Output-error adaptive bilinear filters

Journal ArticleThis paper presents an overview of several gradient type recursive algorithms for adaptive nonlinear filters equipped with bilinear system models. Bilinear models are attractive because they can approximate a large class of nonlinear systems with great parsimony in the use of coefficients. Two algorithms of complexity O(N3) (N is the memory span of the bilinear system model used in the adaptive filter) multiplications per sample and two other algorithms of complexity O(N2) multiplications per sample are presented in this paper. The results of several computer experiments show that at least one of the O(N2) complexity algorithms works almost as well as the more complex algorithms

A stability result for RLS adaptive bilinear filters

Journal ArticleAbstract- This letter considers recursive least squares (RLS) adaptive nonlinear filtering using bilinear system models. It is shown that the extended RLS adaptive bilinear filter, as well as the equation-error RLS adaptive bilinear filter, are guaranteed to be stable in the sense that the time average of the squared estimation error is bounded whenever the underlying process that generates the input signals is stable in the same sense

Output-error LMS bilinear filters with stability monitoring

Journal ArticleABSTRACT This paper introduces output-error LMS bilinear filters with stability monitoring. Bilinear filters are recursive nonlinear systems that belong to the class of polynomial systems. Because of the feedback structure, such models are able to represent many nonlinear systems efficiently. However, the usefulness of adaptive bilinear filters is greatly restricted unless they are guaranteed to perform in a stable manner. A stability monitoring scheme is proposed to overcome the stability problem. The paper concludes with simulation results that demonstrate the usefulness of oiir technique

Analog readout for optical reservoir computers

Reservoir computing is a new, powerful and flexible machine learning technique that is easily implemented in hardware. Recently, by using a time-multiplexed architecture, hardware reservoir computers have reached performance comparable to digital implementations. Operating speeds allowing for real time information operation have been reached using optoelectronic systems. At present the main performance bottleneck is the readout layer which uses slow, digital postprocessing. We have designed an analog readout suitable for time-multiplexed optoelectronic reservoir computers, capable of working in real time. The readout has been built and tested experimentally on a standard benchmark task. Its performance is better than non-reservoir methods, with ample room for further improvement. The present work thereby overcomes one of the major limitations for the future development of hardware reservoir computers.Comment: to appear in NIPS 201

Low-complexity RLS algorithms using dichotomous coordinate descent iterations

In this paper, we derive low-complexity recursive least squares (RLS) adaptive filtering algorithms. We express the RLS problem in terms of auxiliary normal equations with respect to increments of the filter weights and apply this approach to the exponentially weighted and sliding window cases to derive new RLS techniques. For solving the auxiliary equations, line search methods are used. We first consider conjugate gradient iterations with a complexity of O(N-2) operations per sample; N being the number of the filter weights. To reduce the complexity and make the algorithms more suitable for finite precision implementation, we propose a new dichotomous coordinate descent (DCD) algorithm and apply it to the auxiliary equations. This results in a transversal RLS adaptive filter with complexity as low as 3N multiplications per sample, which is only slightly higher than the complexity of the least mean squares (LMS) algorithm (2N multiplications). Simulations are used to compare the performance of the proposed algorithms against the classical RLS and known advanced adaptive algorithms. Fixed-point FPGA implementation of the proposed DCD-based RLS algorithm is also discussed and results of such implementation are presented

Adaptive bilinear predictors

Journal ArticleThis paper considers an extended recursive least squares (RLS) adaptive bilinear predictor. It is shown that the extended RLS adaptive bilinear predictor is guaranteed to be stable in the sense that the time average of the squared a-posteriori prediction error signal is bounded whenever the input signal is bounded in the same sense. It also shows that the a-priori prediction error itself is bounded whenever the desired signal is bounded. This paper also contains simulation results to demonstrate the usefulness of the extended RLS adaptive bilinear predictor

Adaptive algorithms for identifying recursive nonlinear systems

Journal ArticleABSTRACT This paper presents two fast least-squares lattice algorithms for adaptive non-linear filters equipped with system models involving nonlinear feedback. Such models can approximate a large class of non-linear systems adequately, and usually with considerable parsimony in the number of coefficients required. For simplicity of presentation, we consider the bilinear system model in the paper, even though the results are applicable to more general system models. The computational complexity of the algorithms is an order of magnitude smaller than previously available methods. Results of several experiments that demonstrate the properties of the adaptive bilinear filters as well as compare their performances with two other algorithms that are computationally more expensive are also presented in this paper

Adaptive lattice bilinear filters

Journal ArticleAbstract-This paper presents two fast least squares lattice algorithms for adaptive nonlinear filters equipped with bilinear system models. Bilinear models are attractive for adaptive filtering applications because they can approximate a large class of nonlinear systems adequately, and usually with considerable parsimony in the number of coefficients required. The lattice filter formulation transforms the nonlinear filtering problem into an equivalent multichannel linear filtering problem and then uses multichannel lattice filtering algorithms to solve the nonlinear filtering problem. The lattice filters perform a Gram-Schmidt orthogonalization of the input data and have very good numerical properties. Furthermore, the computational complexity of the algorithms is an order of magnitude smaller than previously available methods. The first of the two approaches is an equation error algorithm that uses the measured desired response signal directly to compute the adaptive filter outputs. This method is conceptually very simple; however, it will result in biased system models in the presence of measurement noise. The second approach is an approximate least squares output error solution. In this case, the past samples of the output of the adaptive system itself are used to produce the filter output at the current time. Results of several experiments that demonstrate and compare the properties of the adaptive bilinear filters are also presented in this paper. These results indicate that the output error algorithm is less sensitive to output measurement noise than the equation error method

Adaptive polynomial filters

Journal ArticleWhile linear filter are useful in a large number of applications and relatively simple from conceptual and implementational view points. there are many practical situations that require nonlinear processing of the signals involved. This article explains adaptive nonlinear filters equipped with polynomial models of nonlinearity. The polynomial systems considered are those nonlinear systems whose output signals can be related to the input signals through a truncated Volterra series expansion, or a recursive nonlinear difference equation. The Volterra series expansion can model a large class of nonlinear systems and is attractive in filtering applications because the expansion is a linear combination of nonlinear functions of the input signal. The basic ideas behind the development of gradient and recursive least-squares adaptive Volterra filters are first discussed. followed by adaptive algorithms using system models involving recursive nonlinear difference equations. Such systems are attractive because they may be able to approximate many nonlinear systems with great parsimony in the use pf coefficients. Also discussed are current research trends and new results and problem areas associated with these nonlinear filters. A lattice structure for polynomial models is also described