Showing papers on "Invariant extended Kalman filter published in 2022"

Distributed Robust Kalman Filtering for Markov Jump Systems With Measurement Loss of Unknown Probabilities

Abstract: This article is concerned with a distributed filtering problem for Markov jump systems subject to the measurement loss with unknown probabilities. A centralized robust Kalman filter is designed by using variational Bayesian methods and a modified interacting multiple model method based on information theory (IT-IMM). Then, a distributed robust Kalman filter based on the centralized filter and a hybrid consensus method called hybrid consensus on measurement and information (HCMCI) is designed. Moreover, boundedness of the estimation errors and the estimation error covariances are studied for the distributed robust Kalman filter.

Eye Tracking Algorithm Based on Multi Model Kalman Filter

Abstract: One of the most important pieces of Human Machine Interface (HMI) equipment is an eye tracking system that is used for many different applications. This paper aims to present an algorithm in order to improve the efficiency of eye tracking in the image by means of a multi-model Kalman filter. In the classical Kalman filter, one model is used for estimation of the object, but in the multi-model Kalman filter, several models are used for estimating the object. The important features of the multiple-model Kalman filter are improving the efficiency and reducing its estimating errors relative to the classical Kalman filter. The proposed algorithm consists of two parts. The first step is recognizing the initial position of the eye, and Support Vector Machine (SVM) has been used in this part. In the second part, the position of the eye is predicted in the next frame by using a multi-model Kalman filter, which applies constant speed and acceleration models based on the normal human eye. Doi: 10.28991/HIJ-2022-03-01-02 Full Text: PDF

A Review of Dynamic Phasor Estimation by Non-Linear Kalman Filters

Abstract: Phasor estimation under dynamic conditions has been under study recently by relaxing the amplitude and phase of the static phasor. This paper will review some methods to estimate dynamic phasor by nonlinear Kalman filters. Nonlinear Kalman filters have found an application in the tracking of time-varying amplitude and phase. Five nonlinear Kalman filtering methods for dynamic phasor estimation are examined in this paper. These methods are: EKF1 stands for first-order Extended Kalman filter, EKF2 stands for second-order Extended Kalman, UKF stands for Unscented Kalman filter, GHKF stands for Gauss Hermite Kalman filter, and finally CKF stands for Cubature Kalman filter. This paper describes the theoretical processes of these methods and demonstrates their effectiveness in dynamic phasor estimation by some test signal simulations in MATLAB. The simulation section shows that nonlinear Kalman filters give more accuracy than linear Kalman filters when the phasor is relaxed by modulated amplitude and phase. Moreover, comparative assessments among the performance of five nonlinear Kalman filters are done for dynamic phasor estimation, and also their performances are compared with the other methods which have already been published. According to the simulation results, EKF1 gives the highest accuracy during steady-state ( $2 \times 10^{-13}$ ) because the signal model is more similar to the estimation model of EK1 during the steady-state condition. However, the other non-linear Kalman filters show better performances in dynamic conditions. When the phasor is a time-varying amplitude and phase, filters give the same accuracy ( $TVE=0.5 \%$ ). A step-change in amplitude and phase creates different overshoot and response times, but EKF2 shows the least overshoot (3.2%) and the longest response time (7.6 ms). Computation burden and noise indices can discriminate the methods from other viewpoints. The computation burden of GHKF is drastically increased when the number of states gives rise. CKF shows an appropriate performance when the number of samples and the number of the state increased in the input signal. EKF1 is not a good solution for noise infiltration when SNR is less than 40 dB, but CKF gives the highest accuracy in high noise levels. Compared to the six already pblished methods, CK shows the best performance with a reasonable estimation error ( $TVE=0.1101 \%$ ) and simulation time (0.6146 ms).

A dual‐rate sampled multiple innovation adaptive extended Kalman filter algorithm for state of charge estimation

Abstract: For a lithium battery state space model, to solve the unsuitable problems caused by the single‐rate (same rate) sampled state space model facing resistor‐capacity (R‐C) couples with different time scales, a dual‐rate sampled exponential weighted multiple innovation adaptive extended Kalman filter (AEKF) method is investigated. The details include: (a) By using dual‐rate sampled method, select the suitable sampled rate for their own time scale for different couples (R1‐C1 and R2‐C2) to establish dual‐rate sampled state space equations; (b) Considering noise variation, a recursive noise estimation based AEKF algorithm is adopted to realize adaptive correction of noise; (c) Considering the influences of present and past data, an AEKF algorithm based exponential weighted multiple innovation is studied. Experiment results show that the investigated method is clearly better than the classical single‐rate sampled method with high precision.

Comparison of TRIAD+EKF and TRIAD+UKF Algorithms for Nanosatellite Attitude Estimation

Abstract: Two most commonly used sensors on nanosatellites are magnetometer and sun sensor. In this paper, magnetometer and sun sensor measurements are combined gyro measurements to produce enhanced attitude estimation. Tri-Axial Attitude Determination (TRIAD) algorithm is used with Kalman filter to form a complete attitude filter. Sun sensor and magnetometer measurements are selected as inputs to TRIAD algorithm and output is fed to Kalman filter as a measurement. Two different Kalman filters, extended and unscented, are used with TRIAD algorithm. A comparison is given between performances of both Kalman filter.

A higher-order robust correlation Kalman filter for satellite attitude estimation

Abstract: A higher-order robust correlation Kalman filtering approach is presented to achieve attitude estimation for satellites with unknown modeling errors. A robust correlation Kalman filter (RCKF) is preliminarily derived by using the sequence orthogonal principle. To improve its performance further, a higher-order sigma version of the RCKF is designed by incorporating a novel sigma point generation algorithm. This modified filter can capture the third and the fourth central moment's information of the system posteriori probability density function. It is proved that the proposed filter achieves better estimation accuracy and robustness. The effectiveness of the developed filter is demonstrated by simulation results with it applied to the satellite attitude estimation problem.

Robust Linearly Constrained Invariant Filtering for a Class of Mismatched Nonlinear Systems

Abstract: Standard state estimation techniques require a perfect knowledge of the system’s model, that is, process and measurement equations, inputs and the corresponding noise statistics. In practice this assumption does not hold and therefore robust filtering methods must be accounted for. A new approach to tackle a potential model mismatch via linear constraints within the Kalman filter, and its extended version (EKF), has been recently shown to be a very promising solution. This letter further explores robust linearly constrained filtering in the context of the Invariant EKF (InEKF). With respect to the EKF, the InEKF is a recent filtering technique which has been shown to better handle the particular structure of a class of problems through the use of Lie groups. In this contribution, a new robust linearly constrained InEKF is introduced, together with particular parametric mismatched models and mitigation strategies through linear constraints. Numerical results for an illustrative navigation example are provided to show the performance improvement and support the discussion.

Research on Permanent Magnet Synchronous Motor Control System Based on Adaptive Kalman Filter

Abstract: A sensorless control system of a permanent magnet synchronous motor based on an extended Kalman filter (EKF) algorithm faces problems with inaccurate or mismatched process noise statistics. This problem affects the performance of the filter, resulting in an inaccurate estimation of motor speed. To address the above problem, this paper proposes a parameter-adaptive Kalman filter algorithm that does not depend on precise noise system covariance. This method can significantly reduce the negative impact of the noise statistical mismatch on motor speed estimation. In addition, the method uses adaptive covariance prediction and removes the original covariance checks in the EKF, thus reducing the calculation burden. The simulation results show that, compared with the traditional EKF algorithm, the algorithm proposed in this article can effectively reduce the steady-state jitter and improve the filtering adaptability and calculation accuracy.

Recursive Optimal Finite Impulse Response Filter and Its Application to Adaptive Estimation

Abstract: In this paper, the recursive form of an optimal finite impulse response filter is proposed for discrete time-varying state-space models. The recursive form of the finite impulse response filter is derived by employing finite horizon Kalman filtering with optimally estimated initial conditions. The horizon initial state and its error covariance on the horizon are optimally estimated by using recent finite measurements, in the sense of maximum likelihood estimation, then initiating the finite horizon Kalman filter. The optimality and unbiasedness of the proposed filter are proved by comparison with the conventional optimal finite impulse response filter in batch form. Moreover, an adaptive FIR filter is also proposed by applying the adaptive estimation scheme to the proposed recursive optimal FIR filter as its application. To evaluate the performance of the proposed algorithms, a computer simulation is performed to compare the conventional Kalman filter and adaptive Kalman filters for the gas turbine aircraft engine model.

Equivariant Filter Design for Inertial Navigation Systems with Input Measurement Biases

Abstract: Inertial Navigation Systems (INS) are a key technology for autonomous vehicles applications. Recent advances in estimation and filter design for the INS problem have exploited geometry and symmetry to overcome limitations of the classical Extended Kalman Filter (EKF) approach that formed the mainstay of INS systems since the mid-twentieth century. The industry standard INS filter, the Multiplicative Extended Kalman Filter (MEKF), uses a geometric construction for attitude estimation coupled with classical Euclidean construction for position, velocity and bias estimation. The recent Invariant Extended Kalman Filter (IEKF) provides a geometric framework for the full navigation states, integrating attitude, position and velocity, but still uses the classical Euclidean construction to model the bias states. In this paper, we use the recently proposed Equivariant Filter (EqF) framework to derive a novel observer for biased inertial-based navigation in a fully geometric framework. The introduction of virtual velocity inputs with associated virtual bias leads to a full equivariant symmetry on the augmented system. The resulting filter performance is evaluated with both simulated and real-world data, and demonstrates increased robustness to a wide range of erroneous initial conditions, and improved accuracy when compared with the industry standard Multiplicative EKF (MEKF) approach.

Multifidelity Data Assimilation for Physical Systems

Abstract: Multifidelity methods aim to leverage the availability of models at different levels of fidelity describing the same physical phenomena and are receiving growing attention in computational science. One field that can considerably benefits from statistical multifidelity approaches is data assimilation. This chapter presents a broad overview of multifidelity methods in data assimilation for hierarchies of models and hierarchies of observations. We introduce the theoretical multifidelity Kalman filter, and discuss its practical implementation using an ensemble-based framework as the multifidelity ensemble Kalman filter (MFEnKF). The discussion builds upon the theory of linear and nonlinear control variates. Numerical examples compare the multifidelity and the traditional EnKF.

Kalman Filter for Linear Systems With Unknown Structural Parameters

Abstract: This brief considers Kalman filter for linear systems with unknown structural parameters. We design a Bayesian parameter identification algorithm based on maximum likelihood (ML) criterion and expectation maximization (EM). Under the identification of structural parameter, we perform the Kalman filter to estimate the states. The Kalman filter and the parameter identification algorithm are interactive to estimate the states and the structural parameters. More specifically, first, we use EM algorithm together with Kalman smoother to estimate the structural parameters. Then, on the basis of results provided by the first step, we employ the classical Kalman filter to predict and update the states, which formulates the final proposed Kalman filter. Performance analysis and simulation results verify the presented filter.

A Class of Nonlinear Kalman Filters Under a Generalized Measurement Model With False Data Injection Attacks

Abstract: In this letter, a generalized measurement model (GMM) is established under the attack injecting additive and multiplicative false data, simultaneously. The GMM can be applied to any existing nonlinear Kalman filters (NKFs), such as extended Kalman filter (EKF), cubature Kalman filter (CKF), and geometric unscented Kalman filter (GUF). Based on the constructed GMM, a class of nonlinear Kalman filters with GMM (NKFs-GMM) is proposed to deal with additive false data, multiplicative false data, and simultaneous attacks on additive and multiplicative false data with no increase of computational complexity. Numerical simulations show that the filtering accuracy of NKFs-GMM is superior to that of corresponding NKFs.

A Threshold Extend Kalman Filter Algorithm for State of Charge Estimation of Lithium-Ion Batteries in Electric Vehicles

Abstract: Model-based algorithms are widely employed in state of charge estimation. However, due to the complex operation environment and rich noise in the measured battery voltage and current, it is difficult to estimate terminal voltage accurately based on the battery model, resulting in great estimation deviation of state of charge (SOC). To address the issue, a threshold extended Kalman filter (T-EKF) algorithm based on the influence mechanism analysis of SOC estimation is proposed. In the proposed algorithm, the threshold for SOC, which is set by the residual non-Gauss voltage noise between the measured terminal voltage and the estimated terminal voltage, is employed to improve the robustness of EKF. Then, an experimental platform is built and two different EV operation conditions are selected to verify the algorithm on a Li-ion battery. Combining the comparison among extend Kalman filter (EKF), adaptive extend Kalman filter (AEKF), and the proposed T-EKF, some important results are obtained for the proposed algorithm. 1) The maximum SOC error of the proposed T-EKF are about 1.3% and 2.9% under urban bus operation condition (UBOC) and urban dynamometer driving schedule (UDDS), respectively; 2) the calculation cost of T-EKF is higher than EKF, but is the same as the AEKF; 3) the capacity to correct the initial SOC is maintained in the T-EKF and the oscillation on the estimated SOC curve can be effectively weakened.

A novel maximum correntropy adaptive extended Kalman filter for vehicle state estimation under non-Gaussian noise

Abstract: For vehicle state estimation, conventional Kalman filters work well under Gaussian assumptions. Still, they are likely to degrade dramatically in the practical non-Gaussian situation (especially the noise is heavy-tailed), showing poor accuracy and robustness. This article presents an estimation technique based on the maximum correntropy criterion (MCC) combined with an adaptive extended Kalman filter (AEKF), and an extended Kalman filter (EKF) based on the MCC has also been studied. A lateral-longitudinal coupled vehicle model is developed, while an observer containing the state vectors such as yaw rate, sideslip angle, vehicle velocity and tire cornering stiffness is designed using easily available in-vehicle sensors and low-cost GPS. After analyzing the algorithmic complexity, the proposed algorithm is validated by sine steering input and double lane change driving scenarios. Finally, it is found that MCC combined with AEKF/EKF has stronger robustness and better estimation accuracy than AEKF/EKF in dealing with non-Gaussian noise for vehicle state estimation.

Predicting Time SeriesUsing an Automatic New Algorithm of the Kalman Filter

Abstract: Time series forecasting is one of the main venues followed by researchers in all areas. For this reason, we develop a new Kalman filter approach, which we call the alternative Kalman filter. The search conditions associated with the standard deviation of the time series determined by the alternative Kalman filter were suggested as a generalization that is supposed to improve the classical Kalman filter. We studied three different time series and found that in all three cases, the alternative Kalman filter is more accurate than the classical Kalman filter. The algorithm could be generalized to time series of a different length and nature. Therefore, the developed approach can be used to predict any time series of data with large variance in the model error that causes convergence problems in the prediction.

RKHS based State Estimator for Radar Sensor in Indoor Application

Abstract: For the estimation of targets' states (location, velocity, and acceleration) from nonlinear radar measurements, usually, the improved version of well known Kalman filter: extended Kalman filter (EKF) and unscented Kalman filter (UKF) are used. However, EKF and UKF approximates the nonlinear measurement function either by Jacobian or using sigma points. Consequently, because of the approximation of the measurement function, the EKF and UKF cannot achieve high estimation accuracy. The potential solution is to replace the approximation of nonlinear measurement function with its estimate, obtained in high dimensional reproducing kernel Hilbert space (RKHS). An ample amount of research has been done in this direction, and the combined filter is termed RKHS based Kalman filter. However, there is a shortage of literature dealing with estimating the dynamic state of the target in an indoor environment using RKHS based Kalman filter. Therefore, in this paper, we propose the use of RKHS based Kalman filter for indoor application. Specifically, we validate the suitability of the RKHS based Kalman filtering approach using simulations performed over three different target motion models.

Cooperative Filtering and Parameter Estimation for Polynomial PDEs using a Mobile Sensor Network

Abstract: In this paper, a constrained cooperative Kalman filter is developed to estimate field values and gradients along trajectories of mobile robots collecting measurements. We assume the underlying field is generated by a polynomial partial differential equation with unknown time-varying parameters. A long short-term memory (LSTM) based Kalman filter, is applied for the parameter estimation leveraging the updated state estimates from the constrained cooperative Kalman filter. Convergence for the constrained cooperative Kalman filter has been justified. Simulation results in a 2-dimensional field are provided to validate the proposed method.

Extended Kalman filter and Takagi-Sugeno fuzzy observer for a strip winding system

Abstract: This paper proposes two nonlinear estimation approaches, namely based on Extended Kalman Filter (EKF) and a Takagi-Sugeno Fuzzy Observer with 32 rules (TSFO-32), for a Strip Winding System (SWS) characterized by variable reference input, variable moment of inertia with constant increasing tendency and variable parameters. The SWS is a complex and nonlinear mechatronic system viewed as a controlled process, which wraps a strip with constant linear velocity on a reel, and the variable radius modifies both the angular velocity and the moment of inertia. The motivation of using EKF is the zero stationary error at low speeds. The motivation of using TSFO-32 is that once the Takagi-Sugeno fuzzy models are obtained, various analysis and design tools initially developed for linear systems, which facilitate the observation and/or synthesis of the controller for complex nonlinear systems, can be adapted appropriately and used in these nonlinear systems. Therefore, these tools simplify the design as well-established approaches and algorithms are available. The fuzzy control system stability and observer design conditions are derived and expressed as linear matrix inequalities. The efficiency of TSFO-32 is discussed in this paper in terms of setting a certain convergence rate. The performance of the two nonlinear estimation approaches is validated by means of digital simulations conducted for three values of the moment of inertia.

Robust Linearly Constrained Invariant Filtering for a Class of Mismatched Nonlinear Systems

Abstract: Standard state estimation techniques require a perfect knowledge of the system's model, that is, process and measurement equations, inputs and the corresponding noise statistics. In practice this assumption does not hold and therefore robust filtering methods must be accounted for. A new approach to tackle a potential model mismatch via linear constraints within the Kalman filter, and its extended version (EKF), has been recently shown to be a very promising solution. This letter further explores robust linearly constrained filtering in the context of the Invariant EKF (InEKF). With respect to the EKF, the InEKF is a recent filtering technique which has been shown to better handle the particular structure of a class of problems through the use of Lie groups. In this contribution, a new robust linearly constrained InEKF is introduced, together with particular parametric mismatched models and mitigation strategies through linear constraints. Numerical results for an illustrative navigation example are provided to show the performance improvement and support the discussion.

Student’s t-Kernel-Based Maximum Correntropy Kalman Filter

Abstract: The state estimation problem is ubiquitous in many fields, and the common state estimation method is the Kalman filter. However, the Kalman filter is based on the mean square error criterion, which can only capture the second-order statistics of the noise and is sensitive to large outliers. In many areas of engineering, the noise may be non-Gaussian and outliers may arise naturally. Therefore, the performance of the Kalman filter may deteriorate significantly in non-Gaussian noise environments. To improve the accuracy of the state estimation in this case, a novel filter named Student’s t kernel-based maximum correntropy Kalman filter is proposed in this paper. In addition, considering that the fixed-point iteration method is used to solve the optimal estimated state in the filtering algorithm, the convergence of the algorithm is also analyzed. Finally, comparative simulations are conducted and the results demonstrate that with the proper parameters of the kernel function, the proposed filter outperforms the other conventional filters, such as the Kalman filter, Huber-based filter, and maximum correntropy Kalman filter.

Robust self-adaptive Kalman filter with application in target tracking

Abstract: Kalman filter has been applied extensively to the target tracking. The estimation performance of Kalman filter is closely resulted by the quality of prior information about the process noise covariance (Q) and the measurement noise covariance (R). Therefore, the development of adaptive Kalman filter is mainly to reduce the estimation errors produced by the uncertainty of Q and R. In this paper, the proposed self-adaptive Kalman filter algorithm has solved the problems of covariance-matching method about the determination of the width of the window and the addition of storage burden and that can update Q and R simultaneously. Simulation results confirm that the proposed method outperforms the traditional Kalman filter and has the better estimation performance than the other two adaptive Kalman filters in the target tracking. The developed filtering algorithm has the following characteristics: high robustness, low computing load, easy operation and tuning Q, R simultaneously.

Trajectory PHD Filter for Adaptive Measurement Noise Covariance Based on Variational Bayesian Approximation

Abstract: In order to solve the problem that the measurement noise covariance may be unknown or change with time in actual multi-target tracking, this paper brings the variational Bayesian approximation method into the trajectory probability hypothesis density (TPHD) filter and proposes a variational Bayesian TPHD (VB-TPHD) filter to obtain measurement noise covariance adaptively. By modeling the unknown covariance as the random matrix that obeys the inverse gamma distribution, VB-TPHD filter minimizes the Kullback–Leibler divergence (KLD) and estimates the sequence of multi-trajectory states with noise covariance matrices simultaneously. We propose the Gaussian mixture VB-TPHD (AGM-VB-TPHD) filter under adaptive newborn intensity for linear Gaussian models and also give the extended Kalman (AEK-VB-TPHD) filter and unscented Kalman (AUK-VB-TPHD) filter in nonlinear Gaussian models. The simulation results prove the effectiveness of the idea that the VB-TPHD filter can form robust and stable trajectory filtering while learning adaptive measurement noise statistics. Compared with the tag-VB-PHD filter, the estimated error of the VB-TPHD filter is greatly reduced, and the estimation of the trajectory number is more accurate.