Sequential Extended Kalman Filter Research Articles

Network Analysis of Active and Passive Radar Based on the Extended Kalman Filter

In this current work, a sequential extended Kalman filter (EKF) algorithm is proposed to solve the quandary of regional accuracy disparity for time difference of arrival (TDOA) positioning in passive radar. The proposed approach entails merging the complete set of active radar observation data with the TDOA data of passive radar in a serial fashion, followed by the deployment of the EKF algorithm for the purpose of filtering. The simulation results show that the proposed data fusion method effectively solves the regional accuracy imbalance problem caused by the fuzzy area and no solution area of the TDOA positioning solution through the conflation of the precision merits of active and passive radar, and improves the overall target detection accuracy.

Magnetometer-Only Kalman Filter Based Algorithms for High Accuracy Spacecraft Attitude Estimation (A Comparative Analysis)

Kalman Filter (KF) based algorithms are the most frequently employed attitude estimation algorithms. Typically, a fully observable system necessitates the use of two distinct sensor types. Therefore, relying on a single sensor, such as a magnetometer, for spacecraft attitude estimation is deemed to be a challenge. The present investigation centers on utilizing magnetometers as the exclusive sensor. Several KF based estimation algorithms have been designed and evaluated to give the designer of spacecraft Attitude and Orbit Control System (AOCS) the choice of a suitable algorithm for his mission based on quantitative measures. These algorithms are capable of effectively addressing nonlinearity in both process and measurement models. The algorithms under examination encompass the Extended Kalman Filter (EKF), Sequential Extended Kalman Filter (SEKF), Pseudo Linear Kalman Filter (PSELIKA), Unscented Kalman Filter (USKF), and Derivative Free Extended Kalman Filter (DFEKF). The comparison of the distinct algorithms hinges on key performance metrics, such as estimation error for each axis, computation time, and convergence rate. The resulting algorithms provide numerous benefits, such as diverse levels of high estimation accuracy (with estimation errors ranging from 0.014o to 0.14o), varying computational demands (execution time ranges from 0.0536s to 0.0584s), and the capability to converge despite large initial attitude estimation errors (which reached 170o). These properties render the algorithms appropriate for utilization by spacecraft designers in all operational modes, supplying high-precision attitude estimations better than (0.5o) despite high magnetometer noise levels, which reached (200 nT).

Three-axis high-accuracy spacecraft attitude estimation via sequential extended Kalman filtering of single-axis magnetometer measurements

Magnetometer is a highly advantageous sensor for determining a spacecraft’s attitude. This article provides a solution to the problem of spacecraft attitude estimation using magnetometer measurements only. To ensure full observability of spacecraft attitude states, it is necessary to use at least two types of sensors. Consequently, utilizing a single sensor, such as the magnetometer, poses a significant challenge for any attitude estimation algorithm, including the extended Kalman filter (EKF). Moreover, implementing the EKF algorithm, or any other attitude estimation algorithm, is computationally intensive. To address these issues, an algorithm has been developed that estimates spacecraft attitude angles and attitude rates using a sequential extended Kalman filter (SEKF). This algorithm offers numerous benefits over those found in the literature such as high accuracy, low computational resource requirements, the ability to converge even with large initial attitude and angular velocity estimation errors, and the ability to function even if two of the three measurement channels of the magnetometer are not functioning. With these benefits, the developed SEKF algorithm is capable of operating in all spacecraft operational modes, delivering accurate performance and computation time. In spite of measurements with large noise values, the high accuracy achieved by the SEKF algorithm enables the magnetometer to serve as the sole source of attitude information, even if one or two magnetometer measurement channels are not functioning.

Tire-Road Friction Coefficient Estimation Based on Fusion of Model- and Data-Based Methods

Abstract The tire-road interaction generates vehicle driving forces, which affect vehicle performance such as maximum acceleration and stability. Sequential extended Kalman filter (S-EKF) integrated with a slope method has been used for tire-road friction coefficient estimation with its own limitations, along with several “cause-based” and “effect-based” methods. This research proposes a new stochastic-based evaluation criterion using existing vehicle sensor signals with the help of the data-driven Kriging model. The proposed estimation method is validated by both CarSim™ simulation and experimental studies, respectively, under different road conditions. The results show that the proposed novel criterion has a strong correlation with the road friction coefficient and provide an improved tire-road friction coefficient estimation. A signal fusion estimation scheme based on both S-EKF and proposed evaluations is developed to improve estimation robustness.

Positioning accuracy improvement in high‐speed GPS receivers using sequential extended Kalman filter

It is well known that in high-speed movements, the positioning accuracy of global positioning system (GPS) receivers decreases drastically. The models presented so far to describe high-speed motion do not represent the state of the system precisely, so positioning accuracy with the methods based on these models is not appropriate. Here, a comprehensive method is proposed to solve the accuracy issue of the single-frequency GPS receiver at high-speed motions without increasing the computational complexity. Suitable modelling of the GPS receivers at high-speed motion, using the sequential extended Kalman filter, correct determination of the process noise covariance matrix and accurately estimating the variance of the observations are the basics of the proposed approach. Simulations with different data and motion scenarios (at speeds from 100 to 7300 m/s) show that the proposed method, while not increasing the computational cost, improves the accuracy of positioning more than 70% when compared to the conventional methods.

Capacity estimation of lithium-ion cells by combining model-based and data-driven methods based on a sequential extended Kalman filter

Estimating the capacity of lithium-ion cells employed in electric vehicles is challenging because of the complex vehicle conditions and inconsistent cell decay. This paper proposes a novel capacity estimation method realized by combining model-based and data-driven methods based on a sequential extended Kalman filter (SEKF), to improve the accuracy, and reliability of capacity estimation. First, cycle aging tests are conducted on four cells under different aging stress. Second, the state-of-charge and capacity of the cells are co-estimated using a third-order extended Kalman filter (EKF) driven by dynamic data obtained under different aging stages. The advantages and disadvantages of this data-driven method are investigated. Third, a discrete Arrhenius aging model (DAAM) is developed to estimate the capacity, and its parameter mismatch problem is addressed. Finally, an SEKF estimator is proposed to integrate the capacities obtained using these methods. The SEKF comprises two EKFs connected in series: one to update the model parameters of the DAAM via the feedback provided by the third-order EKF and the other to combine the capacities from the third-order EKF and DAAM. The experimental results show that the proposed SEKF is suitable for capacity estimation with excellent accuracy and stability under different aging stress and dynamic conditions.

Maneuvering Acceleration Estimation Algorithm Using Doppler Radar Measurement

An algorithm to estimate the tangential and normal accelerations directly using the Doppler radar measurement in an online closed loop form is proposed. Specific works are as follows: first, the tangential acceleration and normal acceleration are taken as the state variables to establish a linear state transition equation; secondly, the decorrelation unbiased conversion measurement Kalman filter (DUCMKF) algorithm is proposed to deal with the strongly nonlinear measurement equation; thirdly, the geometric relationship between the range rate and the velocity direction angle is used to obtain two estimators of the velocity direction angle; finally, the interactive multiple model (IMM) algorithm is used to fuse the estimators of the velocity direction angle and then the adaptive IMM of current statistical model based DUCMKF (AIMM-CS-DUCMKF) is proposed. The simulation experiment results show that the accuracy and stability of DUCMKF are better than the sequential extended Kalman filter algorithm, the sequential unscented Kalman filter algorithm, and converted measurement Kalman filter algorithms; on the other hand they show that the AIMM-CS-DUCMKF can obtain the high accuracy of the tangential and normal accelerations estimation algorithm.

Autonomous orbit determination using epoch-differenced gravity gradients and starlight refraction

Autonomous orbit determination via integration of epoch-differenced gravity gradients and starlight refraction is proposed in this paper for low-Earth-orbiting satellites operating in GPS-denied environments. Starlight refraction compensates for the significant along-track position error that occurs from only using gravity gradients and benefits from integration in terms of improved accuracy in radial and cross-track position estimates. The between-epoch differencing of gravity gradients is employed to eliminate slowly varying measurement biases and noise near the orbit revolution frequency. The refraction angle measurements are directly used and its Jacobian matrix derived from an implicit observation equation. An information fusion filter based on a sequential extended Kalman filter is developed for the orbit determination. Truth-model simulations are used to test the performance of the algorithm, and the effects of differencing intervals and orbital heights are analyzed. A semi-simulation study using actual gravity gradient data from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) combined with simulated starlight refraction measurements is further conducted, and a three-dimensional position accuracy of better than 100m is achieved.

Monocular Visual Mapping for Obstacle Avoidance on UAVs

An unmanned aerial vehicle requires adequate knowledge of its surroundings in order to operate in close proximity to obstacles. UAVs also have strict payload and power constraints which limit the number and variety of sensors available to gather this information. It is desirable, therefore, to enable a UAV to gather information about potential obstacles or interesting landmarks using common and lightweight sensor systems. This paper presents a method of fast terrain mapping with a monocular camera. Features are extracted from camera images and used to update a sequential extended Kalman filter. The features locations are parameterized in inverse depth to enable fast depth convergence. Converged features are added to a persistent terrain map which can be used for obstacle avoidance and additional vehicle guidance. Simulation results, results from recorded flight test data, and flight test results are presented to validate the algorithm.

Analysis of Different Feature Selection Criteria Based on a Covariance Convergence Perspective for a SLAM Algorithm

This paper introduces several non-arbitrary feature selection techniques for a Simultaneous Localization and Mapping (SLAM) algorithm. The feature selection criteria are based on the determination of the most significant features from a SLAM convergence perspective. The SLAM algorithm implemented in this work is a sequential EKF (Extended Kalman filter) SLAM. The feature selection criteria are applied on the correction stage of the SLAM algorithm, restricting it to correct the SLAM algorithm with the most significant features. This restriction also causes a decrement in the processing time of the SLAM. Several experiments with a mobile robot are shown in this work. The experiments concern the map reconstruction and a comparison between the different proposed techniques performance. The experiments were carried out at an outdoor environment composed by trees, although the results shown herein are not restricted to a special type of features.

Towards features updating selection based on the covariance matrix of the SLAM system state

SUMMARYThis paper addresses the problem of a features selection criterion for a simultaneous localization and mapping (SLAM) algorithm implemented on a mobile robot. This SLAM algorithm is a sequential extended Kalman filter (EKF) implementation that extracts corners and lines from the environment. The selection procedure is made according to the convergence theorem of the EKF-based SLAM. Thus, only those features that contribute the most to the decreasing of the uncertainty ellipsoid volume of the SLAM system state will be chosen for the correction stage of the algorithm. The proposed features selection procedure restricts the number of features to be updated during the SLAM process, thus allowing real time implementations with non-reactive mobile robot navigation controllers. In addition, a Monte Carlo experiment is carried out in order to show the map reconstruction precision according to the Kullback–Leibler divergence curves. Consistency analysis of the proposed SLAM algorithm and experimental results in real environments are also shown in this work.

Model error and sequential data assimilation: A deterministic formulation

AbstractData assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. These errors are usually modelled on the basis of simple assumptions such as bias, white noise, and first‐order Markov process. In the present work, a formulation of the sequential extended Kalman filter is proposed, based on recent findings on the universal deterministic behaviour of model errors in marked contrast with previous approaches. This new scheme is applied in the context of a spatially distributed system proposed by Lorenz. First, it is found that, for short times, the estimation error is accurately approximated by an evolution law in which the variance of the model error (assumed to be a deterministic process) evolves according to a quadratic law, in agreement with the theory. Moreover, the correlation with the initial condition error appears to play a secondary role in the short‐time dynamics of the estimation error covariance. Second, the deterministic description of the model error evolution, incorporated into the classical extended Kalman filter equations, reveals that substantial improvements of the filter accuracy can be gained compared with the classical white‐noise assumption. The universal short‐time quadratic law for the evolution of the model error covariance matrix seems very promising for modelling estimation error dynamics in sequential data assimilation. Copyright © 2008 Royal Meteorological Society