Related papers: Stable approximation schemes for optimal filters

It is known that Kalman-Bucy filter is stable with respect to initial conditions under the conditions of uniform complete controllability and uniform complete observability (Bishop et. al 2017, Ocone et. al 1996). In this paper, we prove…

Graph-structured data arise in a variety of real-world context ranging from sensor and transportation to biological and social networks. As a ubiquitous tool to process graph-structured data, spectral graph filters have been used to solve…

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity,…

We consider linear recurrent neural networks, which have become a key building block of sequence modeling due to their ability for stable and effective long-range modeling. In this paper, we aim at characterizing this ability on a simple…

This paper develops a connection between the asymptotic stability of nonlinear filters and a notion of observability. We consider a general class of hidden Markov models in continuous time with compact signal state space, and call such a…

We propose a general technique for extracting a larger set of stable information from persistent homology computations than is currently done. The persistent homology algorithm is usually viewed as a procedure which starts with a filtered…

Stability is a fundamental property of dynamical systems, yet to this date it has had little bearing on the practice of recurrent neural networks. In this work, we conduct a thorough investigation of stable recurrent models. Theoretically,…

We consider the Bayesian optimal filtering problem: i.e. estimating some conditional statistics of a latent time-series signal from an observation sequence. Classical approaches often rely on the use of assumed or estimated transition and…

We develop a new algorithm for fitting circles that does not have drawbacks commonly found in existing circle fits. Our fit achieves ultimate accuracy (to machine precision), avoids divergence, and is numerically stable even when fitting…

This work considers the theory underlying a discrete-time quantum filter recently used in a quantum feedback experiment. It proves that this filter taking into account decoherence and measurement errors is optimal and stable. We present the…

This paper examines the stability of the \`a trous algorithm under arbitrary iteration in the context of a more general study of shift-invariant filter banks. The main results describe sufficient conditions on the associated filters under…

One of the main reasons for topological persistence being useful in data analysis is that it is backed up by a stability (isometry) property: persistence diagrams of $1$-parameter persistence modules are stable in the sense that the…

Data assimilation algorithms integrate prior information from numerical model simulations with observed data. Ensemble-based filters, regarded as state-of-the-art, are widely employed for large-scale estimation tasks in disciplines such as…

We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…

The discovery of particle filtering methods has enabled the use of nonlinear filtering in a wide array of applications. Unfortunately, the approximation error of particle filters typically grows exponentially in the dimension of the…

This paper concerns numerical assessment of Monte Carlo error in particle filters. We show that by keeping track of certain key features of the genealogical structure arising from resampling operations, it is possible to estimate variances…

Input estimation is a signal processing technique associated with deconvolution of measured signals after filtering through a known dynamic system. Kitanidis and others extended this to the simultaneous estimation of the input signal and…

We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…

A Wiener filter can be interpreted as a cascade of a whitening- and an estimation filter. This paper gives a detailed investigates of the properties of these two filters. Then the practical consequences for the overall Wiener filter are…

In this paper, we are interested in obtaining answers to the following questions for particle flow filters: Can we provide a theoretical guarantee that particle flow filters give correct results such as unbiased estimates? Are particle…