. The purpose of the combination is to obtain an LMS adaptive filter with fast convergence and small steady-state mean-square deviation (MSD). The linear combination studied is a generalization of the convex combination, in which the combination factor $\lambda(n)$ is restricted to the interval $(0,1)$. The viewpoint is taken that each of the two filters produces dependent estimates of the unknown channel. Thus, there exists a sequence of optimal affine combining coefficients which minimizes the MSE. First, the optimal unrealizable affine combiner is studied and provides the best possible performance for this class. Then two new schemes are proposed for practical applications. The mean-square performances are analyzed and validated by Monte Carlo simulations. With proper design, the two practical schemes yield an overall MSD that is usually less than the MSD's of either filter

A stochastic behavior analysis of stochastic restricted-gradient descent algorithm in reproducing kernel Hilbert spaces

This paper presents a stochastic behavior analysis of a kernel-based stochastic restricted-gradient descent method. The restricted gradient gives a steepest ascent direction within the so-called dictionary subspace. The analysis provides the transient and steady state performance in the mean squared error criterion. It also includes stability conditions in the mean and mean-square sense. The present study is based on the analysis of the kernel normalized least mean square (KNLMS) algorithm initially proposed by Chen et al. Simulation results validate the analysis

Stochastic analysis of an error power ratio scheme applied to the affine combination of two LMS adaptive filters

The affine combination of two adaptive filters that simultaneously adapt on the same inputs has been actively investigated. In these structures, the filter outputs are linearly combined to yield a performance that is better than that of either filter. Various decision rules can be used to determine the time-varying parameter for combining the filter outputs. A recently proposed scheme based on the ratio of error powers of the two filters has been shown by simulation to achieve nearly optimum performance. The purpose of this paper is to present a first analysis of the statistical behavior of this error power scheme for white Gaussian inputs. Expressions are derived for the mean behavior of the combination parameter and for the adaptive weight mean-square deviation. Monte Carlo simulations show good to excellent agreement with the theoretical predictions