Showing papers on "Invariant extended Kalman filter published in 2016"

A Generalized Extended Kalman Filter Implementation for the Robot Operating System

Abstract: Accurate state estimation for a mobile robot often requires the fusion of data from multiple sensors. Software that performs sensor fusion should therefore support the inclusion of a wide array of heterogeneous sensors. This paper presents a software package, robot_localization, for the robot operating system (ROS). The package currently contains an implementation of an extended Kalman filter (EKF). It can support an unlimited number of inputs from multiple sensor types, and allows users to customize which sensor data fields are fused with the current state estimate. In this work, we motivate our design decisions, discuss implementation details, and provide results from real-world tests.

A Linear Kalman Filter for MARG Orientation Estimation Using the Algebraic Quaternion Algorithm

Abstract: Real-time orientation estimation using low-cost inertial sensors is essential for all the applications where size and power consumption are critical constraints. Such applications include robotics, human motion analysis, and mobile devices. This paper presents a linear Kalman filter for magnetic angular rate and gravity sensors that processes angular rate, acceleration, and magnetic field data to obtain an estimation of the orientation in quaternion representation. Acceleration and magnetic field observations are preprocessed through a novel external algorithm, which computes the quaternion orientation as the composition of two algebraic quaternions. The decoupled nature of the two quaternions makes the roll and pitch components of the orientation immune to magnetic disturbances. The external algorithm reduces the complexity of the filter, making the measurement equations linear. Real-time implementation and the test results of the Kalman filter are presented and compared against a typical quaternion-based extended Kalman filter and a constant gain filter based on the gradient-descent algorithm.

Kalman filtering based on the maximum correntropy criterion in the presence of non-Gaussian noise

Abstract: State estimation in the presence of non-Gaussian noise is discussed. Since the Kalman filter uses only second-order signal information, it is not optimal in non-Gaussian noise environments. The maximum correntropy criterion (MCC) is a new approach to measure the similarity of two random variables using information from higher-order signal statistics. The correntropy filter (C-Filter) uses the MCC for state estimation. In this paper we first improve the performance of the C-Filter by modifying its derivation to obtain the modified correntropy filter (MC-Filter). Next we use the MCC and weighted least squares (WLS) to propose an MCC filter in Kalman filter form, which we call the MCC-KF. Simulation results show the superiority of the MCC-KF compared with the C-Filter, the MC-Filter, the unscented Kalman filter, the ensemble Kalman filter, and the Gaussian sum filter, in the presence of two different types of non-Gaussian disturbances (shot noise and Gaussian mixture noise).

The Accurate Continuous-Discrete Extended Kalman Filter for Radar Tracking

Abstract: This paper elaborates the Accurate Continuous-Discrete Extended Kalman Filter grounded in an ODE solver with global error control and its comparison to the Continuous-Discrete Cubature and Unscented Kalman Filters. All these state estimators are examined in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn. The latter is considered to be a challenging one for testing nonlinear filtering algorithms. Our numerical results show that all the methods can be used for practical target tracking, but the Accurate Continuous-Discrete Extended Kalman Filter is more flexible and robust. It treats successfully (and without any manual tuning) the air traffic control scenario for various initial data and for a range of sampling times.

The Tobit Kalman Filter: An Estimator for Censored Measurements

Abstract: Tobit model censored data arise in multiple engineering applications through saturating sensors, limit-of-detection effects, and image frame effects. In this brief, we introduce a novel formulation of the Kalman filter for Tobit Type 1 censored measurements. Our proposed formulation, called the Tobit Kalman filter, is identical to the standard Kalman filter in the no-censoring case. At or near the censored region, the Tobit Kalman filter utilizes a local approximation of the probability of censoring in order to provide a fully recursive estimate of the state and state error covariance. The additional computational burden of the method compared with the standard Kalman filter is limited to the calculation of $m$ normal probability density functions and $m$ normal cumulative density functions per update, where $m$ is the number of measurements.

Robust Kalman filtering for nonlinear multivariable stochastic systems in the presence of non‐Gaussian noise

Abstract: Summary The presence of outliers can considerably degrade the performance of linear recursive algorithms based on the assumptions that measurements have a Gaussian distribution. Namely, in measurements there are rare, inconsistent observations with the largest part of population of observations (outliers). Therefore, synthesis of robust algorithms is of primary interest. The Masreliez–Martin filter is used as a natural frame for realization of the state estimation algorithm of linear systems. Improvement of performances and practical values of the Masreliez-Martin filter as well as the tendency to expand its application to nonlinear systems represent motives to design the modified extended Masreliez–Martin filter. The behaviour of the new approach to nonlinear filtering, in the case when measurements have non-Gaussian distributions, is illustrated by intensive simulations. Copyright © 2015 John Wiley & Sons, Ltd.

A comparative study and review of different Kalman filters by applying an enhanced validation method

Abstract: The Kalman filter is a common state of charge estimation algorithm for lithium-ion cells. Since its first introduction in the application of lithium-ion cells, different implementations of Kalman filters were presented in literature. However, due to non-uniform validation methods and filter tuning parameters, the performance of different Kalman filters is difficult to quantify. On this account, we compare 18 different implementations of Kalman filters with an enhanced validation method developed in our previous work. The algorithms are tested during a low-dynamic, high-dynamic and a long-term current load profile at −10 °C, 0 °C, 10 °C, 25 °C and 40 °C with a fixed set of filter tuning values. To ensure comparability, a quantitative rating technique is used for estimation accuracy, transient behaviour, drift, failure stability, temperature stability and residual charge estimation. The benchmark shows a similar estimation accuracy of all filters with an one and two RC term equivalent circuit model. Furthermore, a strong dependency on temperature during high-dynamic loads is observed. To evaluate the importance of the tuning parameters, the temperature dependency is reduced with an individual filter tuning. It is reasoned, that not only the filter type is significant for the estimation performance, but the filter tuning.

Sliding-Mode Control for a Three-Phase Unity Power Factor Rectifier Operating at Fixed Switching Frequency

Abstract: This paper presents an improved variable hysteresis-band current-control in natural frame for a three-phase unity power rectifier. The proposed control algorithm is based on three decoupled sliding-mode controllers combined with three independent Kalman filters. The use of Kalman filters instead of a nonadaptive state observer improves the quality of the estimated signals in presence of noise, increasing the immunity of the control loop in noisy environments. To reduce drastically the computational load in the Kalman algorithm, a reduced bilinear model is derived which allows to use a Kalman filter algorithm instead of an extended Kalman filter. A fast output-voltage control is also presented which avoids output-voltage variations when a sudden change in the load or a voltage sag appears. Moreover, a fixed switching frequency algorithm is proposed which uses a variable hysteresis-band in combination with a switching decision algorithm, ensuring a switching spectrum concentrated around the desired switching frequency. The overall control proposal has been fully integrated into a digital signal processor. Selected experimental results are introduced to validate the theoretical contributions of this paper.

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

Abstract: 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.

Extended Kalman filter under maximum correntropy criterion

Abstract: As a nonlinear extension of Kalman filter, the extended Kalman filter (EKF) is also based on the minimum mean square error (MMSE) criterion. In general, the EKF performs well in Gaussian noises. But its performance may deteriorate substantially when the system is disturbed by heavy-tailed impulsive noises. In order to improve the robustness of EKF against impulsive noises, a new filter for nonlinear systems is proposed in this paper, namely the maximum correntropy extended Kalman filter (MCEKF), which adopts the maximum correntropy criterion (MCC) as the optimization criterion instead of using the MMSE. In MCEKF, the state mean and covariance matrix propagation equation are used to obtain a prior estimation of the state and covariance matrix, and then a fixed-point algorithm is used to update the posterior estimates. The robustness of the new filter is confirmed by simulation results.

Extended Kalman filter-based parallel dynamic state estimation

Abstract: There is a growing need for accurate and efficient real-time state estimation with increasing complexity, interconnection, and insertion of new devices in power systems. In this paper, a massively parallel dynamic state estimator is developed on a graphic processing unit (GPU), which is especially designed for processing large data sets. Within the massively parallel framework, a lateral two-level dynamic state estimator is proposed based on the extended Kalman filter method, utilizing both supervisory control and data acquisition, and phasor measurement unit (PMU) measurements. The measurements at the buses without PMU installations are predicted using previous data. The results of the GPU-based dynamic state estimator are compared with a multithread CPU-based code. Moreover, the effects of direct and iterative linear solvers on the state estimation algorithm are investigated. The simulation results show a total speed-up of up to 15 times for a 4992-bus system.

Stereo Visual-Inertial Odometry With Multiple Kalman Filters Ensemble

Abstract: In this paper, we present a stereo visual-inertial odometry algorithm assembled with three separated Kalman filters, i.e., attitude filter, orientation filter, and position filter. Our algorithm carries out the orientation and position estimation with three filters working on different fusion intervals, which can provide more robustness even when the visual odometry estimation fails. In our orientation estimation, we propose an improved indirect Kalman filter, which uses the orientation error space represented by unit quaternion as the state of the filter. The performance of the algorithm is demonstrated through extensive experimental results, including the benchmark KITTI datasets and some challenging datasets captured in a rough terrain campus.

Adaptive Three-Step Kalman Filter for Air Data Sensor Fault Detection and Diagnosis

Abstract: Air data sensor fault detection and diagnosis is important for the safety of aircraft. In this paper, first an extension of the robust three-step Kalman filter to nonlinear systems is made by proposing a robust three-step unscented Kalman filter. The robust three-step unscented Kalman filter is found to be sensitive to the initial condition error when dealing with air data sensor fault estimation. A theoretical analysis of this sensitivity is presented and a novel adaptive three-step unscented Kalman filter is proposed which is able to cope with not only the estimation of the air data sensor faults, but also the detection and isolation of faults. The adaptive three-step unscented Kalman filter contains three steps: time update, fault estimation and measurement update. This approach can reduce the sensitivity to the initial condition error. Finally, the air data sensor fault detection and diagnosis performance of the adaptive three-step unscented Kalman filter is validated using simulated aircraft data. Ad...

An improved real-time adaptive Kalman filter with recursive noise covariance updating rules

Abstract: Kalman filter (KF) is used extensively for state estimation. Among its requirements are the process and observation noise covariances which are unknown or partially known in real life applications. Biased initializations of the covariances result in performance degradation of KF or divergence. Therefore, an extensive research is carried on to improve its performance however, relying on a moving window, heavy computations, and the availability of the exact model are the fundamental problems in most of the proposed techniques. In this paper, we are using the idea of the recursive estimation of KF to propose two recursive updating rules for the process and observation covariances respectively designed based on the covariance matching principles. Each rule is a tuned scaled version of the previous covariance in addition to a tuned correction term derived based on the most recent available data. The proposed adaptive Kalman filter AKF avoided the aforementioned problems and proved itself to have an improved performance over the conventional KF. The results show that the AKF estimates are more accurate, have less noise and more stable against biased covariance initializations.

Estimating SE(3) elements using a dual quaternion based linear Kalman filter.

Abstract: Many applications in robotics such as registration, object tracking, sensor calibration, etc. use Kalman filters to estimate a time invariant SE(3) element by locally linearizing a non-linear measurement model. Linearization-based filters tend to suffer from inaccurate estimates, and in some cases divergence, in the presence of large initialization errors. In this work, we use a dual quaternion to represent the SE(3) element and use multiple measurements simultaneously to rewrite the measurement model in a truly linear form with state dependent measurement noise. Use of the linear measurement model bypasses the need for any linearization in prescribing the Kalman filter, resulting in accurate estimates while being less sensitive to initial estimation error. To show the broad applicability of this approach, we derive linear measurement models for applications that use either position measurements or pose measurements. A procedure to estimate the state dependent measurement uncertainty is also discussed. The efficacy of the formulation is illustrated using simulations and hardware experiments for two applications in robotics: rigid registration and sensor calibration.

Online Dereverberation for Dynamic Scenarios Using a Kalman Filter With an Autoregressive Model

Abstract: Reverberant signals can be modeled in the short-time Fourier transform domain using a frequency-dependent autoregressive (AR) model. In state-of-the-art, these AR coefficients have been considered stationary, which does not hold in time-varying environments. We propose to model these AR coefficients using a first-order Markov process, whereas the reverberant microphone signal observations are considered deterministic. This leads to a framework where the AR coefficients can be optimally estimated using a Kalman filter per subband. As a consequence, we can dereverberate the observed signals by applying the estimated AR coefficients as an adaptive linear filter per subband. Estimators for the required statistical parameters in the Kalman filter are derived. Due to the adaptive solution, the algorithm is suitable for real-time applications. It is shown that the proposed method outperforms an existing recursive least-squares solution in terms of reverberation reduction, convergence time, and tracking changes in the acoustic scene.

An Adaptive Complementary Kalman Filter Using Fuzzy Logic for a Hybrid Head Tracker System

Abstract: In this paper, a sensor fusion algorithm that integrates gyroscope and vision measurements using an adaptive complementary Kalman filter is proposed to estimate the attitude of a hybrid head tracker system. In order to make the filter more tolerant to vision measurement fault and more robust to system dynamics, an adaptive fading filter is implemented to the sensor fusion filter, and fuzzy logic is applied to adjust the fading factor, which adapts a Kalman gain of the sensor fusion filter. For recognizing the dynamic condition of the system and vision measurement fault, the normalized square error of attitude and the norm of gyroscope output with designed membership functions are used. The performance of the proposed algorithm is evaluated by simulations. It is confirmed that the proposed algorithm has better performance than the conventional algorithms in high-dynamic conditions and vision measurement fault case.

A performance comparison between extended Kalman Filter and unscented Kalman Filter in power system dynamic state estimation

Abstract: Dynamic State Estimation (DSE) is a critical tool for analysis, monitoring and planning of a power system. The concept of DSE involves designing state estimation with Extended Kalman Filter (EKF) or Unscented Kalman Filter (UKF) methods, which can be used by wide area monitoring to improve the stability of power system. State estimation with EKF and UKF methods can be used for monitoring and estimating the dynamic state variables of multi-machine power systems, which are generator rotor speed and rotor angle. This paper uses Powerfactory to solve power flow analysis of simulations, then a non-linear state estimator is developed in MatLab to solve states by applying the unscented Kalman filter (UKF) and Extended Kalman Filter (EKF) algorithm. Finally, a DSE model is built for a 14 bus power system network to evaluate the proposed algorithm for the networks. This article will focus on comparing and studying the advantages and disadvantages of both methods under transient conditions. It is demonstrated that UKF is easier to implement and accurate in estimation.

A New Adaptive H-Infinity Filtering Algorithm for the GPS/INS Integrated Navigation.

Abstract: The Kalman filter is an optimal estimator with numerous applications in technology, especially in systems with Gaussian distributed noise. Moreover, the adaptive Kalman filtering algorithms, based on the Kalman filter, can control the influence of dynamic model errors. In contrast to the adaptive Kalman filtering algorithms, the H-infinity filter is able to address the interference of the stochastic model by minimization of the worst-case estimation error. In this paper, a novel adaptive H-infinity filtering algorithm, which integrates the adaptive Kalman filter and the H-infinity filter in order to perform a comprehensive filtering algorithm, is presented. In the proposed algorithm, a robust estimation method is employed to control the influence of outliers. In order to verify the proposed algorithm, experiments with real data of the Global Positioning System (GPS) and Inertial Navigation System (INS) integrated navigation, were conducted. The experimental results have shown that the proposed algorithm has multiple advantages compared to the other filtering algorithms.