Performance Of Extended Kalman Filter Research Articles

Estimation of Airship Aerodynamic Forces and Torques Using Extended Kalman Filter

An airship is a lighter than air, aerial vehicle whose model is based on dynamic, aerodynamic, aerostatic and propulsion forces and torques. Apart from other, aerodynamic forces and toques are difficult to measure. In this work, an estimation scheme for aerodynamic forces and torques based on the Extended Kalman Filter (EKF) is presented. It is assumed that the airship attitude and position estimates are available. EKF estimates the airship body axes linear and angular velocities and aerodynamic forces and torques. As the method measures a complete aerodynamic model instead of measuring its individual parameters by utilizing minimum auxiliary state variables, it is computationally non-intensive and can provide online aerodynamic model information that can be used in controller implementation in a real-time environment. Nonlinear simulation environment is developed for the experimental airship and EKF performance is evaluated. For validating the estimator's performance, 3-σ uncertainty bounds and error analysis, estimator convergence analysis and it's closed-loop simulations with Sliding Mode Controller have been performed. The simulation results show that EKF successfully estimates the airship states and aerodynamic forces and torques with minimum estimation error enhancing the model-based nonlinear controller performance.

Optimal Estimation and Tracking Control for Variable-speed Wind Turbine with PMSG

Designing an optimal tracking controller and system observer is a nonlinear problem in the variable-speed wind energy conversion system (WECS). In this paper, an adjusted feedforward and feedback optimal controller with extended Kalman filter (EKF) is introduced to estimate and control the permanent magnet synchronous generator (PMSG) for the maximum power point tracking (MPPT) with several disturbances of the wind speed. An augmented model of wind turbine and PMSG is expanded, and then the parameters of the optimal controller and estimator are obtained. The dynamic stability of the closed-loop system with feedback-feedforward controller (FFC), EKF and speed controller are analyzed. To compare the dynamic performance of EKF and FFC with the conventional controllers, numerical results are demonstrated with the disturbances of the wind speed and faults in power grid.

ASENKRON MOTORUN İNDİRGENMİŞ-DERECELİ UYARLAMALI GENİŞLETİLMİŞ KALMAN FİLTRESİ İLE DURUM VE PARAMETRE KESTİRİMİ

In this study, the design of reduced-order adaptive extended Kalman filter (EKF) for speed-sensorless control of induction motors (IMs) is performed, and its performance is tested using it in a speed-sensorless direct vector controlled drive system under simulations. The proposed observer estimates the stator stationary axis components of rotor fluxes and rotor mechanical speed required for vector control in addition to disturbance load torque. On the other hand, estimation performance of EKFs depends on the correct selection of system ( ) and measurement ( ) error covariance matrices. In the literature, these matrices are generally assumed as constant and determined by the trial-and-error method. However, those matrices are affected by operating conditions of IM and should be updated according to operating conditions in order to obtain higher performance estimations. Since the simultaneously update of both and may lead to divergence or tracking problems, only is updated considering operating conditions by adaptive EKF (AEKF) algorithm having a forgetting factor. In addition, AEKF has been designed as reduced-order with the aim of reduction of its computational burden for real-time applications.

Impact of Observability and Multi-objective Optimization on the Performance of Extended Kalman Filter for DTC of AC Machines

It is well known that the selection of extended Kalman filter (EKF) covariance elements has a considerable bearing on the effectiveness of EKF performance. The observability at very low frequency is also an essential property for the selection of EKF elements. This paper investigates the optimization of the EKF covariance elements when zero frequency is included in the training profile for direct torque control (DTC) of induction motor. In addition, the paper studies the optimization of EKF by speed and torque fitness functions using a non-dominated sorting genetic algorithm-II at zero and high speeds under stable flux regulation. For this purpose, DTC with constant switching frequency controller which has the capability of establishing continuous flux rotation regardless of speed variation is used. The optimized results of EKF for both DTC motor drives and speed and torque cost functions are verified experimentally.

Nonlinear State and Parameter Estimation for Parabolic Trough Collector

We propose and compare various estimation methods for estimating states and parameters for a Parabolic Trough Collector (PTC) which is a key component of a solar thermal power plant. In particular, we compare popular approaches namely Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), both of which implicitly assume Gaussian state densities, with a recently proposed approach named Unscented Gaussian Sum Filter (UGSF) which does not make the Gaussianity assumptions. These filters are compared for various scenarios involving estimation of states along with either spatially constant or spatially varying PTC efficiency. The results demonstrate superior performance of EKF and UKF over UGSF. Further, EKF is identified to have the lowest computational burden which is also acceptable for real-time computations. Thus, use of EKF for estimating states in real-time is proposed, which can then be used in advanced control and optimization strategies.

Robustness Evaluation of Extended and Unscented Kalman Filter for Battery State of Charge Estimation

In this paper, the robustness of model-based state observers including extended Kalman filter (EKF) and unscented Kalman filter (UKF) for state of charge (SOC) estimation of a lithium-ion battery against unknown initial SOC, current noise, and temperature effects is investigated. To more comprehensively evaluate the performance of EKF and UKF, two battery models including the first-order resistor-capacitor equivalent circuit and combined model are considered. A novel method is proposed to identify the parameters of the equivalent circuit model. The performance of SOC estimation is evaluated by employing measurement data from a commercial lithium-ion battery cell. The experiment results show that UKF generally outperforms EKF in terms of estimation accuracy and convergence rate for each battery model. However, the advantages of UKF over EKF with the combined model is not as significant as with the equivalent circuit model. Both EKF and UKF demonstrate strong robustness against current noise. The updates of model parameters corresponding to operational temperatures generally improve the estimation accuracy of EKF and UKF for both models.

Observability analysis for soil moisture estimation

The knowledge of soil moisture is important in studying climatology, earth science and most importantly irrigation decision support systems, but is often hard to determine since it is not possible to use critical measurements including moisture sensors all over the entire agricultural grid sector. As a result, soil moisture at unmeasured region needs to be estimated, which can be done using state estimators such as Kalman based estimators. The model that is used to represent water transfer between atmosphere, plant and soil, also known as agro-hydrological model, is highly nonlinear. Since ‘strong’ rather than ‘weak’ observability of the system ensures better performance of Kalman based estimators to develop a reliable soil moisture estimation algorithm, the main objective of this study is to discuss observability analysis of this nonlinear agro-hydrological system.The study was performed using synthetic data. The extended Kalman filter (EKF) was chosen as the state estimator. As would be expected, the results show that the EKF performance is better in cases where the system is ‘strongly’ observable.

Improving Vehicle Localization in a Smart City with Low Cost Sensor Networks and Support Vector Machines

A smart city’s main purpose is to provide intelligent responses to different problems of the rapid urban population growth. For instance, integrating fleet management solutions into intelligent transportation systems (ITS) can efficiently resolve transportation problems relying on each vehicle information. Usually, the position estimate is ensured by the integration of the Global Positioning System (GPS) and Inertial Navigation Systems (INS). For multisensor data fusion, the Extended Kalman Filter (EKF) is generally applied using the sensor’s measures and the GPS position as a helper. However, the INS are expensive and require more complex computing which induces restrictions on their implementation. Furthermore, the EKF performance depends on the vehicle dynamic variations and may quickly diverge because of environmental changes. In this paper, we present a robust low cost approach using EKF and Support Vector Machines (SVM) to reliably estimate the vehicle position by limiting the EKF drawbacks. The sensors used are a GPS augmented by a low cost wireless sensor network. When GPS signals are available, we train SVM on different dynamics and outage times to learn the position errors so we can correct the future EKF predictions during GPS signal outages. We obtain empirically an improvement of up to 94% over the simple EKF predictions in case of GPS failures.

Comparison of Unscented and Extended Kalman Filters with Application in Vehicle Navigation

The Unscented Kalman Filter (UKF) is a well-known nonlinear state estimation method. It shows superior performance at nonlinear estimation compared to the Extended Kalman Filter (EKF). This paper is devoted to an investigation between UKF and EKF with different feedback control modes in vehicle navigation. Theoretical formulation, simulation and field tests have been carried out to compare the performance of UKF and EKF. The simulation and test results demonstrate that the estimated state of a UKF relies on the measurements and is less sensitive to historical model information. The results also indicate that UKF has benefits for prototype model design due to avoidance of calculation of a Jacobian matrix. EKF, however, is more computationally efficient and more stable.

Improving ultrasonic-based seamless navigation for indoor mobile robots utilizing EKF and LS-SVM

The ultrasonic positioning system is able to provide centimeter-level location information. However, the signal of the system is easy to be disturbed and the outages of the positioning system appear. Inertial measuring units (IMUs) is a self-contained device and can provide long-term navigation information independently, but it has the drawback of error drift. In order to obtain accurate and continuous location information indoors for indoor mobile robots, this work proposed a seamless integrated navigation utilizing extended Kalman filter (EKF) and Least Squares Support Vector Machine (LS-SVM). In this mode, the EKF estimates the position and the velocity of the robot while the signals of ultrasonic positioning system are available. Meanwhile, the compensation model is trained by LS-SVM with corresponding filter states. Once the signals of ultrasonic positioning system are outages, the model is able to correct inertial navigation system (INS) solution as filter does. A prototype of the system has been worked in a real scenario. The results show that the performance of EKF is robust, and the prediction of LS-SVM is able to work as EKF does during the outages.

Analysis of a variational Bayesian adaptive cubature Kalman filter tracking loop for high dynamic conditions

Under high dynamic conditions, a robust tracking loop is essential for accuracy positioning with the global position system. In previous studies, the extended Kalman filter (EKF)-based tracking loop technology has been proven better than the traditional tracking loop technology under high dynamic conditions. However, the performance of EKF may degrade because under high dynamic conditions, the statistics of measurement noise may change with time. In order to improve the robustness of the tracking loop under high dynamic conditions, the variational Bayesian adaptive cubature Kalman filter (VBACKF) algorithm with different types of measurement noise variances is proposed and used to track the carrier and code in this study. In the proposed algorithm, the measurement noise is considered as random variables and dynamically estimated by variational Bayesian theory. We take into consideration the two-measurement model with measurements in-phase and quadra-phase prompt (IP and QP), and the six-measurement model with measurements in-phase and quadra-phase prompt, early and late (IP, QP, IE, QE, IL and QL), and compare the proposed method with the EKF- and CKF-based tracking loops. The analytical and simulation results show that the VBACKF-based tracking loop performs better than both the EKF- and CKF-based tracking loops. Furthermore, the influence on the tracking loop of the different numbers of measurements used in the measurement model is also investigated. The results show that the phase, code and frequency tracking performances of EKF-, CKF- and VBACKF-based six measurements outperform those of the corresponding filter-based two measurements under dynamic conditions.

Self-Localization Over RFID Tag Grid Excess Channels Using Extended Filtering Techniques

Accuracy of target self-localization in RFID tag information networks and grids critically affects its situation awareness. With an insufficient localization accuracy, information about local 2D or 3D surroundings delivered to a target by request may provoke collisions, even fatal. In RFID networking systems, target state can be observed over a big number of tags. For such a case, the extended Kalman filter (EKF) algorithm is modified and a new extended unbiased finite impulse response (EFIR) filtering algorithm is developed. We show that redundant information captured from the tags allows increasing both the localization accuracy and system stability. The common factor here is that the number of tags required to increase accuracy is limited in the target nonlinear medium, by about six in our case. It is also shown that target state observation over the RFID tag excess channels allows mitigating effect of the imprecisely defined noise statistics on the EKF performance and preventing divergence in EKF.

Circular Arrays and Inertial Measurement Unit for DOA/TOA/TDOA-Based Endoscopy Capsule Localization: Performance and Complexity Investigation

This paper investigates the performance of wireless capsule endoscopy (WCE) tracking within the irregular environment of digestion system by integrating directional-of-arrival (DOA), time-of-arrival (TOA) [or time-difference-of-arrival (TDOA)], and inertial measurement unit (IMU) measurements using the extended Kalman filter (EKF). Here, an emitter transmits a signal to the WCE, and the WCE replies the signal back to a set of antenna arrays. Then, the round trip TOA, and the DOA of the signals transmitted from WCE to the antenna arrays are measured. The digestion system path model is considered unknown, and the movement model between two consecutive signals is assumed linear. Simulations are conducted to investigate the EKF performance as a function of the number of antenna arrays, antenna array configuration, and TOA (and TDOA) estimation accuracy. In addition, the impact of IMU on the localization performance will be studied. Simulations confirm the proposed WCE tracking performance. In addition, the computational complexity of the EKF with respect to the number of antenna array is studied.

Bayesian methods for time‐varying state and parameter estimation in induction machines

SummaryThis paper addresses the problem of nonlinear time‐varying state and parameter estimation of induction machines (IMs) on the basis of a third‐order electrical model. The objectives of this paper are threefold. The first objective is to propose the use of an improved particle filter (IPF) with better proposal distribution for nonlinear and non‐Gaussian state and parameter estimation. The second objective is to extend the state and parameter estimation techniques (i.e., extended Kalman filter (EKF), unscented Kalman filter (UKF), particle filter (PF), and IPF) to better handle nonlinear and non‐Gaussian processes without a priori state information, by utilizing a time‐varying assumption of statistical parameters. In this case, the state vector to be estimated at any instant is assumed to follow a Gaussian model, where the expectation and the covariance matrix are both random. The third objective is to compare the performances of EKF, UKF, PF, and IPF in estimating the states of the power process model representing the IM (i.e, the rotor speed, the rotor flux, the stator flux, the rotor resistance, and the magnetizing inductance) and their abilities to estimate some of the key system parameters, which are needed to define the IM process model. The results show that the IPF provides a significant improvement over the PF because, unlike the PF, which depends on the choice of sampling distribution used to estimate the posterior distribution, the IPF yields an optimum choice of the sampling distribution, which also accounts for the observed data. This conclusion is also supported by the experimental results. Copyright © 2014 John Wiley & Sons, Ltd.

Localization Performance Evaluation of Extended Kalman Filter in Wireless Sensors Network

This paper evaluates the positioning and tracking performance of Extended Kalman Filter (EKF) in wireless sensors network. The EKF is a linear approximation of statistical Kalman Filter (KF) and has the capability to work efficiently in non- linear systems. The EKF is based on an iterative process of estimating current state information from the previously estimated state. Its working is based on the linearization of observation model around the mean of current state information. The EKF has small computation complexity and requires low memory compared to other Bayesian algorithms which makes it very suitable for low powered mobile devices. This paper evaluates the localization and tracking performance of EKF for (i) Position (P) model, (ii) Position-Velocity (PV) model and (iii) Position-Velocity-Acceleration (PVA) model. The EKF processes distance measurements from cricket sensors that are acquired through time difference of arrival between ultrasound and Radio Frequency (RF) signals. Further, localization performance under varying number of beacons/sensors is also evaluated in this paper.

Modeling and System Identification using Extended Kalman Filter for a Quadrotor System

Quadrotor has emerged as a popular testbed for Unmanned Aerial Vehicle (UAV) research due to its simplicity in construction and maintenance, and its vertical take-off, landing and hovering capabilities. It is a flying rotorcraft that has four lift-generating propellers; two of the propellers rotate clockwise and the other two rotate counter-clockwise. This paper presents modeling and system identification for auto-stabilization of a quadrotor system through the implementation of Extended Kalman Filter (EKF). EKF has known to be typical estimation technique used to estimate the state vectors and parameters of nonlinear dynamical systems. In this paper, two main processes are highlighted; dynamic modeling of the quadrotor and the implementation of EKF algorithms. The aim is to obtain a more accurate dynamic modelby identify and estimate the needed parameters for thequadrotor. The obtained results demonstrate the performances of EKF based on the flight test applied to the quadrotor system.

The Performance Analysis of an AKF Based Tightly-Coupled INS/GNSS Sensor Fusion Scheme with Non-Holonomic Constraints for Land Vehicular Applications

INS/GNSS integration scheme can overcome the shortcoming of GNSS or INS alone to provide superior performance. The position and velocity from GNSS is an excellent external aid to update the INS with improving its long-term accuracy. Adaptive Kalman Filter (AKF) is based on the maximum likelihood criterion for choosing the most appropriate weight and thus to adjust Kalman gain factors online. The conventional Extended Kalman Filter (EKF) implementation suffers uncertain results while the update measurement covariance matrix R does not meet the case. The primary advantage of AKF is that the filter has less relationship with the priori statistical information because the R varies with time. The innovation sequence is used to derive the measurement weights through the measurement covariance matrices, innovation-based adaptive estimation (IAE) in this study. There are two non-holonomic constraints (NHC) available for land vehicle navigation. Land vehicles will not jump off or slid on the ground under normal condition. Using these constraints, the velocity of the vehicle in the plane perpendicular to the forward direction is almost zero. EKF and AKF based tightly-coupled scheme with NHC are implemented in the study. To validate the performance of EKF and AKF based tightly-coupled INS/GNSS integration scheme with NHC, field scenarios were conducted in the downtown area of Tainan city. The test platform was mounted on the top of a land vehicle and the data fusion of INS/GNSS/NHC can be used as stand-alone positioning tool during GNSS outages of over 1 minute. The preliminary results presented in this study illustrated that AKF based tightly-coupled INS/GNSS integration scheme can provide more stable solutions combined with NHC during GNSS outages of over 1 minute. Generally speaking, the improvement ratio in term of 3D positioning of proposed algorithm reach 40% compared to EKF based tightly-coupled INS/GNSS integration scheme.

Density-based Monte Carlo filter and its applications in nonlinear stochastic differential equation models

Nonlinear stochastic differential equation models with unobservable state variables are now widely used in analysis of PK/PD data. Unobservable state variables are usually estimated with extended Kalman filter (EKF), and the unknown pharmacokinetic parameters are usually estimated by maximum likelihood estimator. However, EKF is inadequate for nonlinear PK/PD models, and MLE is known to be biased downwards. A density-based Monte Carlo filter (DMF) is proposed to estimate the unobservable state variables, and a simulation-based M estimator is proposed to estimate the unknown parameters in this paper, where a genetic algorithm is designed to search the optimal values of pharmacokinetic parameters. The performances of EKF and DMF are compared through simulations for discrete time and continuous time systems respectively, and it is found that the results based on DMF are more accurate than those given by EKF with respect to mean absolute error.

ADDRESSING ISSUES IN INERTIAL NAVIGATION OF MICRO AERIAL VEHICLES (MAV) VIA AN EXTENDED KALMAN FILTER WITH BIASED SENSORS

This paper presents two ways to implement Extended Kalman Filter (EKF) algorithm for Inertial Navigation of a Micro Aerial Vehicle (MAV). The objective is to develop a fully integrated system using Micro electro mechanical systems (MEMS) inertial sensors combined with low-update rate Global positioning system (GPS) measurements. The approach uses three accelerometers, three gyroscopes and GPS measurements to aid the EKF algorithm. Two ways to implement EKF (15-state and splitarchitecture) are presented and observability issues are addressed in each case. EKF performance was evaluated by comparing the estimates with the simulated truth data.

Nonlinear State Estimation of Tire-Road Contact Forces Using a 14 DoF Vehicle Model

The knowledge of the wheel forces is fundamental to the development of Advanced Driver Assistance Systems (ADAS) such as Electronic Stability Control (ESC) and Anti-Roll Control (ARC). However the direct measurement of the wheel forces has been very difficult. To overcome this drawback, it has been a common practice in the industry to estimate the forces at the tire-road contact using mathematical vehicle models and estimators, especially the Extended Kalman Filter (EKF). In this contribution, the performance of the EKF is evaluated using a complete spatial model with 14 degrees of freedom.