Diffusion Maps Kalman Filter for a Class of Systems with Gradient Flows

In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. We combine diffusion maps, a manifold learning technique, with a linear Kalman filter and with concepts from Koopman operator theory. More concretely, using diffusion maps, we construct data-driven virtual state coordinates, which linearize the system model. Based on these coordinates, we devise a data-driven framework for state estimation using the Kalman filter. We demonstrate the strengths of our method with respect to both parametric and non-parametric algorithms in three tracking problems. In particular, applying the approach to actual recordings of hippocampal neural activity in rodents directly yields a representation of the position of the animals. We show that the proposed method outperforms competing non-parametric algorithms in the examined stochastic problem formulations. Additionally, we obtain results comparable to classical parametric algorithms, which, in contrast to our method, are equipped with model knowledge.Comment: 15 pages, 12 figures, submitted to IEEE TS

Detection of multiplicative noise in stationary random processes using second- and higher order statistics

This paper addresses the problem of detecting the presence of colored multiplicative noise, when the information process can be modeled as a parametric ARMA process. For the case of zero-mean multiplicative noise, a cumulant based suboptimal detector is studied. This detector tests the nullity of a specific cumulant slice. A second detector is developed when the multiplicative noise is nonzero mean. This detector consists of filtering the data by an estimated AR filter. Cumulants of the residual data are then shown to be well suited to the detection problem. Theoretical expressions for the asymptotic probability of detection are given. Simulation-derived finite-sample ROC curves are shown for different sets of model parameters

Inference of nonlinear state-space models for sandwich-type lateral flow immunoassay using extended Kalman filtering

Copyright [2011] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, a mathematical model for sandwichtype lateral flow immunoassay is developed via short available time series. A nonlinear dynamic stochastic model is considered that consists of the biochemical reaction system equations and the observation equation. After specifying the model structure, we apply the extend Kalman filter (EKF) algorithm for identifying both the states and parameters of the nonlinear state-space model. It is shown that the EKF algorithm can accurately identify the parameters and also predict the system states in the nonlinear dynamic stochastic model through an iterative procedure by using a small number of observations. The identified mathematical model provides a powerful tool for testing the system hypotheses and also inspecting the effects from various design parameters in a both rapid and inexpensive way. Furthermore, by means of the established model, the dynamic changes of the concentration of antigens and antibodies can be predicted, thereby making it possible for us to analyze, optimize and design the properties of lateral flow immunoassay devices.This work was supported in part by the International Science and Technology Cooperation Project of China under Grant 2009DFA32050, Natural Science Foundation of Fujian Province of China under Grants 2009J01280 and 2009J01281

A Fault Tolerant System for an Integrated Avionics Sensor Configuration

An aircraft sensor fault tolerant system methodology for the Transport Systems Research Vehicle in a Microwave Landing System (MLS) environment is described. The fault tolerant system provides reliable estimates in the presence of possible failures both in ground-based navigation aids, and in on-board flight control and inertial sensors. Sensor failures are identified by utilizing the analytic relationships between the various sensors arising from the aircraft point mass equations of motion. The estimation and failure detection performance of the software implementation (called FINDS) of the developed system was analyzed on a nonlinear digital simulation of the research aircraft. Simulation results showing the detection performance of FINDS, using a dual redundant sensor compliment, are presented for bias, hardover, null, ramp, increased noise and scale factor failures. In general, the results show that FINDS can distinguish between normal operating sensor errors and failures while providing an excellent detection speed for bias failures in the MLS, indicated airspeed, attitude and radar altimeter sensors