Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering

We study causal waveform estimation (tracking) of time-varying signals in a paradigmatic atomic sensor, an alkali vapor monitored by Faraday rotation probing. We use Kalman filtering, which optimally tracks known linear Gaussian stochastic processes, to estimate stochastic input signals that we generate by optical pumping. Comparing the known input to the estimates, we confirm the accuracy of the atomic statistical model and the reliability of the Kalman filter, allowing recovery of waveform details far briefer than the sensor's intrinsic time resolution. With proper filter choice, we obtain similar benefits when tracking partially-known and non-Gaussian signal processes, as are found in most practical sensing applications. The method evades the trade-off between sensitivity and time resolution in coherent sensing.Comment: 15 pages, 4 figure

Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering

We study causal waveform estimation (tracking) of time-varying signals in a paradigmatic atomic sensor, an alkali vapor monitored by Faraday rotation probing. We use Kalman filtering, which optimally tracks known linear Gaussian stochastic processes, to estimate stochastic input signals that we generate by optical pumping. Comparing the known input to the estimates, we confirm the accuracy of the atomic statistical model and the reliability of the Kalman filter, allowing recovery of waveform details far briefer than the sensor's intrinsic time resolution. With proper filter choice, we obtain similar benefits when tracking partially-known and non-Gaussian signal processes, as are found in most practical sensing applications. The method evades the trade-off between sensitivity and time resolution in coherent sensing.Comment: 15 pages, 4 figure

On the Stratonovich – Kalman - Bucy filtering algorithm application for accurate characterization of financial time series with use of state-space model by central banks

The central banks introduce and implement the monetary and financial stabilities policies, going from the accurate estimations of national macro-financial indicators such as the Gross Domestic Product (GDP). Analyzing the dependence of the GDP on the time, the central banks accurately estimate the missing observations in the financial time series with the application of different interpolation models, based on the various filtering algorithms. The Stratonovich – Kalman – Bucy filtering algorithm in the state space interpolation model is used with the purpose to interpolate the real GDP by the US Federal Reserve and other central banks. We overviewed the Stratonovich – Kalman – Bucy filtering algorithm theory and its numerous applications. We describe the technique of the accurate characterization of the economic and financial time series with application of state space methods with the Stratonovich – Kalman - Bucy filtering algorithm, focusing on the estimation of Gross Domestic Product by the Swiss National Bank. Applying the integrative thinking principles, we developed the software program and performed the computer modeling, using the Stratonovich – Kalman – Bucy filtering algorithm for the accurate characterization of the Australian GDP, German GDP and the USA GDP in the frames of the state-space model in Matlab. We also used the Hodrick-Prescott filter to estimate the corresponding output gaps in Australia, Germany and the USA. We found that the Australia, Germany on one side and the USA on other side have the different business cycles. We believe that the central banks can use our special software program with the aim to greatly improve the national macroeconomic indicators forecast by making the accurate characterization of the financial time-series with the application of the state-space models, based on the Stratonovich – Kalman – Bucy filtering algorithm

On the Stratonovich – Kalman - Bucy filtering algorithm application for accurate characterization of financial time series with use of state-space model by central banks

The central banks introduce and implement the monetary and financial stabilities policies, going from the accurate estimations of national macro-financial indicators such as the Gross Domestic Product (GDP). Analyzing the dependence of the GDP on the time, the central banks accurately estimate the missing observations in the financial time series with the application of different interpolation models, based on the various filtering algorithms. The Stratonovich – Kalman – Bucy filtering algorithm in the state space interpolation model is used with the purpose to interpolate the real GDP by the US Federal Reserve and other central banks. We overviewed the Stratonovich – Kalman – Bucy filtering algorithm theory and its numerous applications. We describe the technique of the accurate characterization of the economic and financial time series with application of state space methods with the Stratonovich – Kalman - Bucy filtering algorithm, focusing on the estimation of Gross Domestic Product by the Swiss National Bank. Applying the integrative thinking principles, we developed the software program and performed the computer modeling, using the Stratonovich – Kalman – Bucy filtering algorithm for the accurate characterization of the Australian GDP, German GDP and the USA GDP in the frames of the state-space model in Matlab. We also used the Hodrick-Prescott filter to estimate the corresponding output gaps in Australia, Germany and the USA. We found that the Australia, Germany on one side and the USA on other side have the different business cycles. We believe that the central banks can use our special software program with the aim to greatly improve the national macroeconomic indicators forecast by making the accurate characterization of the financial time-series with the application of the state-space models, based on the Stratonovich – Kalman – Bucy filtering algorithm

Oceanographic applications of the Kalman filter

The Kalman filter is a data-processing algorithm with a distinguished history in systems theory. Its application to oceanographic problems is in the embryo stage. The behavior of the filter is demonstrated in the context of an internal equatorial Rossby wave propagation problem

Observer techniques for estimating the state-of-charge and state-of-health of VRLABs for hybrid electric vehicles

The paper describes the application of observer-based state-estimation techniques for the real-time prediction of state-of-charge (SoC) and state-of-health (SoH) of lead-acid cells. Specifically, an approach based on the well-known Kalman filter, is employed, to estimate SoC, and the subsequent use of the EKF to accommodate model non-linearities to predict battery SoH. The underlying dynamic behaviour of each cell is based on a generic Randles' equivalent circuit comprising of two-capacitors (bulk and surface) and three resistors, (terminal, transfer and self-discharging). The presented techniques are shown to correct for offset, drift and long-term state divergence-an unfortunate feature of employing stand-alone models and more traditional coulomb-counting techniques. Measurements using real-time road data are used to compare the performance of conventional integration-based methods for estimating SoC, with those predicted from the presented state estimation schemes. Results show that the proposed methodologies are superior with SoC being estimated to be within 1% of measured. Moreover, by accounting for the nonlinearities present within the dynamic cell model, the application of an EKF is shown to provide verifiable indications of SoH of the cell pack

Statistical Communication Theory

Contains reports on five research projects.National Science Foundation (Grant GP- 2495)National Institutes of Health (Grant MH-04737-05)National Aeronautics and Space Administration (Grant NsG-496

Stochastic processes, estimation theory and image enhancement

An introductory account of stochastic processes, estimation theory, and image enhancement is presented. The book is primarily intended for first-year graduate students and practicing engineers and scientists whose work requires an acquaintance with the theory. Fundamental concepts of probability were reviewed that are required to support the main topics. The appendices discuss the remaining mathematical background