Machine-learning nonstationary noise out of gravitational-wave detectors

Signal extraction out of background noise is a common challenge in high-precision physics experiments, where the measurement output is often a continuous data stream. To improve the signal-to-noise ratio of the detection, witness sensors are often used to independently measure background noises and subtract them from the main signal. If the noise coupling is linear and stationary, optimal techniques already exist and are routinely implemented in many experiments. However, when the noise coupling is nonstationary, linear techniques often fail or are suboptimal. Inspired by the properties of the background noise in gravitational wave detectors, this work develops a novel algorithm to efficiently characterize and remove nonstationary noise couplings, provided there exist witnesses of the noise source and of the modulation. In this work, the algorithm is described in its most general formulation, and its efficiency is demonstrated with examples from the data of the Advanced LIGO gravitational-wave observatory, where we could obtain an improvement of the detector gravitational-wave reach without introducing any bias on the source parameter estimation

Non-linear minimum variance estimation for discrete-time multi-channel systems

A nonlinear operator approach to estimation in discrete-time systems is described. It involves inferential estimation of a signal which enters a communications channel involving both nonlinearities and transport delays. The measurements are assumed to be corrupted by a colored noise signal which is correlated with the signal to be estimated. The system model may also include a communications channel involving either static or dynamic nonlinearities. The signal channel is represented in a very general nonlinear operator form. The algorithm is relatively simple to derive and to implement

Linear and nonlinear filtering in mathematical finance: a review

Copyright @ The Authors 2010This paper presents a review of time series filtering and its applications in mathematical finance. A summary of results of recent empirical studies with market data are presented for yield curve modelling and stochastic volatility modelling. The paper also outlines different approaches to filtering of nonlinear time series

The Separation Principle in Stochastic Control, Redux

Over the last 50 years a steady stream of accounts have been written on the separation principle of stochastic control. Even in the context of the linear-quadratic regulator in continuous time with Gaussian white noise, subtle difficulties arise, unexpected by many, that are often overlooked. In this paper we propose a new framework for establishing the separation principle. This approach takes the viewpoint that stochastic systems are well-defined maps between sample paths rather than stochastic processes per se and allows us to extend the separation principle to systems driven by martingales with possible jumps. While the approach is more in line with "real-life" engineering thinking where signals travel around the feedback loop, it is unconventional from a probabilistic point of view in that control laws for which the feedback equations are satisfied almost surely, and not deterministically for every sample path, are excluded.Comment: 23 pages, 6 figures, 2nd revision: added references, correction

Model robustness of finite state nonlinear filtering over the infinite time horizon

We investigate the robustness of nonlinear filtering for continuous time finite state Markov chains, observed in white noise, with respect to misspecification of the model parameters. It is shown that the distance between the optimal filter and that with incorrect model parameters converges to zero uniformly over the infinite time interval as the misspecified model converges to the true model, provided the signal obeys a mixing condition. The filtering error is controlled through the exponential decay of the derivative of the nonlinear filter with respect to its initial condition. We allow simultaneously for misspecification of the initial condition, of the transition rates of the signal, and of the observation function. The first two cases are treated by relatively elementary means, while the latter case requires the use of Skorokhod integrals and tools of anticipative stochastic calculus.Comment: Published at http://dx.doi.org/10.1214/105051606000000871 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org