Related papers: A Nonlinear Adaptive Filter Based on the Model of …
This work proposes a low complexity nonlinearity model and develops adaptive algorithms over it. The model is based on the decomposable---or rank-one, in tensor language---Volterra kernels. It may also be described as a product of FIR…
Nonlinear adaptive filters often show some sparse behavior due to the fact that not all the coefficients are equally useful for the modeling of any nonlinearity. Recently, a class of proportionate algorithms has been proposed for nonlinear…
A Monte Carlo filter, based on the idea of averaging over characteristics and fashioned after a particle-based time-discretized approximation to the Kushner-Stratonovich (KS) nonlinear filtering equation, is proposed. A key aspect of the…
We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…
Nonlinear filtering is the problem of online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We…
An efficient algorithm for computing lower bounds on the global linear complexity of nonlinearly filtered PN-sequences is presented. The technique here developed is based exclusively on the realization of bit wise logic operations, which…
A simple nonlinear system modeling algorithm designed to work with limited \emph{a priori }knowledge and short data records, is examined. It creates an empirical Volterra series-based model of a system using an $l_{q}$-constrained least…
We introduce Coarse-Grained Nonlinear Dynamics, an efficient and universal parameterization of nonlinear system dynamics based on the Volterra series expansion. These models require a number of parameters only quasilinear in the system's…
Despite the cheap availability of computing resources enabling faster Monte Carlo simulations, the potential benefits of particle filtering in revealing accurate statistical information on the imprecisely known model parameters or modeling…
For many nonlinear Bayesian state estimation problems, the posterior recursion is not analytically tractable, leading to algorithms that are influenced by numerical approximation errors. These algorithms depend on parameters that affect the…
Over the last decade, both the neural network and kernel adaptive filter have successfully been used for nonlinear signal processing. However, they suffer from high computational cost caused by their complex/growing network structures. In…
Nonlinear models are known to provide excellent performance in real-world applications that often operate in non-ideal conditions. However, such applications often require online processing to be performed with limited computational…
The implementation of optimal statistical inference protocols for high-dimensional quantum systems is often computationally expensive. To avoid the difficulties associated with optimal techniques, here I propose an alternative approach to…
The aim of this paper is to provide a variational interpretation of the nonlinear filter in continuous time. A time-stepping procedure is introduced, consisting of successive minimization problems in the space of probability densities. The…
A split hypercomplex learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of hypercomplex signals of any dimension is proposed. The derivation strictly takes into account the laws of…
Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is…
In this article, we propose a new filtering algorithm based in the Koopman operator, showing that a nonlinear filtering problem can be seen as an equivalent problem where the dynamics is infinite dimensional, but linear. Using Extended…
In this paper we will develop linear and nonlinear filtering methods for a large class of nonlinear wave equations that arise in applications such as quantum dynamics and laser generation and propagation in a unified framework. We consider…
This paper presents a novel filter with low computational demand to address the problem of orientation estimation of a robotic platform. This is conventionally addressed by extended Kalman filtering of measurements from a sensor suit which…
The linearization of nonlinear systems is an important digital enhancement technique. In this paper, a real-time capable post- and pre-linearization method for the widely applicable time-varying discrete-time Volterra series is presented.…