Showing papers on "Invariant extended Kalman filter published in 2017"

Iterated extended Kalman filter based visual-inertial odometry using direct photometric feedback

Abstract: This paper presents a visual-inertial odometry framework that tightly fuses inertial measurements with visual data from one or more cameras, by means of an iterated extended Kalman filter. By employing image patches as landmark descriptors, a photometric error is derived, which is directly integrated as an innovation term in the filter update step. Consequently, the data association is an inherent part of the estimation process and no additional feature extraction or matching processes are required. Furthermore, it enables the tracking of noncorner-shaped features, such as lines, and thereby increases the set of possible landmarks. The filter state is formulated in a fully robocentric fashion, which reduces errors related to nonlinearities. This also includes partitioning of a landmark’s location estimate into a bearing vector and distance and thereby allows an undelayed initialization of landmarks. Overall, this results in a compact approach, which exhibits a high level of robustness with respect to low ...

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.

A Novel Robust Student's t -Based Kalman Filter

Abstract: A novel robust Student's t -based Kalman filter is proposed by using the variational Bayesian approach, which provides a Gaussian approximation to the posterior distribution. Simulation results for a manoeuvring target tracking example illustrate that the proposed filter has smaller root mean square error and bias than existing filters.

Adaptive adjustment of noise covariance in Kalman filter for dynamic state estimation

Abstract: Accurate estimation of the dynamic states of a synchronous machine (e.g., rotor's angle and speed) is essential in monitoring and controlling transient stability of a power system. It is well known that the covariance matrixes of process noise (Q) and measurement noise (R) have a significant impact on the Kalman filter's performance in estimating dynamic states. The conventional ad-hoc approaches for estimating the covariance matrixes are not adequate in achieving the best filtering performance. To address this problem, this paper proposes an adaptive filtering approach to adaptively estimate Q and R based on innovation and residual to improve the dynamic state estimation accuracy of the extended Kalman filter (EKF). It is shown through the simulation on the two-area model that the proposed estimation method is more robust against the initial errors in Q and R than the conventional method in estimating the dynamic states of a synchronous machine.

The Comparisons of Optimized Extended Kalman Filters for Speed-Sensorless Control of Induction Motors

Abstract: This paper presents the comparisons of optimized extended Kalman filters (EKFs) using different fitness functions for speed-sensorless vector control of induction motors (IMs). In order to achieve high performance estimations of states/parameter by EKF algorithm, state and noise covariance matrices must be accurately selected. For this aim, instead of using time-consuming trial-and-error method to determine those covariance matrices, in this paper EKF algorithm is optimized by differential evolution algorithm (DEA) and multi-objective DEA (MODEA) with the utilization of different fitness functions. The optimally obtained set of each covariance matrices is used in EKF algorithm built on the same IM model and thus, the estimation results of the optimized EKF algorithms are compared in real-time experiments in order to conclude which fitness function is better for motion control applications.

Consensus+Innovations Distributed Kalman Filter With Optimized Gains

Abstract: In this paper, we address the distributed filtering and prediction of time-varying random fields represented by linear time-invariant (LTI) dynamical systems. The field is observed by a sparsely connected network of agents/sensors collaborating among themselves. We develop a Kalman filter type consensus + innovations distributed linear estimator of the dynamic field termed as Consensus+Innovations Kalman Filter. We analyze the convergence properties of this distributed estimator. We prove that the mean-squared error of the estimator asymptotically converges if the degree of instability of the field dynamics is within a prespecified threshold defined as tracking capacity of the estimator. The tracking capacity is a function of the local observation models and the agent communication network. We design the optimal consensus and innovation gain matrices yielding distributed estimates with minimized mean-squared error. Through numerical evaluations, we show that the distributed estimator with optimal gains converges faster and with approximately 3dB better mean-squared error performance than previous distributed estimators.

Convergence and Consistency Analysis for a 3-D Invariant-EKF SLAM

Abstract: In this letter, we investigate the convergence and consistency properties of an invariant-extended Kalman filter (RI-EKF) based simultaneous localization and mapping (SLAM) algorithm. Basic convergence properties of this algorithm are proven. These proofs do not require the restrictive assumption that the Jacobians of the motion and observation models need to be evaluated at the ground truth. It is also shown that the output of RI-EKF is invariant under any stochastic rigid body transformation in contrast to SO (3) based EKF SLAM algorithm (SO(3)-EKF) that is only invariant under deterministic rigid body transformation. Implications of these invariance properties on the consistency of the estimator are also discussed. Monte Carlo simulation results demonstrate that RI-EKF outperforms SO(3)-EKF, Robocentric-EKF and the “First Estimates Jacobian” EKF, for three-dimensional point feature-based SLAM.

State of Charge Estimation of Battery Energy Storage Systems Based on Adaptive Unscented Kalman Filter With a Noise Statistics Estimator

Abstract: Since the noise statistics of large-scale battery energy storage systems (BESSs) are often unknown or inaccurate in actual applications, the estimation precision of state of charge (SOC) of BESSs using extended Kalman filter (EKF) or unscented Kalman filter (UKF) is usually inaccurate or even divergent. To resolve this problem, a method based on adaptive UKF (AUKF) with a noise statistics estimator is proposed to estimate accurately SOC of BESSs. The noise statistics estimator based on the modified Sage-Husa maximum posterior is aimed to estimate adaptively the mean and error covariance of measurement and system process noises online for the AUKF when the prior noise statistics are unknown or inaccurate. The accuracy and adaptation of the proposed method is validated by the comparison with the UKF and EKF under different real-time conditions. The comparison shows that the proposed method can achieve better SOC estimation accuracy when the noise statistics of BESSs are unknown or inaccurate.

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 ...

A Speed and Flux Observer of Induction Motor Based on Extended Kalman Filter and Markov Chain

Abstract: To improve the performance of sensorless induction motor (IM) drives, an adaptive speed and flux estimation method based on the multiple-model extended Kalman filter (EKF) with Markov chain for IMs is proposed in this paper. In this algorithm, the multiple model EKF for speed and flux estimation is established, and the transition of the models obeys the Markov chain and the estimation value is obtained by mixing the outputs of different models in different weightings, and the calculation of the weighting is researched. Simultaneously, the transition probability can be continuously self-tuned by the residual sequence, the prior information is modified by the posterior information, and the more accurate transition among the models is obtained. Therefore, the proposed method improves the model adaptability to the actual systems and the environmental variations, and reduces the speed estimation error. The correctness and the effectiveness of the proposed method are verified by the simulation and experimental results.

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.

Four-dimensional ensemble variational data assimilation and the unstable subspace

Abstract: The performance of (ensemble) Kalman filters used for data assimilation in the geosciences critically depends on the dynamical properties of the evolution model. A key aspect is that the error cova...

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.

ECG Denoising Using Marginalized Particle Extended Kalman Filter With an Automatic Particle Weighting Strategy

Abstract: In this paper, a model-based Bayesian filtering framework called the “marginalized particle-extended Kalman filter (MP-EKF) algorithm” is proposed for electrocardiogram (ECG) denoising. This algorithm does not have the extended Kalman filter (EKF) shortcoming in handling non-Gaussian nonstationary situations because of its nonlinear framework. In addition, it has less computational complexity compared with particle filter. This filter improves ECG denoising performance by implementing marginalized particle filter framework while reducing its computational complexity using EKF framework. An automatic particle weighting strategy is also proposed here that controls the reliance of our framework to the acquired measurements. We evaluated the proposed filter on several normal ECGs selected from MIT-BIH normal sinus rhythm database. To do so, artificial white Gaussian and colored noises as well as nonstationary real muscle artifact (MA) noise over a range of low SNRs from 10 to −5 dB were added to these normal ECG segments. The benchmark methods were the EKF and extended Kalman smoother (EKS) algorithms which are the first model-based Bayesian algorithms introduced in the field of ECG denoising. From SNR viewpoint, the experiments showed that in the presence of Gaussian white noise, the proposed framework outperforms the EKF and EKS algorithms in lower input SNRs where the measurements and state model are not reliable. Owing to its nonlinear framework and particle weighting strategy, the proposed algorithm attained better results at all input SNRs in non-Gaussian nonstationary situations (such as presence of pink noise, brown noise, and real MA). In addition, the impact of the proposed filtering method on the distortion of diagnostic features of the ECG was investigated and compared with EKF/EKS methods using an ECG diagnostic distortion measure called the “Multi-Scale Entropy Based Weighted Distortion Measure” or MSEWPRD. The results revealed that our proposed algorithm had the lowest MSEPWRD for all noise types at low input SNRs. Therefore, the morphology and diagnostic information of ECG signals were much better conserved compared with EKF/EKS frameworks, especially in non-Gaussian nonstationary situations.

An invariant-EKF VINS algorithm for improving consistency

Abstract: The main contribution of this paper is an invariant extended Kalman filter (EKF) for visual inertial navigation systems (VINS). It is demonstrated that the conventional EKF based VINS is not invariant under the stochastic unobservable transformation, associated with a translation and a rotation about the gravitational direction. This can lead to inconsistent state estimates as the estimator does not obey a fundamental property of the physical system. To address this issue, we use a novel uncertainty representation to derive a Right Invariant error extended Kalman filter (RIEKF-VINS) that preserves this invariance property. RIEKF-VINS is then adapted to the multi-state constraint Kalman filter framework to obtain a consistent state estimator. Both Monte Carlo simulations and real-world experiments are used to validate the proposed method.

Improved Wi-Fi Indoor Positioning Based on Particle Swarm Optimization

Abstract: Indoor positioning methods based on the received signal strength indication (RSSI) ranging technology are sensitive to various environmental noises, which cause positioning errors. An improved Wi-Fi indoor positioning method using an improved unscented Kalman filter and the particle swarm optimization (PSO) is proposed to reduce ranging error and improve positioning accuracy. The received signals are preprocessed by the improved unscented Kalman filter algorithm and then the improved PSO algorithm is used to optimize position calculation results. To demonstrate the utility of the proposed algorithm, simulations and experiments were performed for estimating the position of objects. Simulating results indicate that the mean error of the proposed algorithm is reduced by 31.87% in comparison with that of the unlicensed Kalman filter method. Experimental results show that the mean error of the proposed algorithm is reduced by 26.72% in comparison with that of the unlicensed Kalman filter method. Therefore, the proposed algorithm can effectively reduce the positioning error and improve the positioning accuracy. In the actual indoor positioning, it could get better positioning results.

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.

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.

Extended Kalman filter for extended object tracking

Abstract: In this work, we present a novel method for tracking an elliptical shape approximation of an extended object based on a varying number of spatially distributed measurements. For this purpose, an explicit nonlinear measurement equation is formulated that relates the kinematic and shape parameters to a measurement by means of a multiplicative noise term. Based on the measurement equation, we derive an extended Kalman filter (EKF) for a closed-form recursive measurement update. The performance of the proposed method is demonstrated with simulations.

Indirect Kalman Filtering Based Attitude Estimation for Low-Cost Attitude and Heading Reference Systems

Abstract: In this paper, a computational efficient attitude estimation method is proposed for the low-cost attitude and heading reference systems. In the proposed method, the velocity and position provided by the Global Positioning System and inertial sensors outputs are first used to construct the vector observations. With the constructed vector observations, an error equations based filtering model is established using the Euler angles as the attitude parameterization. If the attitude has been well initialized, the established model can reduce to a linear state-space model, which enables the application of standard Kalman filtering. For the established attitude estimation model, an indirect Kalman filter is detailedly designed. Car-mounted filed test results demonstrate that the proposed method possesses superiority over the existing methods with consideration of both accuracy and efficiency.

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.

Maximum Correntropy Kalman Filter With State Constraints

Abstract: For linear systems, the original Kalman filter under the minimum mean square error (MMSE) criterion is an optimal filter under a Gaussian assumption. However, when the signals follow non-Gaussian distributions, the performance of this filter deteriorates significantly. An efficient way to solve this problem is to use the maximum correntropy criterion (MCC) instead of the MMSE criterion to develop the filters. In a recent work, the maximum correntropy Kalman filter (MCKF) was derived. The MCKF performs very well in filtering heavy-tailed non-Gaussian noise, and its performance can be further improved when some prior information about the system is available (e.g., the system states satisfy some equality constraints). In this paper, to address the problem of state estimation under equality constraints, we develop a new filter, called the MCKF with state constraints, which combines the advantages of the MCC and constrained estimation technology. The performance of the new algorithm is confirmed with two illustrative examples.