Showing papers on "Alpha beta filter published in 2018"

Model-Free Control for Continuum Robots Based on an Adaptive Kalman Filter

Abstract: Continuum robots with structural compliance have promising potential to operate in unstructured environments. However, this structural compliance brings challenges to the controller design due to the existence of considerable uncertainties in the robot and its kinematic model. Typically, a large number of sensors are required to provide the controller the state variables of the robot, including the length of each actuator and position of the robot tip. In this paper, a model-free method based on an adaptive Kalman filter is developed to accomplish path tracking for a continuum robot using only pressures and tip position. As the Kalman filter operates only with a two-step algebraic calculation in every control interval, the low computational load and real-time control capability are guaranteed. By adding an optimal vector to the control law, buckling of the robot can also be avoided. Through simulation analysis and experimental validation, this control method shows good robustness against the system uncertainty and external disturbance, and lowers the number of sensors.

Dynamic State Estimation With Model Uncertainties Using $H_\infty$ Extended Kalman Filter

Abstract: When implementing Kalman filters to track system dynamic state variables, the dynamical model is assumed to be accurate. However, this assumption may not hold true as power system dynamical model is subjected to various uncertainties, such as varying generator transient reactance in different operation conditions, uncertain inputs, or noise statistics. As a result, the performance of Kalman-type filters can be degraded significantly. To bound the influence of these uncertainties, this letter proposes an $H_\infty$ extended Kalman filter (HEKF) based on the robust control theory. An approach to tune the parameter of HEKF is presented as well. Numerical results on the IEEE 39-bus system demonstrate the effectiveness of the HEKF.

Contact Force Estimation for Robot Manipulator Using Semiparametric Model and Disturbance Kalman Filter

Abstract: Force estimation methods enable robots to interact with the environment or humans compliantly and safely without additional sensing device. In this paper, we present a novel method for estimating unknown contact forces exerted on a robot manipulator. The force estimation method is divided into two steps. The first step is to identify a robot dynamics model. A parametric model is derived first based on rigid-body dynamic (RBD) theory. To improve the model accuracy, a nonparametric compensator trained with multilayer perception (MLP) is added to compensate for errors of the RBD model. The result is a semiparametric model that provides better model accuracy than either the RBD model or the MLP model alone. The second step is to construct a force estimation observer. A novel estimation method called disturbance Kalman filter (DKF) is developed in this paper. The design of DKF based on a time-invariant composite system model is presented. DKF can take both manipulator's dynamics model and disturbance's dynamics model into account. As with Kalman filter, it can provide robust and accurate estimation against uncertainty. Simulation and experimental results, obtained using a six-degrees-of-freedom Kinova Jaco2 manipulator, demonstrate the effectiveness of the proposed method.

Identification of an Autonomous Underwater Vehicle Hydrodynamic Model Using the Extended, Cubature, and Transformed Unscented Kalman Filter

Abstract: Having an accurate mathematical model is essential in design, control, and navigation process of an autonomous underwater vehicle (AUV) Due to the modeling simplifications, the available mathematical models suffer from the uncertainty of their parameters and they usually need an identification phase for improving the modeling accuracy In case of AUVs, the hydrodynamic coefficients of the model play an important role and they should be identified using the available experimental data In this paper, a 6-DoF dynamic model of an AUV is presented and then some of its parameters including viscous damping, the body lift, and control input coefficients that have the highest effects on the modeling error are identified by augmented state model method The extended Kalman filter (EKF), cubature Kalman filter (CKF), and transformed unscented Kalman filter (TUKF) are used as the estimation filters To verify and compare the three estimation filters with consideration of the predetermined hydrodynamic coefficients and spiral maneuver AUV results, these three methods are evaluated The results indicate that the TUKF identifies the best hydrodynamic model due to solving both the CKF nonlocal sampling problem and the EKF linearization problem

The Two-State Implicit Filter Recursive Estimation for Mobile Robots

Abstract: This letter deals with recursive filtering for dynamic systems where an explicit process model is not easily devisable. Most Bayesian filters assume the availability of such an explicit process model, and thus may require additional assumptions or fail to properly leverage all available information. In contrast, we propose a filter that employs a purely residual-based modeling of the available information and thus achieves higher modeling flexibility. While this letter is related to the descriptor Kalman filter, it also represents a step toward batch optimization and allows the integration of further techniques, such as robust weighting for outlier rejection. We derive recursive filter equations that exhibit similar computational complexity when compared to their Kalman filter counterpart—the extended information filter. The applicability of the proposed approach is experimentally confirmed on two different real mobile robotic state estimation problems.

Variable Structure Control in Natural Frame for Three-Phase Grid-Connected Inverters With LCL Filter

Abstract: This paper presents a variable structure control in natural frame for a three-phase gird-connected voltage-source inverter with LCL filter. The proposed control method is based on modifying the converter model in natural reference frame, preserving the low-frequency state-space variables dynamics. Using this model in a Kalman filter (KF), the system state-space variables are estimated allowing us to design three independent current sliding-mode controllers. The main closed-loop features of the proposed method are: first, robustness against grid inductance variations because the proposed model is independent of the grid inductance; second, the power losses are reduced since physical damping resistors are avoided; third, the control bandwidth can be increased due to the combination of a variable hysteresis comparator with the KF; and fourth, the grid-side current is directly controlled providing high robustness against harmonics in the grid. To complete the control scheme, a theoretical stability analysis is developed. Finally, selected experimental results validate the proposed control strategy and permit illustrating all its appealing features.

Online natural gradient as a Kalman filter

Abstract: We cast Amari’s natural gradient in statistical learning as a specific case of Kalman filtering. Namely, applying an extended Kalman filter to estimate a fixed unknown parameter of a probabilistic model from a series of observations, is rigorously equivalent to estimating this parameter via an online stochastic natural gradient descent on the log-likelihood of the observations. In the i.i.d. case, this relation is a consequence of the “information filter” phrasing of the extended Kalman filter. In the recurrent (state space, non-i.i.d.) case, we prove that the joint Kalman filter over states and parameters is a natural gradient on top of real-time recurrent learning (RTRL), a classical algorithm to train recurrent models. This exact algebraic correspondence provides relevant interpretations for natural gradient hyperparameters such as learning rates or initialization and regularization of the Fisher information matrix.

Multi-Area Dynamic State Estimation With PMU Measurements by an Equality Constrained Extended Kalman Filter

Abstract: To achieve higher accuracy of estimated dynamic states, phasor measurement unit (PMU) measurements of buses in a network can be used for dynamic state estimation (DSE). However, it is difficult to coordinate the states of boundary buses in different areas when performing multiarea DSE. By using PMU measurements of buses in the network, this paper proposes an extended Kalman filter-based method with equality constraints to conduct multi-area DSE. First, a corrective strategy is proposed to estimate a corrective internal voltage (CIV) and a corrective rotor angle (CRA) of each generator with all PMUs’ measurements. The proposed corrective strategy can also ensure the consistency of the boundary buses in the multiareas. Then, the CIV and the CRA are used to establish equality constraints for updating the dynamic states with the PMU measurements. An IEEE 30-bus system and an IEEE 118-bus system are used to validate the proposed method, with the results showing the feasibility and accuracy of the proposed method.

Novel hybrid estimator based on model reference adaptive system and extended Kalman filter for speed-sensorless induction motor control:

Abstract: This paper presents a novel hybrid estimator consisting of an extended Kalman filter (EKF) and an active power-based model reference adaptive system (AP-MRAS) in order to solve simultaneous estimat...

Kalman and particle filtering methods for full vehicle and tyre identification

Abstract: This paper considers identification of all significant vehicle handling dynamics of a test vehicle, including identification of a combined-slip tyre model, using only those sensors currently available on most vehicle controller area network buses. Using an appropriately simple but efficient model structure, all of the independent parameters are found from test vehicle data, with the resulting model accuracy demonstrated on independent validation data. The paper extends previous work on augmented Kalman Filter state estimators to concentrate wholly on parameter identification. It also serves as a review of three alternative filtering methods; identifying forms of the unscented Kalman filter, extended Kalman filter and particle filter are proposed and compared for effectiveness, complexity and computational efficiency. All three filters are suited to applications of system identification and the Kalman Filters can also operate in real-time in on-line model predictive controllers or estimators.

Quantized Kalman Filter Tracking in Directional Sensor Networks

Abstract: Moving target tracking in directional sensor networks has recently attracted attention by right of special directional sensing features. Unlike omnidirectional sensors, the directional sensor senses the target only in the direction of its orientation. It can provide quantized direction that indicates the presence or absence of the target in the sensing field, rather than just the analog measurement of sensing signal with respect to the detected target. A quantized Kalman filter (QKF) based on both quantized directions and analog ranging measurements is derived in the minimum mean-square error (MMSE) sense. Its performances of mean square estimation error (MSE) and complexity are also analyzed. Then, a reduced-complexity QKF of high-accuracy is pursued to facilitate its implementation. It is proved that the QKF yields a smaller MSE than the traditional extended Kalman filter (EKF) merely based on analog measurements. The posterior Cram $\acute{e}$ r-Rao lower bound (PCRLB) is introduced as the performance measure. The performance advantages of the proposed QKF are demonstrated using Monte Carlo simulations in a target tracking application using ultrasonic ranging sensors.

Dynamic mode decomposition using a Kalman filter for parameter estimation

Abstract: A novel dynamic mode decomposition (DMD) method based on a Kalman filter is proposed. This paper explains the fast algorithm of the proposed Kalman filter DMD (KFDMD) in combination with truncated proper orthogonal decomposition for many-degree-of-freedom problems. Numerical experiments reveal that KFDMD can estimate eigenmodes more precisely compared with standard DMD or total least-squares DMD (tlsDMD) methods for the severe noise condition if the nature of the observation noise is known, though tlsDMD works better than KFDMD in the low and medium noise level. Moreover, KFDMD can track the eigenmodes precisely even when the system matrix varies with time similar to online DMD, and this extension is naturally conducted owing to the characteristics of the Kalman filter. In summary, the KFDMD is a promising tool with strong antinoise characteristics for analyzing sequential datasets.

Generalized total Kalman filter algorithm of nonlinear dynamic errors-in-variables model with application on indoor mobile robot positioning

Abstract: In this paper, a nonlinear dynamic errors-in-variables (DEIV) model which considers all of the random errors in both system equations and observation equations is presented. The nonlinear DEIV model is more general in the structure, which is an extension of the existing DEIV model. A generalized total Kalman filter (GTKF) algorithm that is capable of handling all of random errors in the respective equations of the nonlinear DEIV model is proposed based on the Gauss–Newton method. In addition, an approximate precision estimator of the posteriori state vector is derived. A two dimensional simulation experiment of indoor mobile robot positioning shows that the GTKF algorithm is statistically superior to the extended Kalman filter algorithm and the iterative Kalman filter (IKF) algorithm in terms of state estimation. Under the experimental conditions, the improvement rates of state variables of positions x, y and azimuth ψ of the GTKF algorithm are about 14, 29, and 66%, respectively, compared with the IKF algorithm.

Diffusion nonlinear Kalman filter with intermittent observations

Abstract: In this article, we consider the distributed nonlinear state estimation over sensor networks under the diffusion Kalman filter paradigm, where data only exchanges among the neighbourhoods of sensor...

Sensor Fault Tolerance Enhancement of DFIG-WTs via Perturbation Observer-Based DPC and Two-Stage Kalman Filters

Abstract: This paper presents a sensor fault-tolerant control (SFTC) strategy, combining perturbation observer-based direct power control (PODPC) and two-stage Kalman filter (TSKF) to enhance the fault tolerance of a doubly fed induction generator-based wind turbine (DFIG-WT) subject to rotor and stator current sensor faults. In the PODPC scheme, the interactions between active and reactive power control loops are represented by newly introduced perturbation states, and the feedback linearization control is realized with the state estimations derived from perturbation observers to achieve the decoupled power control. No rotor current sensors nor parameters of DFIG-WT are required in the implementation of PODPC. Stator current TSKFs are designed to generate residuals for fault detection and isolation, and provide current estimations to replace the faulty current measurements for system reconfiguration under stator current sensor faults. Simulation studies undertaken on a grid-connected DFIG-WT system reveal that the proposed SFTC strategy is immune to rotor current sensor faults, and it provides strong fault tolerance to stator current sensor faults.

A solution to dynamic errors-in-variables within system equations

Abstract: We noticed that if INS data is used as system equations of a Kalman filter algorithm for integrated direct geo-referencing, one encounters with a dynamic errors-in-variables (DEIV) model. Although DEIV model has been already considered for observation equations of the Kalman filter algorithm and a solution namely total Kalman filter (TKF) has been given to it, this model has not been considered for system equations (dynamic model) of the Kalman filter algorithm. Thus, in this contribution, for the first time we consider DEIV model for both observation equations and system equations of the Kalman filter algorithm and propose a least square prediction namely integrated total Kalman filter in contrast to the TKF solution of the previous approach. The variance matrix of the unknown parameters are obtained. Moreover, the residuals for all variables are predicted. In a numerical example, integrated direct geo-referencing problem is solved for a GPS–INS system.

On the observer matching condition and unknown input observer design based on the system left-invertibility concept:

Abstract: This paper considers the problems of unknown input observer (UIO) designs when the so-called observer matching condition (OMC) is not satisfied. Firstly, the system left-invertibility (SLI) concept...

Computationally Efficient Self-Tuning Controller for DC–DC Switch Mode Power Converters Based on Partial Update Kalman Filter

Abstract: In this paper, a partial update Kalman Filter (PUKF) is presented for the real-time parameter estimation of a dc–dc switch mode power converter. The proposed estimation algorithm is based on a novel combination between the classical Kalman filter (KF) and an M-Max partial adaptive filtering technique. The proposed PUKF offers a significant reduction in computational effort compared to the conventional implementation of the KF, with 50% less arithmetic operations. Furthermore, the PUKF retains comparable overall performance to the classical KF. To demonstrate an efficient and cost effective explicit self-tuning controller, the proposed estimation algorithm (PUKF) is embedded with a Banyasz/Keviczky proportional, integral, derivative (PID) controller to generate a new computationally light self-tuning controller. Experimental and simulation results clearly show the superior dynamic performance of the explicit self-tuning control system compared to a conventional pole placement design based on a precalculated average model.

Stochastic Feedback Based Kalman Filter for Nonlinear Continuous-Discrete Systems

Abstract: For continuous-discrete filtering with unpredictable approximation errors, by proposing the novel stochastic feedback scheme, this note elaborates a closed-loop adaptive Kalman filter for nonlinear continuous-discrete systems. In conventional filters, unknown approximation errors might arise due to the integration/discretization and linearization of continuous model, and ruin the optimality of Kalman theory. As the main contribution of this note, the stochastic feedback based covariance adaption scheme does not require the approximation steps; instead, the posteriori sequence is mined as a feedback to adapt the priori error covariance, so that the unpredictable errors and costly calculations can be reduced or controlled in the novel closed-loop filtering structure. The new approach's advantages in computational cost, adaptability, and accuracy have been demonstrated by the numerical simulations.

Adaptive Kalman Filtering for Systems Subject to Randomly Delayed and Lost Measurements

Abstract: This paper investigates the problem of state estimation for discrete-time linear systems where the observation data are transmitted from the sensor to the filter subject to random delay and dropout The loss and latency of the measurements are modeled by a group of Bernoulli distributed random variables with uncertain probabilities, which appear in the Kalman filter parameters An adaptation factor, which is defined by comparing the theoretical and practical values of the innovation covariance, is employed to adjust the filter gains during estimation Simulation results are presented to verify the improved performance of the proposed adaptive filter

Enhanced Polynomial Chaos-Based Extended Kalman Filter Technique for Parameter Estimation

Abstract: The Generalized Polynomial Chaos mathematical technique, when integrated with the Extended Kalman Filter method, provides a parameter estimation and state tracking method. The truncation of the series expansions degrades the link between parameter convergence and parameter uncertainty which the filter uses to perform the estimations. An empirically derived correction for this problem is implemented, that maintains the original parameter distributions. A comparison is performed to illustrate the improvements of the proposed approach. The method is demonstrated for parameter estimation on a regression system, where it is compared to the Recursive Least Squares method.

The Right Invariant Nonlinear Complementary Filter for Low Cost Attitude and Heading Estimation of Platforms

Abstract: This paper presents a novel filter with low computational demand to address the problem of orientation estimation of a robotic platform. This is conventionally addressed by extended Kalman filtering of measurements from a sensor suit which mainly includes accelerometers, gyroscopes, and a digital compass. Low cost robotic platforms demand simpler and computationally more efficient methods to address this filtering problem. Hence nonlinear observers with constant gains have emerged to assume this role. The nonlinear complementary filter is a popular choice in this domain which does not require covariance matrix propagation and associated computational overhead in its filtering algorithm. However, the gain tuning procedure of the complementary filter is not optimal, where it is often hand picked by trial and error. This process is counter intuitive to system noise based tuning capability offered by a stochastic filter like the Kalman filter. This paper proposes the right invariant formulation of the complementary filter, which preserves Kalman like system noise based gain tuning capability for the filter. The resulting filter exhibits efficient operation in elementary embedded hardware, intuitive system noise based gain tuning capability and accurate attitude estimation. The performance of the filter is validated using numerical simulations and by experimentally implementing the filter on an ARDrone 2.0 micro aerial vehicle platform.

Backstepping and sliding modes for observer design of distributed parameter system

Abstract: The observer design for partial differential equations has so far been an open problem. In this paper, an observer design for systems with distributed parameters using sliding modes theory and backstepping-like procedure in order to achieve exponential convergence is presented. Such an observer is built using the knowledge available within and throughout an integral transformation of Volterra with the output injection functions. The gains of the observer, which are attained by solving a partial differential equations system with output injection, will guarantee the exponential convergence of the observer. The design method is applied to an epidemic system to consider the sensitive population S.

A new methodology for an adaptive state observer design for a class of nonlinear systems with unknown parameters in unmeasured state dynamics

Abstract: An adaptive state observer is an adaptive observer that does not require the persistent excitation condition to estimate the state. The usual structural requirement for designing this kind of observers is that the unknown parameters explicitly appear in the measured state dynamics. This paper deals with the problem of adaptive state observer synthesis for a class of nonlinear systems with unknown parameters in unmeasured state dynamics. The novelty of the proposed approach is that it requires neither a canonical form nor the approximation of some of the output’s time derivatives. Firstly, we establish a new matrix equality that characterizes the structure of almost all systems found in the very small literature dealing with this problem. Then, this equality is exploited in the construction of the adaptation law. This simplifies the design procedure and makes it very similar to the conventional adaptive state observer design procedure. The problem of finding the observer gains is expressed as a linear matr...

Transformation of nonlinear discrete-time system into the extended observer form

Abstract: The paper addresses the problem of transforming discrete-time single-input single-output nonlinear state equations into the extended observer form, which, besides the input and output, also depends on a finite number of their past values. Necessary and sufficient conditions for the existence of both the extended coordinate and output transformations, solving the problem, are formulated in terms of differential one-forms, associated with the input–output equation, corresponding to the state equations. An algorithm for transformation of state equations into the extended observer form is proposed and illustrated by an example. Moreover, the considered approach is compared with the method of dynamic observer error linearisation, which likewise is intended to enlarge the class of systems transformable into an observer form.

Spacecraft attitude estimation based on matrix Kalman filter and recursive cubature Kalman filter

Abstract: An interlaced matrix Kalman filter, which is based on vector observations and gyro measurements, is proposed for spacecraft attitude estimation in this paper. It combines the matrix Kalman filter a...

MEMS Gyroscope Raw Data Noise Reduction Using Fading Memory Filter

Abstract: Nowadays, MEMS sensors are widely used in systems such as autonomous vehicles, but they still suffer from high stochastic errors such as Angle random walk (ARW) noise, which causes failure in real-signals and produces an error in the position and attitude of mobile systems. So far, many filters are developed to reduce the amount of noise in the output of the MEMS sensors. The computational overhead, the rate of noise reduction, and the phase-delay of the filter are the most important characteristics of choosing a suitable filter. In this paper, a low pass filter based on the alpha-beta filter with a very low computational overhead is proposed to reduce the amount of noise. In order to find the optimal filter gain, the improvement in the positioning is selected as a criterion, which is a tradeoff between the amount of noise reduction and the phase delay of the filtered signal. In this work, the KITTI database is used to evaluate the proposed filter. The results show that the proposed filter reduces the sensor’s noise and improves the positioning of the moving car, significantly.

Backing Up a Truck on Gaussian and Non-Gaussian Impulsive Noise with Extended Kalman Filter and Fuzzy Controller

Abstract: Truck backing-up problem is a typical test bed for fuzzy control system. The control performance affects the safety of the truck well, but has not been studied when location of the truck is given by GPS which introduces sensing noises into the system. In this paper, we study the impact of noise on control performance of the system, and we propose an extended Kalman filter which claims to adapt to only Gaussian noise for improving control performance in Gaussian and non-Gaussian impulsive noise situation. To implement the filter, we propose screening the input to get the output of the fuzzy controller such that the partial derivative of the input–output function of the controller required by the extended Kalman filter is computationally available. Our simulation results of the truck system with and without noise, the noise being Gaussian and non-Gaussian impulsive, and the system with and without the extended Kalman filter, indicate that the average performance of the system with the filter is much better than that without the filter no matter the noise is Gaussian or impulsive, the great power of the extended Kalman filter in dealing with even non-Gaussian impulsive noises for fuzzy truck control, while the great deviation from the average performance makes an urgent call for non-Gaussian version of the extended Kalman filter to adapt to more general non-Gaussian impulsive noise situation.