Kalman Filter For State Estimation Research Articles

Extended Kalman Filter Sensor Fusion in Practice for Mobile Robot Localization

Self-driving vehicles and autonomously guided robots could be very beneficial to today's civilization. However, the mobile robot's position must be accurately known, which referred as the localization with the task of tracking the dynamic position, in order for the robot to be active and useful. This paper presents a robot localization method with a known starting location by a real-time reconstructed environment model that represented as an occupancy grid map. The extended Kalman filter (EKF) is formulated as a nonlinear model-based estimator for fuse Odometry and a LIDAR range finder sensor. Because the occupancy grid map for the area is provided, just the inaccuracies of the LIDAR range finder will be considered. The experimental results on the “turtlebot” robot using robot operating system (ROS) show a significant improvement in the pose of the robot using the Kalman filter compared with sample Odometry. This paper also establishes the framework for using a Kalman filter for state estimation, providing all relevant mathematical equations for differential drive robot, this technique can be used to a variety of mobile robots.

Ensemble kalman filter and particle filter-based state estimation on electrical power systems

In this article, a referential study of the sequential importance sampling particle filter with a systematic resampling and the ensemble Kalman filter is provided to estimate the dynamic states of several synchronous machines connected to a modified 14-bus test case, when a balanced three-phase fault is applied at a bus bar near one of the generators. Both are supported by Monte Carlo simulations with practical noise and model uncertainty considerations. Such simulations were carried out in MATLAB by the Power System Toolbox, whereas the evaluation of the Particle Filter and the Ensemble Kalman Filter by script files developed inside the toolbox. The results obtained show that the particle filter has higher accuracy and more robustness to measurement and model noise than the ensemble Kalman filter, which helps support the feasibility of the method for dynamic state estimation applications.

State Estimation for HALE UAVs With Deep-Learning-Aided Virtual AOA/SSA Sensors for Analytical Redundancy

High-altitudelong-endurance (HALE) unmanned aerial vehicles (UAVs) are employed in a variety of fields because of their ability to fly for a long time at high altitudes, even in the stratosphere. Two paramount concerns exist: enhancing their safety during long-term flight and reducing their weight as much as possible to increase their energy efficiency based on analytical redundancy approaches. In this letter, a novel deep-learning-aided navigation filter is proposed, which consists of two parts: an end-to-end mapping-based synthetic sensor measurement model that utilizes long short-term memory (LSTM) networks to estimate the angle of attack (AOA) and sideslip angle (SSA) and an unscented Kalman filter for state estimation. Our proposed method can not only reduce the weight of HALE UAVs but also ensure their safety by means of an analytical redundancy approach. In contrast to conventional approaches, our LSTM-based method achieves better estimation by virtue of its nonlinear mapping capability.

Estimation of flexible space tether state based on end measurement by finite element Kalman filter state estimator

• Finite element Kalman filter to estimate unmeasurable state of tether by measures at tether ends. • Novel measurement model combining real measures at boundary and virtual measures in tether by FEM. • Singularity of reconstruct unmeasurable state by boundary state is eliminated by Kalman filter. This paper proposes a novel finite element Kalman filter to estimate the unmeasurable state of space tether systems based on the measured state at its ends only. The finite element method calculates the unmeasurable internal state as the virtual measurement based on the dynamic model of the system by imposing the input of measured state at the boundary to the model using the Lagrange multiplier method in the spatial space. Combining the real and virtual measurement into a hybrid measurement model of the system, the full state is reconstructed and propagated in the temporal space by the extended Kalman filter. Two state-space system models, the dynamics-based and kinematics-based state models, in the Kalman filter are explored. The observability and stability of the newly proposed finite element Kalman filter are examined and proved. The advantages of the proposed state estimator are (i) the singularity in the virtual measurement of state caused by the number of internal state greater than the number of state measured at the boundary is eliminated in the statistic meaning by the Kalman filter, and (ii) the effects of noises of the observation data and the uncertainties of model discretization are considered and minimized. The correctness and effectiveness of the proposed state estimator is demonstrated by the numerical analysis of a space tether system orbiting around the Earth. The results show the proposed state estimator with only measured state at the ends of the tether successfully provides an accurate time history estimation of geometric configuration and motion of the entire tether. Moreover, the results also show the difference caused by the dynamics-based and kinematics-based system models in the state estimator is negligible. The kinematics-based system model should be used in the state estimator due to its significantly low computational load. Finally, the proposed method can be easily applied for the state estimation process for other space tethered spacecraft systems.

Optimal closed-loop wake steering – Part 1: Conventionally neutral atmospheric boundary layer conditions

Abstract. Strategies for wake loss mitigation through the use of dynamic closed-loop wake steering are investigated using large eddy simulations of conventionally neutral atmospheric boundary layer conditions in which the neutral boundary layer is capped by an inversion and a stable free atmosphere. The closed-loop controller synthesized in this study consists of a physics-based lifting line wake model combined with a data-driven ensemble Kalman filter (EnKF) state estimation technique to calibrate the wake model as a function of time in a generalized transient atmospheric flow environment. Computationally efficient gradient ascent yaw misalignment selection along with efficient state estimation enables the dynamic yaw calculation for real-time wind farm control. The wake steering controller is tested in a six-turbine array embedded in a statistically quasi-stationary, conventionally neutral flow with geostrophic forcing and Coriolis effects included. The controller statistically significantly increases power production compared to the baseline, greedy, yaw-aligned control provided that the EnKF estimation is constrained and informed with a physics-based prior belief of the wake model parameters. The influence of the model for the coefficient of power Cp as a function of the yaw misalignment is characterized. Errors in estimation of the power reduction as a function of yaw misalignment are shown to result in yaw steering configurations that underperform the baseline yaw-aligned configuration. Overestimating the power reduction due to yaw misalignment leads to increased power over the greedy operation, while underestimating the power reduction leads to decreased power; therefore, in an application where the influence of yaw misalignment on Cp is unknown, a conservative estimate should be taken. The EnKF-augmented wake model predicts the power production in yaw misalignment with a mean absolute error over the turbines in the farm of 0.02P1, with P1 as the power of the leading turbine at the farm. A standard wake model with wake spreading based on an empirical turbulence intensity relationship leads to a mean absolute error of 0.11P1, demonstrating that state estimation improves the predictive capabilities of simplified wake models.

Nonlinear observability of unicycle multi-robot teams subject to nonuniform environmental disturbances

In this work, we consider the problem of localizing a team of robots, without access to direct pose measurements, under the influence of nonuniform environmental disturbances and measurement bias. Specifically, we are interested in the conditions under which teams remain range-only localizable when the environmental disturbances vary from robot to robot. We approach this problem through nonlinear observability and graph theory. After analyzing the system’s observability properties, we present theorems that identify the structural conditions under which the system maintains local weak observability. We demonstrate that rigid structures are important not only in defining multi-robot interactions, but also in characterizing the influence of nonuniform disturbances. We also give several example systems to cement intuition on the derived conditions. An observability-based planner is then presented that guides a subset of robots toward trajectories that are highly observable through finite-horizon optimization on robot headings. Simulations are then presented, along with an extended Kalman filter for state estimation, and a comparison to previous methods, to corroborate and demonstrate the results derived.

Dynamic State Estimation of Power Systems by $p$ -Norm Nonlinear Kalman Filter

The problem of dynamic state estimation of power systems is relevant to the monitoring of real-time operation of essential power distribution infrastructure. The nonlinear Kalman filter is utilized for dynamic state estimation of power systems based on available measurements from phasor measurement units. However, measurements are corrupted by non-Gaussian noise and exhibit varying levels of sensitivity to outliers, therefore degrading estimation accuracy. This study proposes a robust mixed p-norm square root unscented Kalman filter for state estimation of power systems. Unlike traditional nonlinear Kalman filters which utilize the minimum mean square error criterion, the mixed p-norm square root unscented Kalman filter utilizes a mixed p-norm optimization for weighting the measurement errors to improve robustness against outliers and alleviate the filtering degradation caused by abnormal measurements. The performance of the p-norm square root unscented Kalman filter is demonstrated in the WSCC 3-machine system and the NPCC 48-machine system. Simulation results demonstrate that the p-norm square root unscented Kalman filter achieves superior accuracy than the commonly used nonlinear Kalman filters.

Comparison of Model Predictive Control (MPC) and Linear-Quadratic Gaussian (LQG) Algorithm for Electrohydraulic Steering Control System

The paper compares the performance of two embedded controllers applied in electrohydraulic steering systems – model predictive controller (MPC) and linear-quadratic Gaussian (LQG) controller with Kalman filtering for state estimation. Both controllers are designed on the basis of single input multiple output “black box” model obtained via identification approach. The controllers are implemented into industrial logic controller for mobile applications and their workability is experimentally checked with a laboratory model of a steering system for non-road mobile machinery. The results corresponding to investigation of performance of the closed-loop system are presented.

Unscented Kalman filter state estimation for manipulating unmanned aerial vehicles

Abstract Manipulating unmanned aerial vehicles (MUAVs) are aerial robots equipped with a mechanism to physically interact with the environment. State estimation of such robots is a challenging problem due to inherent couplings, nonlinearities and uncertainties of MUAV complex dynamics and, therefore, popular algorithms such as extended Kalman filter may not be applicable. With the above considerations, this paper formulates two variants of the unscented Kalman filter using (i) general and (ii) spherical unscented transform to address state estimation problem in MUAVs. In order to examine the effect of estimation quality on overall control performance, first the coupled dynamics of a quadcopter endowed with a robotic manipulator is presented. Next, a linear–quadratic–Gaussian (LQG) control is designed to achieve simultaneous control of the quadcopter and its manipulator. Then, the performance of each unscented Kalman filter algorithm is compared with that of extended Kalman filter in the context of estimation accuracy, overall control performance, and algorithm execution time. Additionally, sensitivity of the proposed approaches to increasing noise levels and total loss of sensory data are examined.

Design and implementation of hybrid Kalman filter for state estimation of power system under unbalanced loads

State estimation technique plays a vital role in predicting the stability of the power system and is done by estimating the primary variables (states) of the system. Voltage magnitudes (V) and angles (δ) at network buses define the state of a power system. Supervisory control and data acquisition is used to monitor and control the power system state variables where in accurate state variable estimation is quite complex due to the presence of noise in the measured data. State estimation (SE) using conventional techniques such as weighted least square, regularised least square, Kalman filter predict the state vectors with still random error due to its parametric limitations. This study proposes hybrid Kalman filter based SE where the limitation in efficient handling of more number of variables using Kalman filter is addressed by regularising the state variables with constrains and the results are validated for 62-bus Indian utility system. The simulation results explain the operational efficiency of the hybrid Kalman filtering method under various load variation conditions and the results are compared with SE using conventional Kalman filtering method.

Double hybrid Kalman filtering for state estimation of dynamical systems

In this paper authors present a new approaches to the hybrid Kalman filtering and modified hybrid Kalman filtering, with the changed order of methods inside (Unscented Kalman Filter and Extended Kalman Filter). For these algorithms, the modification based on double use of Hybrid Kalman Filters (Excented and Unscented) has been proposed. This new modification has been checked for Hybrid Kalman Particle Filters too, for the variable number of particles. Based on the obtained results, one can see that duplication of hybrid filters can improve the estimation quality.

Comparative study of methods for integrated model identification and state of charge estimation of lithium-ion battery

Abstract Model-based observers appeal to both research and industry utilization due to the high accuracy and robustness. To further improve the robustness to dynamic work conditions and battery ageing, the online model identification is integrated to the state estimation, giving rise to the co-estimation methods. This paper systematically compares three types of co-estimation methods for the online state of charge of lithium-ion battery. This first method is dual extended Kalman filter which uses two parallel filters for co-estimation. The second method is a typical data-model fusion method which uses recursive least squares for model identification and extended Kalman filter for state estimation. Meanwhile, a noise compensating method based on recursive total least squares and Rayleigh quotient minimization is exploited for online model identification, which is further designed in conjunction with the extended Kalman filter to estimate the state of charge. Simulation and experimental studies are carried out to compare the performances of three methods in terms of the accuracy, convergence property, and noise immunity. The computing cost and tuning effort are further discussed to give insights to the application prospective of different methods.

Intelligent attitude and flapping angles estimation of flybarless helicopters under near-hover conditions

Abstract Inaccuracy of measurements, associated with most of the commercial-off-the-shelf (COTS) Inertial Measurement Unit (IMU), impede achieving an accurate attitude estimation during autonomous near-hover flight. Moreover, the unmeasured states of the Tip Path Plane (TPP) flapping angles of the main rotor make the estimation and control of unmanned helicopters more challenging. In this paper, an intelligent adaptive fuzzy data fusion algorithm is designed to obtain more accurate estimates of the attitude and flapping angles for a flybarless miniature helicopter. In this algorithm, the filter's measurement noise matrix is continuously adapted using the Innovative-based Adaptive Estimation (IAE) technique. This technique is based on evaluating the discrepancy between the actual and theoretical covariance of the filter's innovation sequence. A well-tuned multi-input, single output Fuzzy Inference System (FIS) takes the value of this evaluated discrepancy and its rate of change as inputs and provides the required adjustment value as an output based on a set of predefined fuzzy rules. Compared to the conventional Kalman Filter (KF) state estimation results, the proposed intelligent estimation results have demonstrated an obvious enhancement in estimating the attitude and the flapping angles. The estimated flapping angles have been also used to estimate the moments and forces of the helicopter rotors under near-hover assumptions. An actual near-hover flight was conducted to validate the performance of the proposed intelligent estimation method.

A marginalized unscented Kalman filter for efficient parameter estimation with applications to finite element models

Abstract This paper focuses on the problem of combined state/parameter estimation in dynamical systems with many degrees of freedom, for instance finite element models, using measured data from the system and nonlinear Bayesian filtering techniques for the estimation. A highly efficient nonlinear Kalman filtering technique is developed, based on a combination of linear or extended Kalman filtering for state estimation and unscented filtering for parameter learning. Such a combination is implemented by applying the principle of marginalization to the unscented transform. This method leads to a very efficient state/parameter filtering algorithm by taking advantage of the fact that Jacobians of the system equations with respect to the dynamic states, required in extended Kalman filtering, can be easily related to outputs of the finite element analysis required for forward propagation. For linear dynamical systems this approach yields an algorithm with identical accuracy as the UKF but reduced computational time, as demonstrated on several medium-size examples. For nonlinear systems, the resulting algorithm is also superior to the UKF in terms of computational time, due to the fact that Jacobians are functions of the tangent stiffness matrix of the system, whose computation is required for propagation in finite element analysis. It is also shown that, even though this algorithm relies on linearization for propagation of moments of the dynamic states, this reduction in accuracy compared to a generic UKF does not affect learning of the parameters for the systems considered herein.

Nonlinear estimator design based on extended Kalman filter approach for state estimation of articulated heavy vehicle

In this article, in order to measure the state variables directly in an articulated heavy vehicle, the extended Kalman filter approaches are proposed. For this purpose, using Kane’s method, a nonlinear model is developed for the articulated vehicle, including the motion equations of longitudinal, lateral, and yaw motion of the tractor, and the hitch articulation angle between the tractor and the semi-trailer. Using TruckSim software, the articulated vehicle model is verified through high-velocity lane change maneuver (a single sinusoidal wave with an amplitude of 5° and a frequency of 0.5 Hz) under the dry and slippery road condition. The simulation results showed that the proposed model is close to the real vehicle model and can be used in the estimator development. Then, the state estimation algorithm is designed and implemented using extended Kalman filter for real-time estimation of the states. To evaluate the performance of the extended Kalman filter, simulations with two maneuvers including high-velocity lane change maneuvers in the dry road and slippery road are carried out. The simulation results demonstrate the impressive performance of the extended Kalman filter for state estimation of the articulated vehicle in critical conditions such as the slippery road and the high velocity.

Variational Bayesian adaptation of noise covariances in multiple target tracking problems

Abstract Multiple Target Tracking (MTT) is the process of computing the number of targets present in a surveillance area. MTT requires estimation of state variables and data association. New measurements are associated with existing tracks, clutter or new tracks. MTT generally involves unknown number of targets. Mostly because of computational complexity faced by MTT algorithms, it is a difficult and challenging problem. Computational load, underlying assumptions of known number of targets, and high cluttered environment are the main reasons, which available methods cannot address properly. Rao-Blackwellized has been used for multiple target tracking. It uses Kalman filter for state estimation and particle filter for data association. Our objective is to extend Rao-Blackwellized Monte Carlo Data Association (RBMCDA) that estimates number of targets and maintains track continuity enabling persistent tracking of targets. RBMCDA has been tested with seven different resampling methods in an effort to obtain the best resampling method. Gating validation and Variational Bayesian have been incorporated for multi target tracking problem. The modified RBMCDAs are applied to different case studies for its performance evaluation.

기동 특성을 가진 표적의 상태 추정을 위한 기동 보상 Kalman 필터

본 논문에서는 기동 특성이 존재하는 표적의 상태 추정에 대하여 논한다. 기존에 상태 추정에 사용하던 표적의 운동 방정식의 한계에 대해 서술하며 새로운 운동 방정식을 묘사한다. 또한 표준 Kalman 필터를 사용한 상태 추정 과정에서 표적의 기동 특성이 작용할 경우에 발생하는 필터 이노베이션의 변화와 상태 추정 과정에 발생하는 문제점에 대해 서술하며 이에 대한 해결 방안으로 기동 보상 Kalman 필터를 제안한다. 제안된 필터는 표준 Kalman 필터와 필터 이노베이션을 기반으로 기동 특성을 추정하는 퍼지 기동 추정기를 결합한 것으로 상태 추정 성능을 개선한다. 제안된 필터의 성능을 확인하기 위해 속력에 대한 기동 특성을 갖는 표적에 대해 표준 Kalman 필터와 제안된 기동 보상 Kalman 필터를 사용한 상태 추정 시뮬레이션을 수행하여 결과를 비교하고 분석한다.

Extended Kalman filtering for state estimation of a Hill muscle model

The objectives of this study are five-fold: (i) design an extended Kalman filter (EKF) for the single-muscle and two-muscle Hill models; (ii) design an EKF for unknown-input estimation of the muscle models; (iii) investigate the detectability of the muscle models; (iv) examine the robustness of the EKF to modeling errors; and (v) improve state estimation by incorporating physical constraints into the estimator. Two noisy measurements are available for state estimation: muscle length, which is measured from joint angles; and muscle activation, which is measured from electromyography sensors. Simulation results verify that the EKF is an effective approach for estimation of the activation signals and the states of the system if the system is detectable; the EKF outperforms the high gain observer; and the EKF is robust to modeling errors. The standard deviations of the estimation errors are in the range 0.01-0.1 mm for the muscle lengths, which is one to two orders of magnitude more accurate than the measurements. The standard deviations of the dimensionless muscle activation estimation errors are in the range 0.01-0.02, which is one order of magnitude more accurate than the measurements. A projection approach accounts for constraints to further improve the estimates.

The Extended Kalman Filter for State Estimation of Dynamic UV Flash Processes

Abstract We present an extended Kalman filter for state estimation of semi-explicit index-1 differential-algebraic equations. It is natural to model dynamic UV flash processes with such differential-algebraic equations. The UV flash is a mathematical statement of the second law of thermodynamics. It is therefore important to thermodynamically rigorous models of many phase equilibrium processes. State estimation of UV flash processes has applications in control, prediction, monitoring, and fault detection of chemical processes in the oil and gas industry, e.g. separation, distillation, drilling of oil wells, multiphase flow in oil pipes, and oil production. We present a numerical example of a UV flash separation process. It involves soft sensing of vapor-liquid compositions based on temperature and pressure measurements.

Time-Domain Power Quality State Estimation Based on Kalman Filter Using Parallel Computing on Graphics Processing Units

A methodology is developed to assess the time-domain power quality state estimation (PQSE) in electrical systems based on the Kalman filter implemented using parallel processing techniques through graphics processing units (GPUs) to reduce the execution time. The measurements used by the state estimation algorithm are taken from the simulation and transient propagation response of the power network. The parallel Kalman filter (PKF) state estimation obtains the waveforms for busbar voltages and line currents with several sources of time-varying electromagnetic transients. The PKF is evaluated using the compute unified device architecture (CUDA) platform and the CUDA basic linear algebra subprograms library, the parallel filter is executed on GPU cards. Case studies are applied to solve the time-domain state estimation using the proposed PKF-PQSE method, obtaining an execution time reduction and including time-varying harmonics, short circuit faults, and load transient conditions. The speed-up depends on the number of state variables modeling the electrical system under analysis. The PKF-PQSE results are successfully compared and validated against the power systems computer aided design/electromagnetic transients including direct current simulator.