Showing papers on "Alpha beta filter published in 2011"

Unscented kalman filter for power system dynamic state estimation

Abstract: A new estimation method for power system dynamic state estimation, the unscented Kalman filter (UKF), is presented. It is based on the application of the unscented transformation (UT) combined with the Kalman filter theory. One of the challenges in the process of power system estimation is coping with a highly non-linear mathematical model of network equations, which is usually approximated through a linearisation. The new derivative free estimation method overcomes this limitation using the UT and achieves better accuracy with simpler implementation. The UKF is derived and demonstrated using three different test power systems under typical network and measurement conditions. Its performance is compared with the classical extended Kalman filter. The simplicity of the new estimator and its low computational demand make it a better option to be applied in the next generation of dynamic system estimators.

Bridging the ensemble Kalman filter and particle filters: the adaptive Gaussian mixture filter

Abstract: The nonlinear filtering problem occurs in many scientific areas. Sequential Monte Carlo solutions with the correct asymptotic behavior such as particle filters exist, but they are computationally too expensive when working with high-dimensional systems. The ensemble Kalman filter (EnKF) is a more robust method that has shown promising results with a small sample size, but the samples are not guaranteed to come from the true posterior distribution. By approximating the model error with a Gaussian distribution, one may represent the posterior distribution as a sum of Gaussian kernels. The resulting Gaussian mixture filter has the advantage of both a local Kalman type correction and the weighting/resampling step of a particle filter. The Gaussian mixture approximation relies on a bandwidth parameter which often has to be kept quite large in order to avoid a weight collapse in high dimensions. As a result, the Kalman correction is too large to capture highly non-Gaussian posterior distributions. In this paper, we have extended the Gaussian mixture filter (Hoteit et al., Mon Weather Rev 136:317–334, 2008) and also made the connection to particle filters more transparent. In particular, we introduce a tuning parameter for the importance weights. In the last part of the paper, we have performed a simulation experiment with the Lorenz40 model where our method has been compared to the EnKF and a full implementation of a particle filter. The results clearly indicate that the new method has advantages compared to the standard EnKF.

An outlier-robust Kalman filter

Abstract: We introduce a novel approach for processing sequential data in the presence of outliers. The outlier-robust Kalman filter we propose is a discrete-time model for sequential data corrupted with non-Gaussian and heavy-tailed noise. We present efficient filtering and smoothing algorithms which are straightforward modifications of the standard Kalman filter Rauch-Tung-Striebel recursions and yet are much more robust to outliers and anomalous observations. Additionally, we present an algorithm for learning all of the parameters of our outlier-robust Kalman filter in a completely unsupervised manner. The potential of our approach is borne out in experiments with synthetic and real data.

Design of a Nonlinear Observer for Vehicle Velocity Estimation and Experiments

Abstract: This brief presents a nonlinear observer for estimating the longitudinal and lateral velocities based on Dugoff's tire model and vehicle dynamics. The observer has a fixed gain structure and can make full use of information about acceleration measurements and nonlinear vehicle model. A sufficient condition is derived to guarantee the stability of the observer, and the robustness of the observer with respect to additive disturbances is analyzed with the help of input-to-state stability theory. The performance of the observer is compared with that of existing approaches and evaluated experimentally under a variety of maneuvers and road conditions.

An Iterative Ensemble Kalman Filter

Abstract: The ensemble Kalman filter is a Monte Carlo method for state estimation of nonlinear models, developed as an alternative or improvement of the extended Kalman filter. In this technical note we introduce an iterative extension to the ensemble Kalman filter. Iterations are introduced to improve the estimates in the cases where the relationship between the model and observations is not linear. The iterations converge, but to a solution where the data are overfitted. An essential stopping criteria is therefore introduced for the proposed method.

Efficient Decoding With Steady-State Kalman Filter in Neural Interface Systems

Abstract: The Kalman filter is commonly used in neural interface systems to decode neural activity and estimate the desired movement kinematics. We analyze a low-complexity Kalman filter implementation in which the filter gain is approximated by its steady-state form, computed offline before real-time decoding commences. We evaluate its performance using human motor cortical spike train data obtained from an intracortical recording array as part of an ongoing pilot clinical trial. We demonstrate that the standard Kalman filter gain converges to within 95% of the steady-state filter gain in 1.5 ± 0.5 s (mean ±s.d.). The difference in the intended movement velocity decoded by the two filters vanishes within 5 s, with a correlation coefficient of 0.99 between the two decoded velocities over the session length. We also find that the steady-state Kalman filter reduces the computational load (algorithm execution time) for decoding the firing rates of 25±3 single units by a factor of 7.0±0.9. We expect that the gain in computational efficiency will be much higher in systems with larger neural ensembles. The steady-state filter can thus provide substantial runtime efficiency at little cost in terms of estimation accuracy. This far more efficient neural decoding approach will facilitate the practical implementation of future large-dimensional, multisignal neural interface systems.

Extended Kalman Filter vs. Error State Kalman Filter for Aircraft Attitude Estimation

Abstract: The Kalman filter (KF) is the optimal estimator that minimizes the mean square error when the state and measurement dynamics are linear in nature, provided the process and measurement noise processes are modeled as white Gaussian. However, in the real world, one encounters a large number of scenarios where either the process or measurement model (or both) are nonlinear. In such cases a class of suboptimal Kalman filter implementations called extended Kalman filters (EKF) are used. EKFs operate by linearizing the nonlinear model around the current reference trajectory and then designing the Kalman filter gain for the linearized model. Recently, an alternative approach has emerged for a certain class of problems where the error in the states is estimated using a Kalman filter, rather than the state itself. This error state KF (ErKF) approach, by deriving the error state dynamics, via the perturbation of the nonlinear plant, lends itself to optimal updates in the error states and optimal prediction and updates in the error state covariance. This is because the error state dynamics are linear, thereby satisfying a condition for optimal Kalman filtering. This paper offers a comparison between the EKF and ErKF via simulations and shows that the ErKF performance is robust to a variety of aircraft maneuvers performed. Furthermore, this paper shows that the ErKF, unlike the EKF, need not be repeatedly tuned with respect to the noise covariances in order to obtain acceptable estimation performance.

A Moment Matching Ensemble Filter for Nonlinear Non-Gaussian Data Assimilation

Abstract: The ensemble Kalman filter is now an important component of ensemble forecasting. While using the linear relationship between the observation and state variables makes it applicable for large systems, relying on linearity introduces nonnegligible bias since the true distribution will never be Gaussian. This paper analyzes the bias of the ensemble Kalman filter from a statistical perspective and proposes a debiasing method called the nonlinear ensemble adjustment filter. This new filter transforms the forecast ensemble in a statistically principled manner so that the updated ensemble has the desired mean and variance. It is also easily localizable and, hence, potentially useful for large systems. Its performance is demonstrated and compared with other Kalman filter and particle filter variants through various experiments on the Lorenz-63 and Lorenz-96 systems. The results show that the new filter is stable and accurate for challenging situations such as nonlinear, high-dimensional systems with spar...

Observer design on the Special Euclidean group SE(3)

Abstract: This paper proposes a nonlinear pose observer designed directly on the Lie group structure of the Special Euclidean group SE(3). We use a gradient-based observer design approach and ensure that the derived observer innovation can be implemented from position measurements. We prove local exponential stability of the error and instability of the non-zero critical points. Simulations indicate that the observer is indeed almost globally stable as would be expected.

State estimation in wall-bounded flow systems. Part 3. The ensemble Kalman filter

Abstract: State estimation of turbulent near-wall flows based on wall measurements is one of the key pacing items in model-based flow control, with low- Re channel flow providing the canonical testbed. Model-based control formulations in such settings are often separated into two subproblems: estimation of the near-wall flow state via skin friction and pressure measurements at the wall, and (based on this estimate) control of the near-wall flow field fluctuations via actuation of the fluid velocity at the wall. In our experience, the turbulent state estimation sub-problem has consistently proven to be the more difficult of the two. Though many estimation strategies have been tested on this problem (by our group and others), none have accurately captured the turbulent flow state at the outer boundary of the buffer layer (5 ≤ y + ≤ 30), which is deemed to be an important milestone, as this is the approximate range of the characteristic near-wall turbulent structures, the accurate estimation of which is important for the control problem. Leveraging the ensemble Kalman filter (an effective variant of the Kalman filter which scales well to high-dimensional systems), the present paper achieves at least an order of magnitude improvement (in the near-wall region) over the best results available in the published literature on the estimation of low-Reynolds number turbulent channel flow based on wall information alone.

Cubature information filter and its applications

Abstract: This paper presents a new estimation algorithm called cubature information filtering for nonlinear systems. The proposed algorithm is developed from an extended information filter and a recently developed cubature Kalman filter. Unlike the extended Kalman filter, the proposed filter does not require the evaluation of Jacobians during state estimation. The efficacy of the proposed algorithm is demonstrated by simulation examples on frequency demodulation and localization problem and is compared with unscented information filtering.

Phase and amplitude imaging from noisy images by Kalman filtering.

Abstract: We propose and demonstrate a computational method for complex-field imaging from many noisy intensity images with varying defocus, using an extended complex Kalman filter. The technique offers dynamic smoothing of noisy measurements and is recursive rather than iterative, so is suitable for adaptive measurements. The Kalman filter provides near-optimal results in very low-light situations and may be adapted to propagation through turbulent, scattering, or nonlinear media.

A Novel Delta Operator Kalman Filter Design and Convergence Analysis

Abstract: This paper focuses on the development of a delta operator Kalman filter and its convergence analysis. The delta operator Kalman filter is designed to estimate the state vectors of a delta operator system. Note that the designed delta operator Kalman filter can express both continuous-time and discrete-time cases. Then, the convergence analysis of the delta operator Kalman filter is also investigated by using Lyapunov approach in delta domain. Furthermore, this paper gives fundamental results for the analysis and application of the delta operator Kalman filter as a state observer in an inverted pendulum model. Some experimental results of an inverted pendulum on a laboratory-scale setup are presented to illustrate the effectiveness of the designed Kalman filter and its implementation.

Robust Ensemble Filtering and Its Relation to Covariance Inflation in the Ensemble Kalman Filter

Abstract: A robust ensemble filtering scheme based on the H∞ filtering theory is proposed. The optimal H∞ filter is derived by minimizing the supremum (or maximum) of a predefined cost function, a criterion different from the minimum variance used in the Kalman filter. By design, the H∞ filter is more robust than the Kalman filter, in the sense that the estimation error in the H∞ filter in general has a finite growth rate with respect to the uncertainties in assimilation, except for a special case that corresponds to the Kalman filter.The original form of the H∞ filter contains global constraints in time, which may be inconvenient for sequential data assimilation problems. Therefore a variant is introduced that solves some time-local constraints instead, and hence it is called the time-local H∞ filter (TLHF). By analogy to the ensemble Kalman filter (EnKF), the concept of ensemble time-local H∞ filter (EnTLHF) is also proposed. The general form of the EnTLHF is outlined, and some of its special cases are di...

On the Kalman Filter error covariance collapse into the unstable subspace

Abstract: . When the Extended Kalman Filter is applied to a chaotic system, the rank of the error covariance matrices, after a sufficiently large number of iterations, reduces to N+ + N0 where N+ and N0 are the number of positive and null Lyapunov exponents. This is due to the collapse into the unstable and neutral tangent subspace of the solution of the full Extended Kalman Filter. Therefore the solution is the same as the solution obtained by confining the assimilation to the space spanned by the Lyapunov vectors with non-negative Lyapunov exponents. Theoretical arguments and numerical verification are provided to show that the asymptotic state and covariance estimates of the full EKF and of its reduced form, with assimilation in the unstable and neutral subspace (EKF-AUS) are the same. The consequences of these findings on applications of Kalman type Filters to chaotic models are discussed.

An efficient implementation of the second order extended Kalman filter

Abstract: The second order extended Kalman filter (EKF2) is based on a second order Taylor expansion of a nonlinear system, in contrast to the more common (first order) extended Kalman filter (EKF1). Despite a solid theoretical ground for its approximation, it is seldom used in applications, where the EKF and the unscented Kalman filter (UKF) are the standard algorithms. One reason for this might be the requirement for analytical Jacobian and Hessian of the system equations, and the high complexity that scales with the state order n x as n5 x . We propose a numerical algorithm which is based on an extended set of sigma points (compared to the UKF) that needs neither Jacobian nor Hessian (or numerical approximations of these). Further, it scales as n4 x , which is an order of magnitude better than the EKF2 algorithm presented in literature.

An adaptive observer for joint estimation of states and parameters in both state and output equations

Abstract: An adaptive observer is a recursive algorithm for joint state–parameter estimation of parameterized state-space systems Previous works on globally convergent adaptive observers consider unknown parameters either in state equations or in output equations, but not in both of them In this paper, a new adaptive observer is designed for linear time-varying systems with unknown parameters in both state and output equations Its global convergence for simultaneous estimation of states and parameters is formally established under appropriate assumptions A numerical example is presented to illustrate the performance of this adaptive observer Copyright © 2011 John Wiley & Sons, Ltd

A critical evaluation and experimental verification of Extended Kalman Filter, Unscented Kalman Filter and Neural State Filter for state estimation of three phase induction motor

Abstract: This paper deals with the design and implementation of Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Neural State Filter (NSF) for the state estimation of a three-phase induction motor. Extensive simulation studies have been carried out to assess the relative performance of the three filters under various machine operating conditions and model uncertainties. Filter performance for similar conditions was verified with experimental data and found to be consistent with simulation results. The simulation and experimental results indicate that for most conditions EKF estimates are better than UKF while error in NSF estimates is large. However NSF performance is relatively better than other two filters for specific condition like large parameter uncertainty.

Kalman filter-based disturbance observer and its applications to sensorless force control

Abstract: Force estimation plays a very important role in many application areas. The disturbance observer is significantly becoming the preferred approach since it offers distinct advantages of improving the robustness of force control and the accuracy of force estimation. However, one of the main disadvantages is the limitation from white Gaussian noise. This paper proposes an improved design methodology for the disturbance observer. The main contribution of the work described in this paper is the design of disturbance observers combined with a Kalman filter with a multisensor system. From the experimental results, white Gaussian noise was reduced and fast response in contact motion was achieved. The effectiveness of the proposed disturbance observer has been confirmed through comparisons with conventional methods in 1-d.o.f. linear motor systems.

Adaptive Kalman filtering for closed-loop Brain-Machine Interface systems

Abstract: Brain-Machine Interface (BMI) decoding algorithms are often trained offline, but this paradigm ignores both the non-stationarity of neural signals and the feedback that exists in online, closed-loop control. To address these problems, we have developed an Adaptive Kalman Filter (AKF), a Kalman filter variant that adaptively updates its model parameters during training. For a Kalman filter decoder, batch retraining methods require completely re-estimating the parameter matrices from sufficient data to perform regression accurately, even if only small changes are necessary. Conversely, the AKF is designed to update the decoder parameters continuously and more intelligently. We simulated a population of 41 neurons learning to control a 2D computer cursor. The AKF yielded significantly faster skill acquisition and better robustness to perturbation and neuron loss than a standard Kalman filter with periodic batch retraining.

A Probabilistic Collocation-Based Kalman Filter for History Matching

Abstract: Original SPE manuscript received for review 17 January 2010. Revised manuscript received for review 9 May 2010. Paper (SPE 140737) peer approved 13 July 2010. Summary The ensemble Kalman filter (EnKF) has been used widely for data assimilation. Because the EnKF is a Monte Carlo-based method, a large ensemble size is required to reduce the sampling errors. In this study, a probabilistic collocation-based Kalman filter (PCKF) is developed to adjust the reservoir parameters to honor the production data. It combines the advantages of the EnKF for dynamic data assimilation and the polynomial chaos expansion (PCE) for efficient uncertainty quantification. In this approach, all the system parameters and states and the production data are approximated by the PCE. The PCE coefficients are solved with the probabilistic collocation method (PCM). Collocation realizations are constructed by choosing collocation point sets in the random space. The simulation for each collocation realization is solved forward in time independently by means of an existing deterministic solver, as in the EnKF method. In the analysis step, the needed covariance is approximated by the PCE coefficients. In this study, a square-root filter is employed to update the PCE coefficients. After the analysis, new collocation realizations are constructed. With the parameter collocation realizations as the inputs and the state collocation realizations as initial conditions, respectively, the simulations are forwarded to the next analysis step. Synthetic 2D water/oil examples are used to demonstrate the applicability of the PCKF in history matching. The results are compared with those from the EnKF on the basis of the same analysis. It is shown that the estimations provided by the PCKF are comparable to those obtained from the EnKF. The biggest improvement of the PCKF comes from the leading PCE approximation, with which the computational burden of the PCKF can be greatly reduced by means of a smaller number of simulation runs, and the PCKF outperforms the EnKF for a similar computational effort. When the correlation ratio is much smaller, the PCKF still provides estimations with a better accuracy for a small computational effort.