Showing papers on "Alpha beta filter published in 2017"

A Robust Iterated Extended Kalman Filter for Power System Dynamic State Estimation

Abstract: This paper develops a robust iterated extended Kalman filter (EKF) based on the generalized maximum likelihood approach (termed GM-IEKF) for estimating power system state dynamics when subjected to disturbances. The proposed GM-IEKF dynamic state estimator is able to track system transients in a faster and more reliable way than the conventional EKF and the unscented Kalman filter (UKF) thanks to its batch-mode regression form and its robustness to innovation and observation outliers, even in position of leverage. Innovation outliers may be caused by impulsive noise in the dynamic state model while observation outliers may be due to large biases, cyber attacks, or temporary loss of communication links of PMUs. Good robustness and high statistical efficiency under Gaussian noise are achieved via the minimization of the Huber convex cost function of the standardized residuals. The latter is weighted via a function of robust distances of the two-time sequence of the predicted state and innovation vectors and calculated by means of the projection statistics. The state estimation error covariance matrix is derived using the total influence function, resulting in a robust state prediction in the next time step. Simulation results carried out on the IEEE 39-bus test system demonstrate the good performance of the GM-IEKF under Gaussian and non-Gaussian process and observation noise.

The Invariant Extended Kalman Filter as a Stable Observer

Abstract: We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic nonlinear observer on Lie groups, for continuous-time systems with discrete observations. One of the main features of invariant observers for left-invariant systems on Lie groups is that the estimation error is autonomous. In this paper we first generalize this result by characterizing the (much broader) class of systems for which this property holds. For those systems, the Lie logarithm of the error turns out to obey a linear differential equation. Then, we leverage this “log-linear” property of the error evolution, to prove for those systems the local stability of the IEKF around any trajectory, under the standard conditions of the linear case. One mobile robotics example and one inertial navigation example illustrate the interest of the approach. Simulations evidence the fact that the EKF is capable of diverging in some challenging situations, where the IEKF with identical tuning keeps converging.

Experimental validation of the Kalman-type filters for online and real-time state and input estimation:

Abstract: In this study, a novel dual implementation of the Kalman filter proposed by Eftekhar Azam et al. (2014, 2015) is experimentally validated for simultaneous estimation of the states and input of structural systems. By means of numerical simulations, it has been shown that the proposed method outperforms existing techniques in terms of robustness and accuracy for the estimated displacement and velocity time histories. Herein, dynamic response measurements, in the form of displacement and acceleration time histories from a small-scale laboratory building structure excited at the base by a shake table, are considered for evaluating the performance of the proposed Dual Kalman filter and in order to compare this with available alternatives, such as the augmented Kalman filter (Lourens et al., 2012b) and the Gillijn De Moore filter (GDF) (2007b). The suggested Bayesian approach requires the availability of a physical model of the system in addition to output-only measurements from limited degrees of freedom. Two ...

Distributed state estimation, fault detection and isolation filter design for heterogeneous multi-agent linear parameter-varying systems

Abstract: In this study, the authors present a new approach for the design of distributed state estimation and fault detection and isolation (FDI) filters for a class of linear parameter-varying multi-agent systems, where the state-space representations of the agents are not identical. The developed formulation for the FDI offers a distributed filter design method, in which each agent uses sensor measurements both locally and from the neighbouring agents. Each FDI filter is in the ‘unknown input observer’ form which are designed so that their outputs, i.e. residual signals, are: (i) robust with respect to the external disturbance inputs and (ii) sensitive with respect to the fault signals. Moreover, it is shown that using the proposed methodology each agent is able to estimate not only its own states, but also states of its nearest neighbours in the presence of external disturbances and faults. Finally, a numerical example is given to illustrate the efficacy of the main results of the paper.

A New Quaternion-Based Kalman Filter for Real-Time Attitude Estimation Using the Two-Step Geometrically-Intuitive Correction Algorithm

Abstract: In order to reduce the computational complexity, and improve the pitch/roll estimation accuracy of the low-cost attitude heading reference system (AHRS) under conditions of magnetic-distortion, a novel linear Kalman filter, suitable for nonlinear attitude estimation, is proposed in this paper. The new algorithm is the combination of two-step geometrically-intuitive correction (TGIC) and the Kalman filter. In the proposed algorithm, the sequential two-step geometrically-intuitive correction scheme is used to make the current estimation of pitch/roll immune to magnetic distortion. Meanwhile, the TGIC produces a computed quaternion input for the Kalman filter, which avoids the linearization error of measurement equations and reduces the computational complexity. Several experiments have been carried out to validate the performance of the filter design. The results demonstrate that the mean time consumption and the root mean square error (RMSE) of pitch/roll estimation under magnetic disturbances are reduced by 45.9% and 33.8%, respectively, when compared with a standard filter. In addition, the proposed filter is applicable for attitude estimation under various dynamic conditions.

Current Control of Grid-Connected Inverter With LCL Filter Based on Extended-State Observer Estimations Using Single Sensor and Achieving Improved Robust Observation Dynamics

Abstract: In the context of distributed generation and renewable energy penetration toward smart grid, grid-connected inverter with LCL filter has drawn many attentions, whose current control conventionally requires several sensors to realize active damping and grid synchronization. In this paper, a novel full status observation strategy based on extended state observer (ESO) is proposed using inverter current feedback only and without grid voltage sensor. The proposed observation strategy contains observation and transformation process. Unlike conventional Luenberger observer, by using ESO, the system parameters do not appear in observation process, thus the observer dynamics and parameter mismatch error can be separately handled, providing more robust observation dynamics during parameter variation. Parameter mismatch study was carried out, and it is found that purposely choosing the observer parameters smaller than the real value can achieve relatively low estimation error and a large adaption range for parameter variation. The proposed observation strategy is simple to implement, without the need of expert knowledge-based parameter tuning such as pole placement. Experimental tests validated that the proposed observation-based control is able to give satisfactory performance in both dynamic and steady states, as well as adaption for system parameter variation.

Distributed consensus extended Kalman filter: a variance-constrained approach

Abstract: This study is concerned with the distributed state estimation problem for non-linear systems over sensor networks. By using the strategy of consensus on prior estimates, a distributed extended Kalman filter (EKF) is developed for each node to guarantee an optimised upper bound on the state estimation error covariance despite consensus terms and linearisation errors. The Kalman gain matrix is derived for each node by solving two Riccati-like difference equations. It is shown that the estimation error is bounded in mean square under certain conditions. The effectiveness of the proposed filter is evaluated on an indoor localisation of a mobile robot with visual tracking systems.

Distributed extended Kalman filter with nonlinear consensus estimate

Abstract: This paper is concerned with the distributed filtering problem for discrete-time nonlinear systems over a sensor network. In contrast with the distributed filters with linear consensus estimate, a distributed extended Kalman filter (EKF) is developed with nonlinear consensus estimate. Specifically, a new nonlinear consensus protocol with polynomial form is proposed to generate the consensus estimate. By using the variance-constrained approach, the Kalman gain matrix is determined for each node to guarantee an optimized upper bound on the state estimation error covariance despite consensus terms and linearization errors. It is shown that the Kalman gain matrix can be derived by solving two Riccati-like difference equations. The effectiveness of the proposed filter is evaluated on an indoor localization of a mobile robot with visual tracking systems.

The eXogenous Kalman Filter (XKF)

Abstract: It is well known that the time-varying Kalman Filter (KF) is globally exponentially stable and optimal in the sense of minimum variance under some conditions. However, nonlinear approximations such as the extended KF linearises the system about the estimated state trajectories, leading in general to loss of both global stability and optimality. Nonlinear observers tend to have strong, often global, stability properties. They are, however, often designed without optimality objectives considering the presence of unknown measurement errors and process disturbances. We study the cascade of a global nonlinear observer with the linearised KF, where the estimate from the nonlinear observer is an exogenous signal only used for generating a linearised model to the KF. It is shown that the two-stage nonlinear estimator inherits the global stability property of the nonlinear observer, and simulations indicate that local optimality properties similar to a perfectly linearised KF can be achieved. This two-stag...

Robust Student’s t-Based Stochastic Cubature Filter for Nonlinear Systems With Heavy-Tailed Process and Measurement Noises

Abstract: In this paper, a new robust Student’s t-based stochastic cubature filter (RSTSCF) is proposed for a nonlinear state–space model with heavy-tailed process and measurement noises. The heart of the RSTSCF is a stochastic Student’s t-spherical radial cubature rule (SSTSRCR), which is derived based on the third-degree unbiased spherical rule and the proposed third-degree unbiased radial rule. The existing stochastic integration rule is a special case of the proposed SSTSRCR when the degrees of freedom parameter tends to infinity. The proposed filter is applied to a maneuvering bearings-only tracking example, in which an agile target is tracked and the bearing is observed in clutter. Simulation results show that the proposed RSTSCF can achieve higher estimation accuracy than the existing Gaussian approximate filter, Gaussian sum filter, Huber-based nonlinear Kalman filter, maximum correntropy criterion-based Kalman filter, and robust Student’s t-based nonlinear filters, and is computationally much more efficient than the existing particle filter.

Linear Optimal Unbiased Filter for Time-Variant Systems Without Apriori Information on Initial Conditions

Abstract: In this technical note, an optimal unbiased filter (OUF) is derived for time-variant systems to relax the initial condition assumption in Kalman filter (KF). By minimizing the mean square errors subject to the unbiasedness condition a solution is derived in a batch computation form first. To facilitate the on-line application, a recursive realization is further developed. The effect of removing the initial condition assumption on the estimation performance is analysed, and we show that the proposed algorithm converges to the KF asymptotically. Two-state harmonic model and four-state moving target tracking model are employed to demonstrate that the OUF can improve transient estimation performance significantly and can be used in place of the KF when the apriori information about the initial state values is not available.

Adaptive Sliding Mode Control With Parameter Estimation and Kalman Filter for Precision Motion Control of a Piezo-Driven Microgripper

Abstract: Microgrippers driven by piezoelectric actuators have been widely applied in various fields demanding high accuracy. However, it is challenging to achieve a higher precision due to the presence of hysteresis and disturbances. This brief presents a new approach to achieve a precision motion control by overcoming the mentioned problems. The reported solution is derived by integrating three main components, i.e., the online estimation of unknown parameters for the ideal plant, the position prediction with Kalman filter, and an adaptive sliding mode control algorithm. The estimated parameters converge to their real values, which are guaranteed by Lyapunov criterion. Using the estimated parameters, the position is predicted with the Kalman filter. The adaptive law and the control law are designed based on sliding mode strategy to attenuate the influence of the unknown and unmodeled parts. The stability of the control system is proved by resorting to Lyapunov theorem. The effectiveness of the proposed control approach is verified through simulation and experimental investigations on a prototype gripper device.

State of Charge Estimation for Lithium-Ion Battery Based on Nonlinear Observer: An H∞ Method

Abstract: This work is focused on the state of charge (SOC) estimation of a lithium-ion battery based on a nonlinear observer. First, the second-order resistor-capacitor (RC) model of the battery pack is introduced by utilizing the physical behavior of the battery. Then, for the nonlinear function of the RC model, a one-sided Lipschitz condition is proposed to ensure that the nonlinear function can play a positive role in the observer design. After that, a nonlinear observer design criterion is presented based on the H ∞ method, which is formulated as linear matrix inequalities (LMIs). Compared with existing nonlinear observer-based SOC estimation methods, the proposed observer design criterion does not depend on any estimates of the unknown variables. Consequently, the convergence of the proposed nonlinear observer is guaranteed for any operating conditions. Finally, both the static and dynamic experimental cases are given to show the efficiency of the proposed nonlinear observer by comparing with the classic extended Kalman filter (EKF).

Stochastic Stability Condition for the Extended Kalman Filter With Intermittent Observations

Abstract: In order to tackle the intermittent observations, this brief addresses the stochastic stability problem of the extended Kalman filter by means of analyzing the prediction error covariance matrix (PECM) and the estimation error performance of the estimator. With the transmitted measurement output of the filter modeled as a Bernoulli process, the existence of a crucial arrival rate is proved such that the PECM is mean bounded when the arrival rate exceeds a threshold value. Moreover, offline sufficient conditions for the stochastic stability of the estimation error are also derived. A numerical example is given to demonstrate the feasibility of the proposed method.

Distributed Unbiased FIR Filtering With Average Consensus on Measurements for WSNs

Abstract: Industrial wireless sensor networks (WSNs) often operate under harsh conditions that require robustness from an estimator of a measured quantity. We propose a novel distributed unbiased finite-impulse response (UFIR) filter called micro-UFIR filter that, unlike the micro-Kalman filter (micro-KF), is robust against modeling errors in uncertain noise environments. The micro-UFIR filter is derived based on average consensus on measurements and, unlike the micro-KF, requires only one consensus filter. Better robustness of the micro-UFIR filter is shown analytically and confirmed by simulations of a WSN and a vehicle travelling along a circular trajectory under unpredictable impacts, impulsive noise, and errors in the noise statistics.

Stable Kalman filter and neural network for the chaotic systems identification

Abstract: In this research, a modified Kalman filter is introduced for the adaptation of a neural network. The modified Kalman filter is an improved version of the extended Kalman filter based in the following two changes: (1) a term of the weights adaptation is modified in the modified algorithm to assure the uniform stability, convergence of the weights error, and local minimums avoidance, (2) the activation functions are used instead of the Jacobian terms in the modified algorithm to assure the boundedness of the weights error. The suggested algorithm is applied for the chaotic systems identification.

Covariance Correction Step for Kalman Filtering with an Attitude

Abstract: Redundant attitude representations are often used in Kalman filters for estimating dynamic states that include an attitude. A minimal three-element attitude deviation is combined with a reference attitude, where the deviation is included in the filter state and has an associated covariance estimate. This paper derives a reset step that adjusts the covariance matrix when information is moved from the attitude deviation to the reference attitude. When combined with the extended or unscented Kalman filter prediction and measurement steps, the reset allows one to easily construct a Kalman filter for a system for which the state includes an attitude. This algorithm is closely related to (and a correction to) the multiplicative extended Kalman filter or the unscented quaternion estimator, depending on whether the reset is combined with an extended or unscented Kalman filter. In comparison to the multiplicative extended Kalman filter, it is more general and includes a reset after the measurement update, as well ...

Tobit Kalman filter with time-correlated multiplicative measurement noise

Abstract: Kalman filters for discrete-time linear systems with censored measurements have been developed, of which the Tobit Kalman filter has been shown an effective candidate. In this study, the authors expand the Tobit Kalman filter to discrete-time linear systems with time-correlated multiplicative measurement noise. By introducing several new terms including the estimates for the products of multiplicative measurement noise and the state as well as their error covariance matrices, the proposed filter can be implemented in a recursive manner. A numerical example involving radar tracking is provided to show the effectiveness of the proposed filter.

An Asynchronous Adaptive Direct Kalman Filter Algorithm to Improve Underwater Navigation System Performance

Abstract: In the conventional integrated navigation systems, such as direct Kalman filter, the statistical information of the process and measurement noises is considered constant. In real applications, due to the variation of vehicle dynamics, the environmental conditions and imperfect knowledge of the filter statistical information, the process and measurement covariance matrices are unknown and time dependent. To improve performance of the direct Kalman filter algorithm, this paper presents an asynchronous adaptive direct Kalman filter (AADKF) algorithm for underwater integrated navigation system. The designed navigation system is composed of a high-rate strapdown inertial navigation system along with low-rate auxiliary sensors with different sampling rates. The auxiliary sensors consist of a global positioning system (GPS), a Doppler velocity log (DVL), a depthmeter, and an inclinometer. Performance of the proposed algorithm is investigated using real measurements. The experimental results indicate the proposed AADKF algorithm outperforms asynchronous direct Kalman filter (ADKF) algorithm, i.e., the relative root mean square error (RMSE) of the estimated position is reduced by 61% on average.

Convergence Analysis of a Family of Robust Kalman Filters Based on the Contraction Principle

Abstract: In this paper, we analyze the convergence of a family of robust Kalman filters. For each filter of this family, the model uncertainty is tuned according to the so-called tolerance parameter. Assuming that the corresponding state-space model is reachable and observable, we show that the $N$-fold composition of the corresponding Riccati-like mapping is strictly contractive provided that the tolerance is sufficiently small and, accordingly, the filter converges.

Diffuse Kalman Filter

Abstract: The estimation problem of the state and the parameters of the discrete dynamic plants in the absence of a priori statistical information about initial conditions or its incompletion is considered in this chapter. Diffuse analogues of the Kalman filter and the extended Kalman filter are obtained. As a practical application, the problems of constructing the filter with a sliding window, observers restoring state in a finite time, recurrent neural networks training and state estimation of nonlinear systems with partly unknown dynamics are considered.

Kalman Filter and its Modern Extensions for the Continuous-time Nonlinear Filtering Problem

Abstract: This paper is concerned with the filtering problem in continuous-time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter which provides an exact solution for the linear Gaussian problem, (ii) the ensemble Kalman-Bucy filter (EnKBF) which is an approximate filter and represents an extension of the Kalman-Bucy filter to nonlinear problems, and (iii) the feedback particle filter (FPF) which represents an extension of the EnKBF and furthermore provides for an consistent solution in the general nonlinear, non-Gaussian case. The common feature of the three algorithms is the gain times error formula to implement the update step (to account for conditioning due to the observations) in the filter. In contrast to the commonly used sequential Monte Carlo methods, the EnKBF and FPF avoid the resampling of the particles in the importance sampling update step. Moreover, the feedback control structure provides for error correction potentially leading to smaller simulation variance and improved stability properties. The paper also discusses the issue of non-uniqueness of the filter update formula and formulates a novel approximation algorithm based on ideas from optimal transport and coupling of measures. Performance of this and other algorithms is illustrated for a numerical example.

Discrete-time Kalman filter for Takagi–Sugeno fuzzy models

Abstract: In this work, the Kalman Filter (KF) and Takagi–Sugeno fuzzy modeling technique are combined to extend the classical Kalman linear state estimation to the nonlinear field. The framework for such extension is given, and in this sense the discrete-time fuzzy Kalman filter (DFKF) is obtained. It will be shown that the fuzzy version gives some advantages when is compared with the Extended Kalman Filter (EKF), which is the most typical extension of the KF to the nonlinear field. The proposed approach provides a significantly smaller processing time than the processing time of the EKF while the mean square error is also reduced. Finally, some examples, such as the Lorenz chaotic attractor and under actuated mechatronic system (pendubot), are used to compare the DFKF and EKF.