Extended Kalman Filter Technique Research Articles

Estimation of sub-criticality using extended Kalman filtering technique

Reactivity is widely used as the paramount means for defining nuclear reactor status. The measurement of reactivity can be only made in an indirect way. Traditionally, reactivity is estimated by the Inverse Point Kinetics (IPK) method. However, this technique suffers from some serious drawbacks like high sensitivity to reactor parameters and less immunity to noise content in the input signals, hence effective only during power range operation. In this paper, the extended Kalman filter (EKF) technique, which is based on stochastic model of reactor kinetics is proposed for subcriticality estimation in nuclear reactor. The proposed technique can work in noisy environment and modeling errors and uncertainties in parameters do not affect the estimation severely as the feedback gain is continuously adjusted during the estimation process. The performance of proposed technique for the reactivity estimation has been evaluated using power variation data sets collected from a PHWR (Pressurized Heavy Water Reactor) and a research reactor. It has been found that with the application of EKF technique, reactivity in a highly subcritical core can be estimated with reasonable accuracy. The EKF based approach has been found to yield higher accuracy, noise suppression and robustness than done by IPK based approach.

Dual extended Kalman filter for combined estimation of vehicle state and road friction

Vehicle state and tire-road adhesion are of great use and importance to vehicle active safety control systems. However, it is always not easy to obtain the information with high accuracy and low expense. Recently, many estimation methods have been put forward to solve such problems, in which Kalman filter becomes one of the most popular techniques. Nevertheless, the use of complicated model always leads to poor real-time estimation while the role of road friction coefficient is often ignored. For the purpose of enhancing the real time performance of the algorithm and pursuing precise estimation of vehicle states, a model-based estimator is proposed to conduct combined estimation of vehicle states and road friction coefficients. The estimator is designed based on a three-DOF vehicle model coupled with the Highway Safety Research Institute(HSRI) tire model; the dual extended Kalman filter (DEKF) technique is employed, which can be regarded as two extended Kalman filters operating and communicating simultaneously. Effectiveness of the estimation is firstly examined by comparing the outputs of the estimator with the responses of the vehicle model in CarSim under three typical road adhesion conditions(high-friction, low-friction, and joint-friction). On this basis, driving simulator experiments are carried out to further investigate the practical application of the estimator. Numerical results from CarSim and driving simulator both demonstrate that the estimator designed is capable of estimating the vehicle states and road friction coefficient with reasonable accuracy. The DEKF-based estimator proposed provides the essential information for the vehicle active control system with low expense and decent precision, and offers the possibility of real car application in future.

Network-Wide Traffic State Estimation Using Loop Detector and Floating Car Data

In real-time traffic management and intelligent transportation systems (ITS) applications, an accurate picture of the prevailing traffic state in terms of speeds and densities is critical, for which traffic state estimation methods are needed. The most popular and effective techniques used are so-called model-based traffic state estimators, which consist of a dynamic traffic flow model to predict the evolution of the state variables; a set of observation equations relating sensor observations to the system state; and data-assimilation techniques to combine the model predictions with the sensor observations. Commonly, both process and observation models are formulated in Eulerian (space–time) coordinates. However, recent studies show that (first-order) macroscopic traffic flow models can be formulated and solved more efficiently and accurately in Lagrangian (vehicle number–time) coordinates (which move with traffic stream) than in Eulerian coordinates (which are fixed in space). In this article such a Lagrangian system model for state estimation is used. The approach uses the extended Kalman filtering technique, in which the discretized Lagrangian kinematic wave model with an extension (node models) for network discontinuities is used as the process equation and the average relation between vehicle spacing and speed (the fundamental diagram) is used as the observation equation. The Lagrangian state estimator is validated and compared with its Eulerian counterpart based on ground-truth data from a microscopic simulation environment. The results demonstrate that network-wide Lagrangian state estimation is possible and provide evidence that the Lagrangian estimator outperforms the Eulerian approach.

Real-Time Lagrangian Traffic State Estimator for Freeways

Freeway traffic state estimation and prediction are central components in real-time traffic management and information applications. Model-based traffic state estimators consist of a dynamic model for the state variables (e.g., a first- or second-order macroscopic traffic flow model), a set of observation equations relating sensor observations to the system state (e.g., the fundamental diagrams), and a data-assimilation technique to combine the model predictions with the sensor observations [e.g., the extended Kalman filter (EKF)]. Commonly, both process and observation models are formulated in Eulerian (space-time) coordinates. Recent studies have shown that this model can be formulated and solved more efficiently and accurately in Lagrangian (vehicle number-time) coordinates. In this paper, we propose a new model-based state estimator based on the EKF technique, in which the discretized Lagrangian Lighthill-Whitham and Richards (LWR) model is used as the process equation, and in which observation models for both Eulerian and Lagrangian sensor data (from loop detectors and vehicle trajectories, respectively) are incorporated. This Lagrangian state estimator is validated and compared with a Eulerian state estimator based on the same LWR model using an empirical microscopic traffic data set from the U.K. The results indicate that the Lagrangian estimator is significantly more accurate and offers computational and theoretical benefits over the Eulerian approach.

Estimation of vehicle states and tire-road friction using parallel extended Kalman filtering

A model-based estimator design and implementation is described in this paper to undertake combined estimation of vehicle states and tire-road friction coefficients. The estimator is designed based on a vehicle model with three degrees of freedom (3-DOF) and the dual extended Kalman filter (DEKF) technique is employed. Effectiveness of the estimation is examined and validated by comparing the outputs of the estimator with the responses of the vehicle model in CarSim in three typical road adhesion conditions (high-friction, low-friction, and joint-friction roads). Simulation results demonstrate that the DEKF estimator algorithm designed is able to obtain vehicle states (e.g., yaw rate and roll angle) as well as road friction coefficients with reasonable accuracy.

Passivity based control for a magnetically levitated flexible beam with rate estimation via the extended Kalman filtering technique

Passivity based control for a magnetically levitated flexible beam with rate estimation via the extended Kalman filtering technique

Fault Detection and Isolation for a Supermarket Refrigeration System – Part One: Kalman-Filter-Based Methods

AbstractFault Detection and Isolation (FDI) using the Kalman Filter (KF) technique for a supermarket refrigeration system is explored. Four types of sensor fault scenarios, namely drift, offset, freeze and hard-over, are considered for two temperature sensors, and one type of parametric fault scenario, namely freeze-over/dirty built-up, is considered for one heat transfer coefficient between the inside air and the evaporator surface. For fault detection purpose, the fault residual is generated through a KF and then evaluated through CUSUM method. For fault isolation purpose, a bank of KFs arranged by splitting measurements is constructed for sensor fault isolation, while the Multi-Model Adaptive Estimation (MMAE) method is employed to handle parametric fault isolation. All these approaches are extended and checked by using Extended KF technique afterwards. The test results show that the EKF-based FDI method generally performances better and faster than the KF-based method does. However, both methods can not handle the isolation between sensor faults and parametric fault.

A Two-Stage Kalman Estimation Approach for the Identification of Nonlinear Structural Parameters

When structural damage occurs, nonlinearity usually exists in damaged structures. So far, some progresses in the identification of nonlinearity in structures have been made. The extended Kalman filter (EKF) has been applied for the identification of nonlinear structural parameters. However, since the extended state vector contains both the state vector and the structural parameters, EKF approach can identify limited numbers of nonlinear structural parameters due to computational convergence difficulty. To overcome such problem, a two-stage Kalman estimator approach, which is not available in the previous literature, is proposed for the identification of nonlinear structural parameters under limited acceleration output measurements. In the first stage, state vector of a nonlinear structure is considered as an implicit function of the nonlinear structural parameters, and the parametric vector is estimated directly based on the Kalman estimator. In the second stage, state vector of the nonlinear structure is updated by applying the Kalman estimator with the structural parameters being estimated in the first stage. Therefore, analytical recursive solutions for the structural nonlinear parameters and state vector are respectively derived and presented, by using the Kalman estimator method respectively. The proposed approach is straightforward. Moreover, it can greatly reduce the time of iteration calculation. To demonstrate the accuracy and effectiveness of the proposed approach, numerical example of identifying the parameters of a 6-story hysteretic shear building is conducted. Simulation results show that the proposed approach is able to identify nonlinear structural systems involving a large number of unknown parameters compared with the conventional EKF technique.

Optimal Investment Strategies under Stochastic Volatility - Estimation and Applications

This paper studies the impact of stochastic volatility (SV) on optimal investment decisions. We consider three different SV models: an extended Stein/Stein model, the Heston Model and an extended Heston Model with a constant elasticity variance (CEV) process and derive the the long-term optimal investment strategies under each of these processes. Since volatility is not a directly observable quantity, extended Kalman filter techniques are adopted to deal with this partial information problem. Optimal investment strategies based on the CEV volatility model are obtained by adopting the Backward Markov Chain approximation method since analytical solutions are no longer available. We find in the empirical investigation that the Heston model is favored as a more parsimonious model compared with the other two models. All three investment strategies based on the three SV models contain a positive intertemporal hedging term in addition to the static mean-variance portfolio. However, in their details the three investment strategies differ from each other. We also ?nd that the investment strategies are sensitive to the CEV parameter.

Experimental airborne NH∞ vision-based simultaneous localization and mapping in unknown environments

This article aims to present a robust airborne three-dimensional (3D) visual simultaneous localization and mapping (VSLAM) solution based on a stereovision system embedded in a remotely piloted helicopter. The proposed solution enables an unmanned aerial vehicle to construct a reliable map and localize itself in this map without any user intervention. The main contributions of this article are threefold: first, based on an adaptive scale-invariant feature transform algorithm, a robust approach for feature extraction and matching is proposed. Second, an adaptation of the non-linear H∞ filtering scheme is presented to the VSLAM problem, for which a 3D vision-based observation model is suggested. This filtering scheme avoids issues linked with the classical extended Kalman filtering techniques such as linearization errors, initialization problems, and noise statistics assumptions. Finally, a reliable map management approach, based on the k-nearest landmark concept, is presented to allow efficient loop closing detection and map building. This approach reduces significantly the complexity of the airborne VSLAM algorithm by making it independent of the landmark number. Experimental results using real data sets show the performance and the robustness of the proposed airborne VSLAM solution to build a reliable map and localize the unmanned aerial vehicle within this map.

Memory-Efficient Fully Coupled Filtering Approach for Observational Model Building

Generally, training neural networks with the global extended Kalman filter (GEKF) technique exhibits excellent performance at the expense of a large increase in computational costs which can become prohibitive even for networks of moderate size. This drawback was previously addressed by heuristically decoupling some of the weights of the networks. Inevitably, ad hoc decoupling leads to a degradation in the quality (accuracy) of the resultant neural networks. In this paper, we present an algorithm that emulates the accuracy of GEKF, but avoids the construction of the state covariance matrix-the source of the computational bottleneck in GEKF. In the proposed algorithm, all the synaptic weights remain connected while the amount of computer memory required is similar to (or cheaper than) the memory requirements in the decoupling schemes. We also point out that the new method can be extended to derivative-free nonlinear Kalman filters, such as the unscented Kalman filter and ensemble Kalman filters.

A Support Vector Regression Approach for Recursive Simultaneous Data Reconciliation and Gross Error Detection in Nonlinear Dynamical Systems

The quality of process data in a chemical plant significantly affects the performance and benefits gained from activities like performance monitoring, online optimization, and control. Since many chemical processes often show nonlinear dynamics, techniques like extended Kalman filter (EKF) and nonlinear dynamic data reconciliation (NDDR) have been developed to improve the data quality. Recently, the recursive nonlinear dynamic data reconciliation (RNDDR) technique has been proposed, which combines the merits of EKF and NDDR techniques. However, the RNDDR technique cannot handle measurements with gross errors. In this paper, a support vector (SV) regression approach for recursive simultaneous data reconciliation and gross error detection in nonlinear dynamical systems is proposed. SV regression is a compromise between the empirical risk and the model complexity, and for data reconciliation it is robust to random and gross errors. By minimizing the regularized risk instead of the maximum likelihood in the RNDDR, our approach could achieve not only recursive nonlinear dynamic data reconciliation but also gross error detection simultaneously. The nonlinear dynamic system simulation results in this paper show that the proposed approach is robust, efficient, stable, and accurate for simultaneous data reconciliation and gross error detection in nonlinear dynamic systems within a recursive real-time estimation framework. It can also give better performance of control.

The applicability of a small autonomous vehicle towed array system to ocean acoustic measurements and signal processing

An array was developed to demonstrate, and quantify the performance characteristics of an autonomous-vehicle towed-array system. This technology provides for a cost effective tool for the measurement of coherent signal propagation, depth dependent and directional noise fields and to establish quantitative limits on array performance. The tangential drag on a forty-meter length array composed of a reinforced tube with an outer diameter of 2.8 cm is extrapolated to be between 20-28 N for diameter Reynold's number of approximately 40k. The hydrophone- preamplifier groups have a sensitivity of −174 {plus minus} 1.5 dB re 1μPa/V between 100 Hz to 10 kHz. with an adjustable spacing between 0.5 and 1.5m. The system tow stability enabled the use of the synthetic Hankel transform to estimate the modal horizontal wave number spectrum and the identification of interface wave speeds at frequencies up to 1000 Hz.. The formation of synthetic apertures combined with model based extended Kalman filter techniques was found to demonstrate both narrow band and broadband tracking. Finally the system is shown to provide a unique measurement capability for directional noise measurement in shallow water environments.

Application of Particle Filtering for Estimating the Dynamics of Nuclear Systems

System dynamics estimation is a crucial issue for the safe operation and control of nuclear power plants. Typically, the estimation is based on a model of the plant dynamics and related measurements. In practice, the non-linearity of the dynamics and non-Gaussianity of the noise associated to the process and measurements lead to inaccurate results even with advanced approaches, such as the Kalman, Gaussian-sum and grid-based filters. On the contrary, accurate results may be obtained with Monte Carlo-based estimation methods, also called particle filters. The present paper illustrates the developments of a previous work by the same authors with regards to the comparison of the so called sampling importance resampling filter method with the standard and extended Kalman filtering techniques. Two case studies are analyzed to separately highlight the effect of non-linearity and non-Gaussianity in the process noise.

Experimental Evaluation of Braided EKF for Sensorless Control of Induction Motors

Temperature- and frequency-dependent variations of the rotor (R'r) and stator (Rs) resistances pose a challenge in the accurate estimation of flux and velocity in the sensorless control of induction motors (IMs) over a wide speed range. Solutions have been sought to the problem by signal injection and/or by the use of different algorithms for the different parameters and states of the same motor. In this paper, a novel Extended-Kalman-Filter (EKF)-based estimation technique is developed for the solution of the problem based on the consecutive operation of two EKF algorithms at every time step. The proposed ldquobraidedrdquo EKF technique is experimentally tested under challenging parameter and load variations in a wide speed range, including low speed. The results demonstrate a significantly increased accuracy in the estimation of Rs and R'r, as well as load torque, flux, and velocity in transient and steady state, when compared with single EKFs or other approaches taken to estimate these parameters and states in the sensorless control of IMs. The improved results also motivate the utilization of the new estimation approach in combination with a variety of control methods which depend on accurate knowledge of a high number of parameters and states.

Adaptive Carrier Synchronization Using Decision-Aided Kalman Filtering Algorithms

A new adaptive carrier recovery algorithm is proposed by using the decision-aided extended Kalman filtering technique. In order to reduce computational complexity of the Kalman recursions, the state model in the new algorithm uses only phase rather than both phase and frequency which are usually used in conventional modeling. The frequency is considered as an input term to the system equation and estimated by a phase error detector. A reduced observation model is also introduced to relieve computing load from multiple matrix to scalar operations in the Kalman recursions. Simulations show that the proposed one-state Kalman algorithm has better performance and lower complexity than the two-state Kalman algorithm for synchronization applications. The new algorithm is applied to the cable modem downstream system to demonstrate its effectiveness with FPGA implementation results.

Robust and reliable estimation via Unscented Recursive Nonlinear Dynamic Data Reconciliation

The quality of process data in a chemical plant significantly affects the performance and benefits gained from activities like performance monitoring, online optimization and control. Since many chemical processes often exhibit nonlinear dynamics, techniques like Extended Kalman Filter (EKF) and Nonlinear Dynamic Data Reconciliation (NDDR) have been developed to improve the data quality. There are various issues that arise with the use of either of these techniques: EKF cannot handle inequality or equality constraints, while the NDDR has high computational cost. Recently a recursive estimation technique for nonlinear dynamic processes has been proposed which combines the merits of EKF and NDDR techniques. This technique, named as Recursive Nonlinear Dynamic Data Reconciliation (RNDDR), provides state and parameter estimates that satisfy bounds and other constraints imposed on them. However, the estimate error covariance matrix in RNDDR is computed in the same manner as in EKF, that is, the effects of both nonlinearity and constraints are neglected in the computation of the estimate error covariance matrix. A relatively new method known as the Unscented Kalman Filter has been developed for nonlinear processes, in which the statistical properties of the estimates are computed without resorting to linearization of the nonlinear equations. This leads to improved accuracy of the estimates. In this paper, we combine the merits of the Unscented Kalman Filter and the RNDDR to obtain the Unscented Recursive Nonlinear Dynamic Data Reconciliation (URNDDR) technique. This technique addresses all concerns arising due to the presence of nonlinearity and constraints within a recursive estimation framework, resulting in an efficient, accurate and stable method for real-time state and parameter estimation for nonlinear dynamic processes.

Dual extended Kalman filter for vehicle state and parameter estimation

The article demonstrates the implementation of a model-based vehicle estimator, which can be used for combined estimation of vehicle states and parameters. The estimator is realised using the dual extended Kalman filter (DEKF) technique, which makes use of two Kalman filters running in parallel, thus ‘splitting’ the state and parameter estimation problems. Note that the two problems cannot be entirely separated due to their inherent interdependencies. This technique provides several advantages, such as the possibility to switch off the parameter estimator, once a sufficiently good set of estimates has been obtained. The estimator is based on a four-wheel vehicle model with four degrees of freedom, which accommodates the dominant modes only, and is designed to make use of several interchangeable tyre models. The paper demonstrates the appropriateness of the DEKF. Results to date indicate that this is an effective approach, which is considered to be of potential benefit to the automotive industry.

Dynamic State Estimation of Power System Harmonics with Bad Data

In this article, a robust extended Kalman filter (REKF) technique is proposed for dynamic harmonic state estimation. The proposed state estimator is capable of estimating the harmonic states of the power system in real time even in the presence of bad data in the measurements. From the simulation results obtained from IEEE 14 bus test system under various operating conditions, it has been observed that the estimation performance of the proposed technique is very close to the true simulated values.

Time series analysis in astronomy: Limits and potentialities

In this paper we consider the problem of the limits concerning the physical information that can be extracted from the analysis of one or more time series (light curves) typical of astrophysical objects. On the basis of theoretical considerations and numerical simulations, we show that with no a priori physical model there are not many possibilities to obtain interpretable results. For this reason, the practice to develop more and more sophisticated statistical methods of time series analysis is not productive. Only techniques of data analysis developed in a specific physical context can be expected to provide useful results. The field of stochastic dynamics appears to be an interesting framework for such an approach. In particular, it is shown that modelling the experimental time series by means of the stochastic differential equations (SDE) represents a valuable tool of analysis. For example, besides a more direct connection between data analysis and theoretical models, in principle the use of SDE permits the analysis of a continuous signal independent of the characteristics (e.g., frequency, regularity, ...) of the sampling with which the experimental time series were obtained. In this respect, an efficient approach based on the extended Kalman filter technique is presented. Its performances and limits are discussed and tested through numerical experiments. Freely downloadable software is made available.