Showing papers on "Alpha beta filter published in 2014"

Minimal Invasive Equivalent Grid Impedance Estimation in Inductive–Resistive Power Networks Using Extended Kalman Filter

Abstract: Real-time estimation of the equivalent grid impedance and the equivalent grid voltage seen from a power converter connected to the public electric distribution network by means of extended Kalman filter is addressed. The theoretical background of the extended Kalman filter used for equivalent grid impedance estimation is introduced. Practical aspects like the use of the filter in an environment with highly distorted voltage waveforms, the tuning of the noise covariance matrices, and the implementation on a laboratory system are discussed. The theoretical analysis is verified on a 22-kW test-bench where a grid impedance emulator is used to simulate grid impedance steps in the laboratory environment. The proposed extended Kalman filter is designed to utilize the noise that is already present at the connection point of the power converter to overcome the need of active disturbance injection to estimate the equivalent grid impedance. Thus, electrical equipment connected close to the grid-connected converter is only affected marginally by the equivalent grid impedance estimation technique.

Bearing Degradation Evaluation Using Recurrence Quantification Analysis and Kalman Filter

Abstract: This paper presents an integrated approach, which combines recurrence quantification analysis (RQA) with the Kalman filter, for bearing degradation evaluation. The RQA, a nonlinear signal processing method, is applied to extracting recurrence plot entropy features from vibration signals as input to build an autoregression (AR) model. This AR model is used to estimate parameters of the dynamic model of the bearing, and the Kalman filter is then utilized to obtain optimal prediction results on the bearing degradation state from its dynamic model. Case studies performed on two test-to-failure experiments indicate that the presented approach can predict occurrence of the bearing failure 50 min in advance.

Accurate Numerical Implementation of the Continuous-Discrete Extended Kalman Filter

Abstract: This paper addresses an accurate and effective implementation of the continuous-discrete extended Kalman filtering method. The technique under discussion is grounded in numerical solution of the moment differential equations to predict the state mean of the stochastic dynamical system and the corresponding error covariance matrix. Here, we apply an efficient embedded Runge-Kutta pair possessing superior stability and many other attractive features, including automatic global error control, in order to improve performance of the complex computational procedure consisting of the extended Kalman filter and the underlying adaptive ODE solver. Thus, we introduce a new continuous-discrete adaptive extended Kalman filter and show its advantage over the standard variant on two test examples. In practice, this technique allows for much longer sampling intervals without any loss of accuracy, and that improves the applied potential of the extended Kalman filtering method, significantly.

A Two-Stage Kalman Filter Approach for Robust and Real-Time Power System State Estimation

Abstract: As electricity demand continues to grow and renewable energy increases its penetration in the power grid, real-time state estimation becomes essential for system monitoring and control. Recent development in phasor technology makes it possible with high-speed time-synchronized data provided by phasor measurement units (PMUs). In this paper, we present a two-stage Kalman filter approach to estimate the static state of voltage magnitudes and phase angles, as well as the dynamic state of generator rotor angles and speeds. Kalman filters achieve optimal performance only when the system noise characteristics have known statistical properties (zero-mean, Gaussian, and spectrally white). However, in practice, the process and measurement noise models are usually difficult to obtain. Thus, we have developed the adaptive Kalman filter with inflatable noise variances (AKF with InNoVa), an algorithm that can efficiently identify and reduce the impact of incorrect system modeling and/or erroneous measurements. In stage one, we estimate the static state from raw PMU measurements using the AKF with InNoVa; then in stage two, the estimated static state is fed into an extended Kalman filter to estimate the dynamic state. The simulations demonstrate its robustness to sudden changes of system dynamics and erroneous measurements.

Kalman and smooth variable structure filters for robust estimation

Abstract: The extended Kalman filter (EKF) and the unscented Kalman filter (UKF) are among the most popular estimation methods. The smooth variable structure filter (SVSF) is a relatively new sliding mode estimator. In an effort to use the accuracy of the EKF and the UKF and the robustness of the SVSF, the filters have been combined, resulting in two new estimation strategies, called the EK-SVSF and the UK-SVSF, respectively. The algorithms were validated by testing them on a well-known target tracking computer experiment.

Continuous-Discrete Time Observers for a Class of MIMO Nonlinear Systems

Abstract: This technical note addresses the observer design problem for a class of continuous-time dynamical systems with non-uniformly sampled measurements. More specifically, we propose an observer that runs in continuous-time with an output error correction term that is updated in a mixed continuous-discrete fashion. The proposed observer is actually an impulsive system since it is described by a set of differential equations with instantaneous state impulses corresponding to the measured samples and their estimates. Nevertheless, we shall show that such an impulsive system can be put under the form of a hybrid system composed of a continuous-time high gain observer coupled with an inter-sample output predictor. Two design features of the proposed observer are worth emphasizing. Firstly, the observer calibration is achieved through the tuning of a scalar design parameter. Secondly, the exponential convergence to zero of the observation error is established under a well-defined condition on the maximum value of the sampling partition diameter. Simulations results involving a flexible joint robot arm are given in order to highlight the performance of the proposed observer.

A Class of Quaternion Kalman Filters

Abstract: The existing Kalman filters for quaternion-valued signals do not operate fully in the quaternion domain, and are combined with the real Kalman filter to enable the tracking in 3-D spaces. Using the recently introduced HR-calculus, we develop the fully quaternion-valued Kalman filter (QKF) and quaternion-extended Kalman filter (QEKF), allowing for the tracking of 3-D and 4-D signals directly in the quaternion domain. To consider the second-order noncircularity of signals, we employ the recently developed augmented quaternion statistics to derive the widely linear QKF (WL-QKF) and widely linear QEKF (WL-QEKF). To reduce computational requirements of the widely linear algorithms, their efficient implementation are proposed and it is shown that the quaternion widely linear model can be simplified when processing 3-D data, further reducing the computational requirements. Simulations using both synthetic and real-world circular and noncircular signals illustrate the advantages offered by widely linear over strictly linear quaternion Kalman filters.

Sensorless Control of Distributed Power Generators With the Derivative-Free Nonlinear Kalman Filter

Abstract: A control method for distributed interconnected power generation units is developed. The power system comprises permanent-magnet synchronous generators (PMSGs), which are connected to each other through transformers and tie-lines. A derivative-free nonlinear Kalman filtering approach is introduced aiming at implementing sensorless control of the distributed power generators. In the proposed derivative-free Kalman filtering method, the generator's model is first subjected to a linearization transformation that is based on differential flatness theory and next state estimation is performed by applying the standard Kalman filter recursion to the linearized model. Unlike Lie algebra-based estimator design methods, the proposed approach provides estimates of the state vector of the PMSG without the need for derivatives and Jacobian calculation. Moreover, by redesigning the proposed derivative-free nonlinear Kalman filter as a disturbance observer, it is possible to estimate at the same time the nonmeasurable elements of each generator's state vector, the unknown input power (torque), and the disturbance terms induced by interarea oscillations. The efficient real-time estimation of the aggregate disturbance that affects each local generator makes possible to introduce a counterdisturbance control term, thus maintaining the power system on its nominal operating conditions.

EKF/UKF Maneuvering Target Tracking using Coordinated Turn Models with Polar/Cartesian Velocity

Abstract: Nonlinear Kalman filter adaptations such as extended Kalman filters (EKF) or unscented Kalman filters (UKF) provide approximate solutions to state estimation problems in nonlinear models. The algorithms utilize mean values and covariance matrices to represent the probability densities in the otherwise intractable Bayesian filtering equations. As a consequence, their estimation performance can show significant dependence on the choice of state coordinates. The here considered problem of tracking maneuvering targets using coordinated turn (CT) models is one practically relevant example: The velocity in the target state can either be formulated in Cartesian or polar coordinates. We extend a previous study to a broader range of CT models that allow for changes in target speed and turn rate, and investigate UKF as well as EKF variants in terms of their performance and sensitivity to noise parameters. The results advocate for the use of polar CT models.

FPGA-Based High-Performance Force Control System With Friction-Free and Noise-Free Force Observation

Abstract: In this paper, a novel force-sensing method is proposed for a high-performance force control system based on friction-free and noise-free force observation. A periodic signal is inserted into the control system for friction reduction. A combination of a high-order disturbance observer (DOB) (HDOB) and a Kalman filter is constructed to perform the force sensing. The HDOB is designed to estimate the force and reject oscillatory disturbances in the estimation. The force-sensing bandwidth is improved through effective noise suppression by the Kalman filter. Additionally, this paper proposes the application of the HDOB to the bilateral control system of a different master-slave mechanism. All the control algorithms are implemented in a field-programmable gate array with a high sampling rate that also enables the widening of the bandwidth of the force control system. The effectiveness of the proposed method is verified by experimental results.

Interval observer composed of observers for nonlinear systems

Abstract: For a family of continuous-time nonlinear systems with input, output and uncertain terms, a new interval observer design is proposed. The main feature of the constructed interval observer is that it is composed of two copies of a classical observer whose corresponding error equations are, in general, not cooperative. The interval observer is globally asymptotically stable under an appropriate choice of dynamic output feedback which uses the values of the output and the bounds provided by the interval observer itself.

Robustness and Sensitivity Metrics for Tuning the Extended Kalman Filter

Abstract: In this paper, a robustness metric and a sensitivity metric have been defined, which can be used to determine a suitable combination of the filter tuning parameters of the extended Kalman filter. These metrics are related to the innovation covariance and their derivation necessitates a change of paradigm from the estimated states to the estimated measurements. The characteristics of these metrics have been inferred in detail and these have been used to predict the root-mean-squared error (RMSE) performances in a 2-D falling body problem. To do so, a general method has been proposed in this paper to obtain an initial choice of the filter tuning parameters based on the available literature. The RMSE performances are then obtained for a range of variation of the most critical tuning parameter, namely the filter process noise covariance. In general, the characteristics predicted from the metrics correlate significantly with the RMSE performances, and hence these can be used to obtain the desired tradeoff between robustness and sensitivity in various filter applications.

Estimation of saturated data using the Tobit Kalman filter

Abstract: Saturated, clipped or censored data arises in multiple engineering applications including sensors systems and image based tracking. The saturation limits of a measurement consist of an upper limit and lower limit on the measurements. When a measurement is near a saturated region or in saturated region a standard Kalman filter will be biased and unable to track the true states. In this paper, we use a novel formulation of the Kalman filter for Tobit Type 1 censored measurements. The proposed formulation, called the Tobit Kalman filter for saturated data, converges to the standard Kalman filter in the no-censoring case. A motivating example is presented to demonstrate the usefulness of an estimator for censored data.

Stochastically resilient extended Kalman filtering for discrete-time nonlinear systems with sensor failures

Abstract: Missing sensor data is a common problem, which severely influences the overall performance of modern data-intensive control and computing applications. In order to address this important issue, a novel resilient extended Kalman filter is proposed for discrete-time nonlinear stochastic systems with sensor failures and random observer gain perturbations. The failure mechanisms of multiple sensors are assumed to be independent of each other with different failure rates. The locally unbiased robust minimum mean square filter is designed for state estimation under these conditions. The performance of the proposed estimation method is verified by means of numerical Monte Carlo simulation of two different nonlinear stochastic systems, involving a sinusoidal system and a Lorenz oscillator system.

Fault detection in non-linear systems based on GP-EKF and GP-UKF algorithms

Abstract: In this paper, two new fault detection methods are proposed for non-linear systems. The proposed methods are based on combining an extended Kalman filter (EKF) and an unscented Kalman filter (UKF) with Gaussian processes (GPs). One of the major advantages of these algorithms is that they do not need the system's model while they have an accurate and fast operation in fault detection. In order to show the promising performance of the proposed algorithms, they are applied to an aeroplane tracking system with a highly non-linear dynamics. Superiority of the GP-UKF over GP-EKF in fault detection is also shown based on the simulation results.

Descriptor-Type Kalman Filter and TLS EXIN Speed Estimate for Sensorless Control of a Linear Induction Motor

Abstract: This paper proposes a speed observer for linear induction motors (LIMs), which is composed of two parts: 1) a linear Kalman filter (KF) for the online estimation of the inductor currents and induced part flux linkage components; and 2) a speed estimator based on the total least squares (TLS) EXIN neuron. The TLS estimator receives as inputs the state variables, estimated by the KF, and provides as output the LIM linear speed, which is fed back to the KF and the control system. The KF is based on the classic space-vector model of the rotating induction machine. The end effects of the LIMs have been considered an uncertainty treated by the KF. The TLS EXIN neuron has been used to compute, in recursive form, the machine linear speed online since it is the only neural network able to solve online, in a recursive form, a TLS problem. The proposed KF TLS speed estimator has been tested experimentally on a suitably developed test setup, and it has been compared with the classic extended KF.

Invariant particle filtering with application to localization

Abstract: The recently introduced Invariant Extended Kalman Filter (IEKF) is an extended Kalman filter designed for systems admitting symmetries, that possesses interesting convergence properties, and a relative independence of the filter behavior with respect to the system's trajectory. In the present paper, the ideas are extended to a broad class of systems introducing the notion of “conditional invariance”, that is, invariance properties of the system once some of the state variables are known. We exploit this structure by devising an Invariant Rao-Blackwellized Particle Filter: those state variables are sampled, and the rest are marginalized out using IEKFs. The striking property of the obtained particle filter is that the Kalman gains are identical for all particles, leading to a drastic reduction of the computational burden. The strong potential of the method is illustrated by the challenging and realistic problem of localization from noisy inertial sensors and a noisy GPS having a randomly jumping bias.

Cascade synthesis of a state observer with nonlinear correcting influences

Abstract: For the synthesis problem for an invariant tracking system for a nonlinear automated control object under incomplete measurements, we develop a decompositional procedure of observer state synthesis with sigmoidal correcting influences in order to get current estimates of the unmeasured state variables and existing uncertainties. This observer in the pre-limit situation possesses the advantages of an observer with discontinuous correcting influences operating in sliding mode; in particular, it lets us estimate external influences without introducing their dynamical model. Unlike a sliding mode observer whose order has been extended due to filters over discontinuous correcting influences, the dimension of this observer equals the dimension of the control object, and in a microprocessor implementation this observer ensures better quality (smoothness) of the signals being estimated.

Observer design for differentiable Lipschitz nonlinear systems with time-varying parameters

Abstract: This paper develops observer design techniques in a unified framework for both time invariant and parameter varying Lipschitz nonlinear systems that are differentiable w.r.t. state variables. First, a new sufficient condition for asymptotic convergence is developed for both the extended Luenberger observer and a two-DOF nonlinear observer for time-invariant nonlinear systems. In addition to ensuring asymptotic convergence, extension of this observer design technique to optimization of a L2 performance criterion is presented, which enables the observer to handle the unknown disturbance inputs as well as ensure robustness to model uncertainty. Next, augmentation of this technique to parameter varying nonlinear (PVNL) systems is developed. Different from methods suggested in the LPV literature, a simple but non-conservative finite dimensional relaxation method for quadratic parameter dependent LMIs is presented. These results constitute perhaps the first systematic observer design methodology in literature for PVNL systems. Finally, a simulation result for vehicle slip angle estimation is presented to verify the performance of the developed observer design methods.

Synchronization of the fractional-order chaotic system via adaptive observer

Abstract: The means to design the observer for a class of fractional-order chaotic systems is investigated. A novel Lyapunov function is proposed and a robust adaptive observer is designed to synchronize a given fractional-order chaotic system. The constructed observer could guarantee the error of state converges to zero asymptotically. Simulation results demonstrate the effectiveness and robustness of the proposed scheme.