Networked distributed fusion estimation under uncertain outputs with random transmission delays, packet losses and multi-packet processing

This paper investigates the distributed fusion estimation problem for networked systems whose mul- tisensor measured outputs involve uncertainties modelled by random parameter matrices. Each sensor transmits its measured outputs to a local processor over different communication channels and random failures –one-step delays and packet dropouts–are assumed to occur during the transmission. White sequences of Bernoulli random variables with different probabilities are introduced to describe the ob- servations that are used to update the estimators at each sampling time. Due to the transmission failures, each local processor may receive either one or two data packets, or even nothing and, when the current measurement does not arrive on time, its predictor is used in the design of the estimators to compensate the lack of updated information. By using an innovation approach, local least-squares linear estimators (filter and fixed-point smoother) are obtained at the individual local processors, without requiring the signal evolution model. From these local estimators, distributed fusion filtering and smoothing estimators weighted by matrices are obtained in a unified way, by applying the least-squares criterion. A simula- tion study is presented to examine the performance of the estimators and the influence that both sensor uncertainties and transmission failures have on the estimation accuracy.This research is supported by Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación and Fondo Europeo de Desarrollo Regional FEDER (grant no. MTM2017-84199-P)

Information fusion algorithms for state estimation in multi-sensor systems with correlated missing measurements

In this paper, centralized and distributed fusion estimation problems in linear discrete-time stochastic systems with missing observations coming from multiple sensors are addressed. At each sensor, the Bernoulli random variables describing the phenomenon of missing observations are assumed to be correlated at instants that differ m units of time. By using an innovation approach, recursive linear filtering and fixed-point smoothing algorithms for the centralized fusion problem are derived in the least-squares sense. The distributed fusion estimation problem is addressed based on the distributed fusion criterion weighted by matrices in the linear minimum variance sense. For each sensor subsystem, local least-squares linear filtering and fixed-point smoothing estimators are given and the estimation error cross-covariance matrices between any two sensors are derived to obtain the distributed fusion estimators. The performance of the proposed estimators is illustrated by numerical simulation examples where scalar and two-dimensional signals are estimated from missing observations coming from two sensors, and the estimation accuracy is analyzed for different missing probabilities and different values of m.Ministerio de Ciencia e Innovación (Programa FPU and Grant No. MTM2011-24718

Parametric and Nonparametric Volatility Measurement

Volatility has been one of the most active areas of research in empirical finance and time series econometrics during the past decade. This chapter provides a unified continuous-time, frictionless, no-arbitrage framework for systematically categorizing the various volatility concepts, measurement procedures, and modeling procedures. We define three different volatility concepts: (i) the notional volatility corresponding to the ex-post sample-path return variability over a fixed time interval, (ii) the ex-ante expected volatility over a fixed time interval, and (iii) the instantaneous volatility corresponding to the strength of the volatility process at a point in time. The parametric procedures rely on explicit functional form assumptions regarding the expected and/or instantaneous volatility. In the discrete-time ARCH class of models, the expectations are formulated in terms of directly observable variables, while the discrete- and continuous-time stochastic volatility models involve latent state variable(s). The nonparametric procedures are generally free from such functional form assumptions and hence afford estimates of notional volatility that are flexible yet consistent (as the sampling frequency of the underlying returns increases). The nonparametric procedures include ARCH filters and smoothers designed to measure the volatility over infinitesimally short horizons, as well as the recently-popularized realized volatility measures for (non-trivial) fixed-length time intervals.

Parametric and Nonparametric Volatility Measurement

Volatility has been one of the most active areas of research in empirical finance and time series econometrics during the past decade. This chapter provides a unified continuous-time, frictionless, no-arbitrage framework for systematically categorizing the various volatility concepts, measurement procedures, and modeling procedures. We define three different volatility concepts: (i) the notional volatility corresponding to the ex-post sample-path return variability over a fixed time interval, (ii) the ex-ante expected volatility over a fixed time interval, and (iii) the instantaneous volatility corresponding to the strength of the volatility process at a point in time. The parametric procedures rely on explicit functional form assumptions regarding the expected and/or instantaneous volatility. In the discrete-time ARCH class of models, the expectations are formulated in terms of directly observable variables, while the discrete- and continuous-time stochastic volatility models involve latent state variable(s). The nonparametric procedures are generally free from such functional form assumptions and hence afford estimates of notional volatility that are flexible yet consistent (as the sampling frequency of the underlying returns increases). The nonparametric procedures include ARCH filters and smoothers designed to measure the volatility over infinitesimally short horizons, as well as the recently-popularized realized volatility measures for (non-trivial) fixed-length time intervals.

Covariance-Based Estimation from Multisensor Delayed Measurements with Random Parameter Matrices and Correlated Noises

The optimal least-squares linear estimation problem is addressed for a class of discrete-time multisensor linear stochastic systems subject to randomly delayed measurements with different delay rates. For each sensor, a different binary sequence is used to model the delay process. The measured outputs are perturbed by both random parameter matrices and one-step autocorrelated and cross correlated noises. Using an innovation approach, computationally simple recursive algorithms are obtained for the prediction, filtering, and smoothing problems, without requiring full knowledge of the state-space model generating the signal process, but only the information provided by the delay probabilities and the mean and covariance functions of the processes (signal, random parameter matrices, and noises) involved in the observation model. The accuracy of the estimators is measured by their error covariance matrices, which allow us to analyze the estimator performance in a numerical simulation example that illustrates the feasibility of the proposed algorithms

Robust RLS Wiener Fixed-Interval Smoother in Linear Discrete-Time Stochastic Systems with Uncertain Parameters

This paper proposes the robust RLS Wiener filter and fixed-interval smoothing algorithms based on the innovation approach. As a result, the robust RLS Wiener filtering algorithm is same as the existing robust RLS Wiener filtering algorithm. The estimation accuracy of the fixed-interval smoother is compared with the robust RLS Wiener filter and the following fixed-interval smoothers. In the proposed robust RLS Wiener fixed-interval smoother, the case, where the observed value is replaced with the robust filtering estimate of the signal, is also simulated. (1) The RLS Wiener fixed-interval smoother in which the filtering estimate of the state is replaced with the robust RLS Wiener filtering estimate. (2) The RTS (Rauch-Tung-Striebel) fixed-interval smoother in which the filtering estimate of the state is replaced with the robust RLS Wiener filtering estimate. (3) The  RLS Wiener fixed-interval smoother and the  RLS Wiener filter. (4) The RLS Wiener fixed-interval smoother in which the filtering estimate of the state is replaced with the robust RLS Wiener filtering estimate and the observed value is replaced with the robust RLS Wiener filtering estimate of the signal. From the simulation results, the most feasible estimation technique for the fixed-interval smoothing estimate is the RLS Wiener fixed-interval smoother. Here, the robust filtering estimate is used and the observed value is replaced with the robust filtering estimate

Outlier resistant filtering and smoothing

AbstractWe consider a stationary Gaussian information process transmitted through an additive noise channel. We assume that the noise and information processes are mutually independent, and we model the noise process as nominally Gaussian with additive outliers. For the above system model, we first develop a theory for outlier resistant filtering and smoothing operations. We then design specific such nonlinear operations, and we study their performance. The performance criteria are the asymptotic mean squared error at the Gaussian nominal model, the breakdown point, and the influence function. We find that the proposed operations combine excellent performance at the nominal model with strong resistance to outliers

Steps and bumps: precision extraction of discrete states of molecular machines using physically-based, high-throughput time series analysis

We report new statistical time-series analysis tools providing significant improvements in the rapid, precision extraction of discrete state dynamics from large databases of experimental observations of molecular machines. By building physical knowledge and statistical innovations into analysis tools, we demonstrate new techniques for recovering discrete state transitions buried in highly correlated molecular noise. We demonstrate the effectiveness of our approach on simulated and real examples of step-like rotation of the bacterial flagellar motor and the F1-ATPase enzyme. We show that our method can clearly identify molecular steps, symmetries and cascaded processes that are too weak for existing algorithms to detect, and can do so much faster than existing algorithms. Our techniques represent a major advance in the drive towards automated, precision, highthroughput studies of molecular machine dynamics. Modular, open-source software that implements these techniques is provided at http://www.eng.ox.ac.uk/samp/members/max/software