Extended Kalman Filter Estimator Research Articles

Vehicle sideslip angle estimation for a four-wheel-independent-drive electric vehicle based on a hybrid estimator and a moving polynomial Kalman smoother

This paper presents a vehicle sideslip angle estimation scheme against noises and outliers in sensor measurements for a four-wheel-independent-drive electric vehicle. The proposed scheme combines a robust unscented Kalman filter estimator based on the 3-DOF vehicle dynamics model and an extended Kalman filter estimator based on the kinematic model to form a hybrid estimator through a weighting factor. The weighting factor can be dynamically adjusted in real time to optimize the overall estimation performance under different driving conditions. The main contributions of this study to the related literature lie in two aspects. Firstly, a robust unscented Kalman filter estimator was incorporated to improve the robustness of dynamics-based estimation to sensor measurement outliers. Secondly, a novel moving polynomial Kalman smoother was included to filter out the noises in sensor measurements. Co-simulations of Matlab/Simulink and Carsim software were conducted under typical vehicle maneuvers and show that the proposed vehicle sideslip angle estimation scheme can obtain satisfied estimation results, with the moving polynomial Kalman smoother exhibiting better phase characteristics and filtering performance relative to commonly-used finite impulse response filters, and the robust unscented Kalman filter estimator being robust to sensor measurement outliers.

Accurate Monocular Visual-Inertial SLAM Using a Map-Assisted EKF Approach

This paper presents a novel tightly-coupled monocular visual-inertial Simultaneous Localization and Mapping algorithm, which provides accurate and robust localization within the globally consistent map in real time on a standard CPU. This is achieved by firstly performing the visual-inertial extended kalman filter(EKF) to provide motion estimate at a high rate. However the filter becomes inconsistent due to the well known linearization issues. So we perform a keyframe-based visual-inertial bundle adjustment to improve the consistency and accuracy of the system. In addition, a loop closure detection and correction module is also added to eliminate the accumulated drift when revisiting an area. Finally, the optimized motion estimates and map are fed back to the EKF-based visual-inertial odometry module, thus the inconsistency and estimation error of the EKF estimator are reduced. In this way, the system can continuously provide reliable motion estimates for the long-term operation. The performance of the algorithm is validated on public datasets and real-world experiments, which proves the superiority of the proposed algorithm.

Design of an indirect adaptive controller for the trajectory tracking of UVMS

For solving the trajectory tracking problem of the underwater vehicle and manipulator system (UVMS) in the presence of dynamic uncertainties and time-varying external disturbances, this paper presents an indirect adaptive control scheme which consists of three parts: an extended Kalman filter (EKF) estimation compensative system, a model-based computed torque controller (CTC), a H∞ robust compensative tracking controller. The contribution of our method is that it can overcome the disadvantages of existing control schemes, which are based on the accurate dynamic model of UVMS, known statistics unmodeled dynamics/external disturbances (e.g., constant or Gaussian), or the accurate, efficient system feedback measurement states by the sensors. According to the Lyapunov stability theorem, it is shown that the proposed indirect adaptive control scheme can guarantee its embedded H∞ robust controller tracking performance for our UVMS. Simulations show that the proposed control scheme can satisfy the design requirements of UVMS in rapid convergence, tracking accuracy, system stability and disturbance attenuation. Therefore, the method presented in this paper can provide a feasible way of controlling the nonlinear UVMS.

Design and implementation of a model predictive observer for AHRS

A GPS-aided Inertial Navigation System (GAINS) is used to determine the orientation? position and velocity of ground and aerial vehicles. The data measured by Inertial Navigation System (INS) and GPS are commonly integrated through an Extended Kalman Filter (EKF). Since the EKF requires linearized models and complete knowledge of predefined stochastic noises? the estimation performance of this filter is attenuated by unmodeled nonlinearity and bias uncertainties of MEMS inertial sensors. The Attitude Heading Reference System (AHRS) is applied based on the quaternion and Euler angles methods. A moving horizon-based estimator such as Model Predictive Observer (MPO) enables us to approximate and estimate linear systems affected by unknown uncertainties. The main objective of this research is to present a new MPO method based on the duality principle between controller and observer of dynamic systems and its implementation in AHRS mode of a low-cost INS aided by a GPS. Asymptotic stability of the proposed MPO is proven by applying Lyapunov's direct method. The field test of a GAINS is performed by a ground vehicle to assess the long-time performance of the MPO method compared with the EKF. Both the EKF and MPO estimators are applied in AHRS mode of the MEMS GAINS for the purpose of real-time performance comparison. Furthermore? we use flight test data of the GAINS for evaluation of the estimation filters. The proposed MPO based on both the Euler angles and quaternion methods yields better estimation performances compared to the classic EKF.

Extended kalman filter for accurate state of charge estimation of lithium-based batteries: a comparative analysis

Nowadays, Lithium-based batteries are widely adopted in Electric Vehicles (EVs). The battery State-Of-Charge (SOC) represents its residual energy. However, it cannot be measured directly with sensors and must be estimated with mathematical techniques. The main objective of this paper is both to present two different battery parameter identification methods and to determine an accurate SOC estimation of Lithium-based batteries based on Extended Kalman Filter (EKF). The different methods of battery SOC estimation are comprehensively discussed. Then, the enhanced closed loop EKF estimator is proposed. For this model-based approach, a suitable model of the cell behavior is required to reach the most precise SOC estimation. Therefore, an accurate model of cell dynamics is necessary for applicable SOC estimation particularly for different current ratings and battery technologies. The hysteresis influence is considered in the Open Circuit Voltage (OCV) as a part of the battery modeling. Two battery parameters identification methods are compared in charging/discharging modes. Through the voltage drop measurement, all the parameters of such electric cell model are identified. Then, the EKF is experimentally implemented using C programming language in micro-controller (PIC18F4585 and PIC18F4685). Finally, the SOC estimation result of EKF is adequately correlated to that of the coulomb counting method with acceptable errors. The experimental results verify that the proposed method of Bo et al. (2015) provides enhanced SOC determination compared to that of Watrin (2013).

A MULTI-LEVEL VISUAL TRACKING ALGORITHM FOR AUTONOMOUS VEHICLES

A multi-level visual tracking algorithm is proposed for autonomous vehicles based on mean-shift algorithm, cam-shift algorithm and extended kalman filter estimator. The proposed multi-level visual tracking algorithm is implemented and included in simulation to check its performance. Simulation results are captured after applying existing algorithms, proposed multi-level visual tracking algorithm and observed their performance. The simulated results show that the proposed multi-level visual tracking algorithm identifies and tracks the ground moving target efficiently.

Improved OCV Model of a Li-Ion NMC Battery for Online SOC Estimation Using the Extended Kalman Filter

Accurate modeling of the nonlinear relationship between the open circuit voltage (OCV) and the state of charge (SOC) is required for adaptive SOC estimation during the lithium-ion (Li-ion) battery operation. Online SOC estimation should meet several constraints, such as the computational cost, the number of parameters, as well as the accuracy of the model. In this paper, these challenges are considered by proposing an improved simplified and accurate OCV model of a nickel manganese cobalt (NMC) Li-ion battery, based on an empirical analytical characterization approach. In fact, composed of double exponential and simple quadratic functions containing only five parameters, the proposed model accurately follows the experimental curve with a minor fitting error of 1 mV. The model is also valid at a wide temperature range and takes into account the voltage hysteresis of the OCV. Using this model in SOC estimation by the extended Kalman filter (EKF) contributes to minimizing the execution time and to reducing the SOC estimation error to only 3% compared to other existing models where the estimation error is about 5%. Experiments are also performed to prove that the proposed OCV model incorporated in the EKF estimator exhibits good reliability and precision under various loading profiles and temperatures.

Estimation of Sideslip Angle Based on Extended Kalman Filter

The sideslip angle plays an extremely important role in vehicle stability control, but the sideslip angle in production car cannot be obtained from sensor directly in consideration of the cost of the sensor; it is essential to estimate the sideslip angle indirectly by means of other vehicle motion parameters; therefore, an estimation algorithm with real-time performance and accuracy is critical. Traditional estimation method based on Kalman filter algorithm is correct in vehicle linear control area; however, on low adhesion road, vehicles have obvious nonlinear characteristics. In this paper, extended Kalman filtering algorithm had been put forward in consideration of the nonlinear characteristic of the tire and was verified by the Carsim and Simulink joint simulation, such as the simulation on the wet cement road and the ice and snow road with double lane change. To test and verify the effect of extended Kalman filtering estimation algorithm, the real vehicle test was carried out on the limit test field. The experimental results show that the accuracy of vehicle sideslip angle acquired by extended Kalman filtering algorithm is obviously higher than that acquired by Kalman filtering in the area of the nonlinearity.

A Multi-Sensor Fusion MAV State Estimation from Long-Range Stereo, IMU, GPS and Barometric Sensors.

State estimation is the most critical capability for MAV (Micro-Aerial Vehicle) localization, autonomous obstacle avoidance, robust flight control and 3D environmental mapping. There are three main challenges for MAV state estimation: (1) it can deal with aggressive 6 DOF (Degree Of Freedom) motion; (2) it should be robust to intermittent GPS (Global Positioning System) (even GPS-denied) situations; (3) it should work well both for low- and high-altitude flight. In this paper, we present a state estimation technique by fusing long-range stereo visual odometry, GPS, barometric and IMU (Inertial Measurement Unit) measurements. The new estimation system has two main parts, a stochastic cloning EKF (Extended Kalman Filter) estimator that loosely fuses both absolute state measurements (GPS, barometer) and the relative state measurements (IMU, visual odometry), and is derived and discussed in detail. A long-range stereo visual odometry is proposed for high-altitude MAV odometry calculation by using both multi-view stereo triangulation and a multi-view stereo inverse depth filter. The odometry takes the EKF information (IMU integral) for robust camera pose tracking and image feature matching, and the stereo odometry output serves as the relative measurements for the update of the state estimation. Experimental results on a benchmark dataset and our real flight dataset show the effectiveness of the proposed state estimation system, especially for the aggressive, intermittent GPS and high-altitude MAV flight.

Distributed Drive Electric Vehicle State Estimation based on Extended Kalman Filter

Abstract This paper researched an estimation method based on Extended Kalman Filter (EKF) for distributed drive electric vehicle states. A 7 DOF closed-loop vehicle simulation platform including driver model of preview follower method and ‘Magic formula’ tire model was established. A general 2-input–1-output and 3 states estimation system was established, considering the white Gauss measurement noise. The estimation algorithm was applied to a four-motor-driven vehicle during a double-lane-change process. The results showed that EKF estimator could effectively estimate the states of distributed drive electric vehicle with varying speed under simulative experimental condition.

Single-Machine Infinite-Bus Power System Excitation Control Design With Resilient Extended Kalman Filter

To effectively control and maintain the transient stability of power systems, traditionally, the extended Kalman filter (EKF) is used as the real-time state estimator (RTSE) to provide the unmeasurable state information. However, the EKF estimation may degrade or even become unstable when the measurement data are inaccurate through random sensor failures, which is a widespread problem in data-intensive power system control applications. To address this issue, this paper proposes an improved EKF that is resilient against sensor failures. This work focuses on the resilient EKF’s (REKF’s) derivation with its application to single-machine infinite-bus (SMIB) power system excitation control. The sensor failure rate is modeled as a binomial distribution with a known mean value. The performance of REKF is compared with the traditional EKF for power system observer-based control under various chances of sensor failures. Computer simulation studies have shown the efficacy and superior performance of the proposed approach in power system control applications.

Lookup-Table-Based DTC of Induction Machines With Improved Flux Regulation and Extended Kalman Filter State Estimator at Low-Speed Operation

Direct torque control (DTC) based on lookup table is known to have poor flux regulation at low speed that can cause a significant deterioration in the speed estimation of a sensorless drive. In this paper, stator flux regulation at low speed is improved under no load by replacing the hysteresis torque comparator with constant switching frequency controller, without any changes to the conventional lookup table; hence, the simple structure of DTC is maintained. In order to reduce the sampling time and hence improve the estimation process at very low speed, a simple fifth-order extended Kalman filter (EKF) is used in this paper. The fast execution time helps the linearization process of the EKF; hence, results in an improvement in its performance. Simulations and experimental results of the proposed sensorless drive system with the EKF estimator proves excellent flux regulation, and good speed robustness and stability at very low speed.

Vehicle state estimation based on Minimum Model Error criterion combining with Extended Kalman Filter

This paper researched an estimation method based on the Minimum Model Error (MME) criterion combing with the Extended Kalman Filter (EKF) for 4WD vehicle states. A general 5-input–3-output and 3 states estimation system was established, considering both the arbitrary nonlinear model error and the white Gauss measurement noise. Aiming at eliminating the estimation error caused by the arbitrary nonlinear model error, the prediction algorithm for the dynamic tire force error was deduced based on the MME criterion, based on which the system model can be effectively updated for higher estimation accuracy. The estimation algorithm was applied to a two-motor-driven vehicle during a double-lane-change process with varying speed under simulative experimental condition. The results showed that the dynamic tire force error could be effectively found for updating the system model, and higher estimation accuracy of the vehicle states were achieved, when compared with the traditional EKF estimator.

Underwater Inertial Navigation With Long Baseline Transceivers: A Near-Real-Time Approach

Inertial navigation systems for underwater vehicles are often aided by acoustic time-of-flight positioning schemes. One widely implemented long baseline (LBL) approach uses a ping-response protocol resulting in asynchronous measurements that depend on the state of the vehicle at two time instants. Such aiding measurements that depend on the state at multiple time instants do not fit the model format of the standard extended Kalman filter (EKF) framework. This paper proposes a near-real-time (NRT) Bayesian smoothing framework for the LBL-aided inertial navigation system application. Within this NRT framework, the time interval between LBL cycles is divided into two intervals defined by the ping-response cycles of LBL. The time instant when all the LBL responses are received will be referred to as the NRT point . Between the LBL ping and the NRT point, a traditional real-time EKF is implemented using the inertial measurement unit and all aiding measurements. After the NRT point, when all the LBL responses have been received, an optimal Bayesian trajectory estimator executes. This maximum a posteriori (MAP) estimation includes all the measurement information already collected up to the NRT point of the current LBL cycle. The MAP output is a smoothed trajectory estimate for the period of time between the LBL ping and the NRT point. At the conclusion of this smoothing process, the current EKF estimate is corrected to the optimal MAP solution and propagated to the current time, and then the EKF estimation process continues to the NRT point of the next LBL cycle. At all times, the approach maintains a real-time state estimate suitable for use by the control system. This paper presents the theoretical solution, discusses the implementation, and presents implementation results to illustrate the accuracy and reliability of this NRT approach.

Sensorless Control of Permanent Magnet Synchronous Motors and EKF Parameter Tuning Research

This paper concerns the parameter tuning and the estimated results postprocessing of the extended Kalman filter for the sensorless control application of permanent magnet synchronous motors. At first an extended Kalman filter parameter tuning method is proposed based on the theoretical and simulation analysis of extended Kalman filter parameters. Furthermore, a sensorless control system is proposed based on the parameter tuning method and the simulation analysis of extended Kalman filter estimation results in different reference speeds and different load torques. The proposed sensorless control system consists of two parts. The first one is a module to self-regulate extended Kalman filter parameters. The second part can correct the estimated speed and the estimated rotation angle based on the reference speed and the electromagnetic torque. Finally, simulation results are presented to verify the feasibility and validity of the proposed sensorless control system.

Model based Online Fault Diagnosis of Automotive Engines using Joint State and Parameter Estimation

In this work, an Extended Kalman Filter (EKF) based tunable diagnoser, which uses a minimal hybrid nonlinear state space model of a spark ignition (SI) four stroke engine, is used for the detection and isolation of a variety of engine system faults including intake manifold leak, injector fault and exhaust manifold leak. The state estimates and innovation sequences from the EKF based estimator are shown to be adequate for the detection and isolation of the faults under consideration. Once a fault is detected and isolated, the diagnoser could be tuned online to perform fault identification by redefining a model/fault parameter as an additional state to be estimated and then performing a joint state and parameter estimation. The engine model and diagnoser are implemented in SimulinkTM and are validated against an AMESimTM model of the engine. For the nominal engine model, the performance of the EKF estimator is compared with two other computationally more expensive nonlinear estimators, namely the Unscented Kalman Filter (UKF) and Rao-Blackwell Particle Filter (RBPF).

Atmospheric Boundary Layer Height Estimation Using a Kalman Filter and a Frequency‐Modulated Continuous‐Wave Radar

An adaptive solution based on an extended Kalman filter (EKF) is proposed to estimate the atmospheric boundary-layer height (ABLH) from frequency-modulated continuous-wave S-band weather-radar returns. The EKF estimator departs from previous works, in which the transition interface between the mixing layer (ML) and the free troposphere (FT) is modeled by means of an erf-like parametric function. In contrast to lidar remote sensing, where aerosols give strong backscatter returns over the whole ML, clear-air radar reflectivity returns (Bragg scattering from refractive turbulence) shows strongest returns from the ML-FT interface. In addition, they are corrupted by “insect” noise (impulsive noise associated with Rayleigh scattering from insects and birds), all of which requires a specific treatment of the problem and the measurement noise for the clear-air radar case. The proposed radar-ABLH estimation method uses: 1) a first preprocessing of the reflectivity returns based on median filtering and threshold-limited decision to obtain “clean” reflectivity signal; 2) a modified EKF with adaptive range intervals as time tracking estimator; and 3) ad hoc modeling of the observation noise covariance. The method has successfully been implemented in clear-air, single-layer, and convective boundary-layer conditions. ABLH estimates from the proposed radar-EKF method have been cross examined with those from a collocated lidar ceilometer yielding a correlation coefficient as high as $\rho=0.93$ (mean signal-to-noise ratio, $\text{SNR} =18$ (linear units), at the ABLH) and in relation to the classic THM.

Design and simulation of a sensorless permanent magnet synchronous motor drive with microprocessor-based PI controller and dedicated hardware EKF estimator

In this study, we propose a digital hardware implementation of a speed controller for a sensorless permanent magnet synchronous motor (PMSM) drive. First, the extended Kalman filter (EKF) is used to estimate the rotor flux angle (FA) and rotor speed. The estimated rotor FA is sent back to the current loop for vector control and the estimated rotor speed is fed back into the speed loop for closed-loop speed control. A PI controller is utilized in the speed loop control process. Second, we propose the architecture of a simple microprocessor based on the register transfer level method and we design machine code for the PI controller based on the proposed simple microprocessor. Third, the current vector controller and the EKF algorithm are implemented in dedicated hardware and the finite state machine method is used to design the computational process. Fourth, the Very high speed IC Hardware Description Language (VHDL) is employed to describe the behaviors of the simple microprocessor, the current vector controller, and the EKF algorithm. Finally, a co-simulation study was performed using Simulink and Modelsim to evaluate the effectiveness and correctness of the proposed system, and we present some simulated cases.

EKF-Based Sensorless Vector Control System of Permanent Magnet Synchronous Motor

As the incomparable advantages, permanent magnetic synchronous motor (PMSM) has been used widely in servo system, numerical control machine. The paper introduces an EKF (extended Kalman filter)-based sensorless vector control system of permanent magnet synchronous motor. The rotorfield-oriented control strategy based on id=0 is selected. After expounding the principle of EKF and recursion algorithm, it derives the Kalman state equation in PMSM rest coordinate, makes a discretization processing, and constructs vector control system based on EKF estimator. The simulation model of vector control system of PMSM with MATLAB/Simulink is built and on this basis, it observes the position and speed of the motor rotor by the use of the EKF estimator. Simulation results demonstrate the EKF estimator can accurate estimates of the PMSM rotor position and speed.

Experimental Evaluation of Torque Performance of Voltage and Current Models using Measured Torque for Induction Motor Drives

<span lang="EN-US">In this paper, two kinds of observers are proposed to investigate torque estimation. The first one is based on a voltage model represented with a low-pass filter (LPF); which is normally used as a replacement for a pure integrator to avoid integration drift problem due to dc offset or measurement error. The second estimator used is an extended Kalman filter (EKF) as a current model, which puts into account all noise problems. Both estimation algorithms are investigated during the steady and transient states, tested under light load, and then compared with the measured mechanical torque. In all conditions, the torque estimation error for EKF has remained within a narrow error band and yielded minimum torque ripples, which motivate the use of the EKF estimation algorithm in high performance control drives of IMs for achieving high dynamic performance. </span>