Related papers: Nonlinear projective filtering I: Application to r…

We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different…

Nonlinearity in many systems is heavily dependent on component variation and environmental factors such as temperature. This is often overcome by keeping signals close enough to the device's operating point that it appears approximately…

In this paper, we consider the time-inhomogeneous nonlinear time series regression for a general class of locally stationary time series. On one hand, we propose sieve nonparametric estimators for the time-varying regression functions which…

In addition to ever-present thermal noise, various communication and sensor systems can contain significant amounts of interference with outlier (e.g. impulsive) characteristics. Such outlier noise can be efficiently mitigated in real-time…

This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…

While recent advancements in foundation models have significantly impacted machine learning, rigorous tests on the performance of time series foundation models (TSFMs) remain largely underexplored. This paper presents an empirical study…

Monitoring is an important body of techniques in runtime verification of real-time, embedded, and cyber-physical systems. Mathematically, the monitoring problem can be formalized as a pattern matching problem against a pattern automaton.…

Model based signal processing or signal analysis or signal representation has a rather different point of view from the more traditional filtering and algorithm based approaches. However, in all of these, the names of Prony, Pad\'e, and…

We propose a novel scheme for laser phase noise measurements with minimized sensitivity to external fluctuations including interferometer vibration, temperature instability, other low-frequency noise, and relative intensity noise. In order…

In addition to ever-present thermal noise, communication and sensor systems can contain significant amounts of interference with outlier (e.g. impulsive) characteristics. Such outlier interference (including that caused by nonlinear signal…

In this paper we introduce a projection method for the space of probability distributions based on the differential geometric approach to statistics. This method is based on a direct L2 metric as opposed to the usual Hellinger distance and…

We study properties of the human electrocardiogram under the working hypothesis that fluctuations beyond the regular structure of single cardiac cycles are unpredictable. On this background we discuss the possibility to use the phase space…

This paper contains the technical foundations from stochastic differential geometry for the construction of geometrically intrinsic nonlinear recursive filters. A diffusion X on a manifold N is run for a time interval T, with a random…

Systems equipped with modern sensing modalities such as vision and lidar gain access to increasingly high-dimensional measurements with which to enact estimation and control schemes. In this article, we examine the continuum limit of…

Multiplicative noise widely exists in radar images, medical images and other important fields' images. Compared to normal noises, multiplicative noise has a generally stronger effect on the visual expression of images. Aiming at the…

In this paper, we investigate time-varying nonlinear time series regression for a broad class of locally stationary time series. First, we propose sieve nonparametric estimators for the time-varying regression functions that achieve uniform…

We propose a method for adaptive nonlinear sequential modeling of vector-time series data. Data is modeled as a nonlinear function of past values corrupted by noise, and the underlying non-linear function is assumed to be approximately…

We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…

We develop methodology allowing to simulate a stationary functional time series defined by means of its spectral density operators. Our framework is general, in that it encompasses any such stationary functional time series, whether linear…

This paper proposes a novel method to filter out the false alarm of LiDAR system by using the temporal correlation of target reflected photons. Because of the inevitable noise, which is due to background light and dark counts of the…