Combinations of adaptive filters

Adaptive filters are at the core of many signal processing applications, ranging from acoustic noise supression to echo cancelation [1], array beamforming [2], channel equalization [3], to more recent sensor network applications in surveillance, target localization, and tracking. A trending approach in this direction is to recur to in-network distributed processing in which individual nodes implement adaptation rules and diffuse their estimation to the network [4], [5].The work of Jerónimo Arenas-García and Luis Azpicueta-Ruiz was partially supported by the Spanish Ministry of Economy and Competitiveness (under projects TEC2011-22480 and PRI-PIBIN-2011-1266. The work of Magno M.T. Silva was partially supported by CNPq under Grant 304275/2014-0 and by FAPESP under Grant 2012/24835-1. The work of Vítor H. Nascimento was partially supported by CNPq under grant 306268/2014-0 and FAPESP under grant 2014/04256-2. The work of Ali Sayed was supported in part by NSF grants CCF-1011918 and ECCS-1407712. We are grateful to the colleagues with whom we have shared discussions and coauthorship of papers along this research line, especially Prof. Aníbal R. Figueiras-Vidal

Towards a neural hierarchy of time scales for motor control

Animals show remarkable rich motion skills which are still far from realizable with robots. Inspired by the neural circuits which generate rhythmic motion patterns in the spinal cord of all vertebrates, one main research direction points towards the use of central pattern generators in robots. On of the key advantages of this, is that the dimensionality of the control problem is reduced. In this work we investigate this further by introducing a multi-timescale control hierarchy with at its core a hierarchy of recurrent neural networks. By means of some robot experiments, we demonstrate that this hierarchy can embed any rhythmic motor signal by imitation learning. Furthermore, the proposed hierarchy allows the tracking of several high level motion properties (e.g.: amplitude and offset), which are usually observed at a slower rate than the generated motion. Although these experiments are preliminary, the results are promising and have the potential to open the door for rich motor skills and advanced control

Digital signal processing algorithms and structures for adaptive line enhancing

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Completely Recursive Least Squares and Its Applications

The matrix-inversion-lemma based recursive least squares (RLS) approach is of a recursive form and free of matrix inversion, and has excellent performance regarding computation and memory in solving the classic least-squares (LS) problem. It is important to generalize RLS for generalized LS (GLS) problem. It is also of value to develop an efficient initialization for any RLS algorithm. In Chapter 2, we develop a unified RLS procedure to solve the unconstrained/linear-equality (LE) constrained GLS. We also show that the LE constraint is in essence a set of special error-free observations and further consider the GLS with implicit LE constraint in observations (ILE-constrained GLS). Chapter 3 treats the RLS initialization-related issues, including rank check, a convenient method to compute the involved matrix inverse/pseudoinverse, and resolution of underdetermined systems. Based on auxiliary-observations, the RLS recursion can start from the first real observation and possible LE constraints are also imposed recursively. The rank of the system is checked implicitly. If the rank is deficient, a set of refined non-redundant observations is determined alternatively. In Chapter 4, base on [Li07], we show that the linear minimum mean square error (LMMSE) estimator, as well as the optimal Kalman filter (KF) considering various correlations, can be calculated from solving an equivalent GLS using the unified RLS. In Chapters 5 & 6, an approach of joint state-and-parameter estimation (JSPE) in power system monitored by synchrophasors is adopted, where the original nonlinear parameter problem is reformulated as two loosely-coupled linear subproblems: state tracking and parameter tracking. Chapter 5 deals with the state tracking which determines the voltages in JSPE, where dynamic behavior of voltages under possible abrupt changes is studied. Chapter 6 focuses on the subproblem of parameter tracking in JSPE, where a new prediction model for parameters with moving means is introduced. Adaptive filters are developed for the above two subproblems, respectively, and both filters are based on the optimal KF accounting for various correlations. Simulations indicate that the proposed approach yields accurate parameter estimates and improves the accuracy of the state estimation, compared with existing methods