Extended Kalman Filter State Research Articles

Relaxing the planar assumption: 3D state estimation for an autonomous surface vessel

Autonomous Surface Vessels (ASVs) are increasingly being proposed as tools to automate environmental data collection, bathymetric mapping and shoreline monitoring. For many applications it can be assumed that the boat operates on a 2D plane. However, with the involvement of exteroceptive sensors like cameras or laser rangefinders, knowing the 3D pose of the boat becomes critical. In this paper, we formulate three different algorithms based on 3D extended Kalman filter state estimation for ASV localization. We compare them using field testing results with ground truth measurements, and demonstrate that the best performance is achieved with a model-based solution in combination with a complementary filter for attitude estimation. Furthermore, we present a parameter identification methodology and show that it also yields accurate results when used with inexpensive sensors. Finally, we present a long-term series (i.e. over a full year) of shoreline monitoring data sets and discuss the need for map maintenance routines based on a variant of the Iterative Closest Point algorithm.

Optimal GPS/accelerometer integration algorithm for monitoring the vertical structural dynamics

AbstractThe vertical structural dynamics is a crucial factor for structural health monitoring (SHM) of civil structures such as high-rise buildings, suspension bridges and towers. This paper presents an optimal GPS/accelerometer integration algorithm for an automated multi-sensor monitoring system. The closed loop feedback algorithm for integrating the vertical GPS and accelerometer measurements is proposed based on a 5 state extended KALMAN filter (EKF) and then the narrow moving window Fast Fourier Transform (FFT) analysis is applied to extract structural dynamics. A civil structural vibration is simulated and the analysed result shows the proposed algorithm can effectively integrate the online vertical measurements produced by GPS and accelerometer. Furthermore, the accelerometer bias and scale factor can also be estimated which is impossible with traditional integration algorithms. Further analysis shows the vibration frequencies detected in GPS or accelerometer are all included in the integrated vertical defection time series and the accelerometer can effectively compensate the short-term GPS outages with high quality. Finally, the data set collected with a time synchronised and integrated GPS/accelerometer monitoring system installed on the Nottingham Wilford Bridge when excited by 15 people jumping together at its mid-span are utilised to verify the effectiveness of this proposed algorithm. Its implementations are satisfactory and the detected vibration frequencies are 1.720 Hz, 1.870 Hz, 2.104 Hz, 2.905 Hz and also 10.050 Hz, which is not found in GPS or accelerometer only measurements.

INS/GPS Fusion for Navigation of Unmanned Aerial Vehicles

This paper presents fusion of inertial navigation system (INS) and global positioning system (GPS) for estimating position, velocities, attitude and heading of an unmanned aerial vehicle (UAV). A 15 state extended Kalman filter (EKF) and a split architecture consisting of 6 state non-linear complementary filter (NCF) and 9 state EKF are investigated in detail. In both these fusion architectures GPS and IMU consisting of 3 axis accelerometers, 3 axis rate gyros and 3 axis magnetometer have been fused in open loop fashion (loosely coupled) to estimate the navigation states. These architectures have been implemented in MATLAB/SIMULINK environment and evaluated in closed loop guidance of MAV with Software-In-Loop-Simulation (SILS) setup. Furthermore, the 15-state EKF algorithm is validated with flight test data obtained from onboard data logger using an off-the shelf autopilot board (Ardupilot Mega APM-2.5) for UAV.

CROSS-COVARIANCE ESTIMATION FOR EKF-BASED INERTIAL AIDED MONOCULAR SLAM

Abstract. Repeated observation of several characteristically textured surface elements allows the reconstruction of the camera trajectory and a sparse point cloud which is often referred to as "map". The extended Kalman filter (EKF) is a popular method to address this problem, especially if real-time constraints have to be met. Inertial measurements as well as a parameterization of the state vector that conforms better to the linearity assumptions made by the EKF may be employed to reduce the impact of linearization errors. Therefore, we adopt an inertial-aided monocular SLAM approach where landmarks are parameterized in inverse depth w.r.t. the coordinate system in which they were observed for the first time. In this work we present a method to estimate the cross-covariances between landmarks which are introduced in the EKF state vector for the first time and the old filter state that can be applied in the special case at hand where each landmark is parameterized w.r.t. an individual coordinate system.

An EKF Based Generalized Estimation Approach for Evasive Targets

A generalized approach is presented in this paper for accurately estimating the states of the targets, which can either be non-maneuvering or undergoing various maneuvers, including the most evasive ‘barrel roll maneuver'. A nine state Extended Kalman filter (EKF) formulation is presented here with three relative positions, three relative velocities, barrel frequency of aircraft, axial acceleration and maneuvering coefficient. A significant advantage of present model is that it is quite generic in nature and can capture barrel roll as well as other maneuvers (including no maneuver) without any change of estimation formulation or tuning parameters. Extensive simulation studies with a predictive guidance shows that the new estimation formulation can lead to very good engagement performance with noisy RF seeker measurement parameters, namely gimbal angles, gimbal angle rates, range and range rate.

LiPB Battery SOC Estimation Using Extended Kalman Filter Improved with Variation of Single Dominant Parameter

This paper proposes the State-of-charge (SOC) estimator of a LiPB Battery using the Extended Kalman Filter (EKF). EKF can work properly only with an accurate model. Therefore, the high accuracy electrical battery model for EKF state is discussed in this paper, which is focused on high-capacity LiPB batteries. The battery model is extracted from a single cell of LiPB 40Ah, 3.7V. The dynamic behavior of single cell battery is modeled using a bulk capacitance, two series RC networks, and a series resistance. The bulk capacitance voltage represents the Open Circuit Voltage (OCV) of battery and other components represent the transient response of battery voltage. The experimental results show the strong relationship between OCV and SOC without any dependency on the current rates. Therefore, EKF is proposed to work by estimating OCV, and then is converted it to SOC. EKF is tested with the experimental data. To increase the estimation accuracy, EKF is improved with a single dominant varying parameter of bulk capacitance which follows the SOC value. Full region of SOC test is done to verify the effectiveness of EKF algorithm. The test results show the error of estimation can be reduced up to max 5%SOC.

A Method for Modeling and Simulation of Differential Drive Mobile Robot Localization Based on EKF Multisensor Fusion

A method was proposed based on principle of EKF (extended Kalman Filter) state estimation to improve the localization precision of differential drive mobile robot. The robot position was estimated by Multisensor fusion of Odometer and laser, which kinematics model, the robot sensor perception model and the sensor error model were presented. The models were introduced into the state estimation and covariance matrix update equation of EKF with match convergence condition and nonlinear error correction covariance matrix.The specific iteration equation was acquired.The simulation results demonstrate the approach of modeling and fusion is accurate and validity.

Adaptive EKF-Based Estimator of Sideslip Angle Using Fusion of Inertial Sensors and GPS

This paper presents an adaptive extended Kalman filter(EKF)-based sideslip angle estimator, which utilizes a sensor fusion concept that combines the high-rate inertial sensors measurements with the low-rate GPS velocity measurements. The sideslip angle estimation is based on a vehicle kinematic model relying on the lateral accelerometer and yaw rate gyro measurements. The vehicle velocity measurements from lowcost, single antenna GPS receiver are used for compensation of potentially large drift-like estimation errors caused by inertial sensors offsets. Adaptation of EKF state covariance matrix ensures a fast convergence of inertial sensors offsets estimates, and consequently a more accurate sideslip angle estimate. By using a detailed simulation analysis, it is found out that the main sources of estimation errors include inaccuracies of pre-estimated vehicle longitudinal velocity obtained from nondriven wheel speed sensors, the GPS velocity signal latency, and the road bank-related disturbances. Several compensation methods are proposed to suppress the influence of these errors.

State-of-Charge Estimation for Lithium-Ion Batteries Using Neural Networks and EKF

This paper presents a method for modeling and estimation of the state of charge (SOC) of lithium-ion (Li-Ion) batteries using neural networks (NNs) and the extended Kalman filter (EKF). The NN is trained offline using the data collected from the battery-charging process. This network finds the model needed in the state-space equations of the EKF, where the state variables are the battery terminal voltage at the previous sample and the SOC at the present sample. Furthermore, the covariance matrix for the process noise in the EKF is estimated adaptively. The proposed method is implemented on a Li-Ion battery to estimate online the actual SOC of the battery. Experimental results show a good estimation of the SOC and fast convergence of the EKF state variables.

Augmented state–extended Kalman filter combined framework for topology estimation in large‐area underwater mapping

AbstractOver the past few years, underwater vehicles have greatly improved as a tool for undersea exploration and navigation. In particular, autonomous navigation, localization, and mapping through optical imaging have become topics of interest for researchers in both underwater robotics and marine science. Underwater imagery can be used to construct image composites (photomosaics) used in many different application areas such as underwater surveying and navigation. For surveying operations with a low‐cost robot limited to a down‐looking camera and a sonar altimeter, it is common practice to ensure that there is enough overlap between time‐consecutive images as this is the only data source of navigation. When the robot revisits a previously surveyed area, it is essential to detect and match the non‐time‐consecutive images to close a loop and, thus, improve trajectory estimation. While creating the mosaic, most of the existing algorithms try to match all image pairs to detect the non‐time‐consecutive overlapping images when there is no additional navigation information. We present a framework to obtain a two‐dimensional mosaic with minimum image matching attempts and simultaneously get the best possible trajectory estimation by exploring the contribution of the image pairs matching to the whole system. Different strategies for choosing match candidates have been tested, and the results are given in different challenging underwater image sequences. © 2010 Wiley Periodicals, Inc.

Relating Torque and Slip in an Odometric Model for an Autonomous Agricultural Vehicle

This paper describes a method of considering the slip that is experienced by the wheels of an agricultural autonomous guided vehicle such that the accuracy of dead-reckoning navigation may be improved. Traction models for off-road locomotion are reviewed. Using experimental data from an agricultural AGV, a simplified form suitable for vehicle navigation is derived. This simplified model relates measurements of the torques applied to the wheels with wheel slip, and is used as the basis of an observation model for odometric sensor data in the vehicle's extended Kalman filter (EKF) navigation system. The slip model parameters are included as states in the vehicle EKF so that the vehicle may adapt to changing surface properties. Results using real field data and a simulation of the vehicle EKF show that positional accuracy can be increased by a slip-aware odometric model, and that when used as part of a multi-sensor navigation system, the consistency of the EKF state estimator is improved.

Grey-box Modeling of Friction: An Experimental Case-study

Grey-box modeling covers the domain where we want to use a balanced amount of white box modeling based on first principles and black-box modeling based on empiricism. The two grey-box models presented combine a white-box model with a black-box model, i.e., a neural network model and a polytopic model that are capable of identifying friction characteristics that are left unexplained by first principles modeling. In an experimental case-study, both grey-box models are applied to identify a rotating arm subjected to friction. An augmented state extended Kalman filter is used iteratively and off-line for the estimation of unknown parameters. For the studied example and defined blackbox topologies, little difference is observed between the two models. In addition, the applicability of the identified models is illustrated in a model basedfriction compensation control scheme with the objective to linearize the system.

Towards a Useful Dynamic Model of the Anaerobic Wastewater Treatment Process: A Practical Illustration of Process Identification

Results are reported from a dynamic modelling study conducted on a pilot scale anaerobic fluidized bed. The objective of the study was to generate data to identify, evaluate and eventually calibrate a dynamic model for on-line estimation and forecasting in a process control system. Experiments consisted of pulse inputs of glucose, propionic acid, and acetic acid during the treatment of a distillery wastewater. The dynamic response of the methane and carbon dioxide production rates, hydrogen content of the biogas, effluent volatile acid concentrations and effluent COD concentrations are shown. A model structure was postulated based on the results observed in the dynamic experiments. An extended Kalman filter state estimation algorithm was employed to provide estimates of unmeasured process states and parameters. The use of the state estimation technique improved the performance of the model, helped locate model inadequacies, and provided information to direct further model development.

Application of the fixed-interval smoother to maneuvering trajectory estimation

This correspondence considers the problem of estimating the state variables and maneuvering parameters for a reentry vehicle. The nonlinear filtering results based upon a tuned nine state extended Kalman filter (EKF) are compared with those obtained by a linearized fixed interval smoother, which reprocesses the output of the EKF, using Monte Carlo simulation experiments.