scholarly journals Physically Consistent Whole-Body Kinematics Assessment Based on an RGB-D Sensor. Application to Simple Rehabilitation Exercises

Sensors ◽  
2020 ◽  
Vol 20 (10) ◽  
pp. 2848
Author(s):  
Jessica Colombel ◽  
Vincent Bonnet ◽  
David Daney ◽  
Raphael Dumas ◽  
Antoine Seilles ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Joint Angle ◽  
Statistical Parametric Mapping ◽  
Biomechanical Model ◽  
Practical Method ◽  
Covariance Matrices ◽  
Whole Body ◽  
Joint Angles ◽  
Optimal Tuning

This work proposes to improve the accuracy of joint angle estimates obtained from an RGB-D sensor. It is based on a constrained extended Kalman Filter that tracks inputted measured joint centers. Since the proposed approach uses a biomechanical model, it allows physically consistent constrained joint angles and constant segment lengths to be obtained. A practical method that is not sensor-specific for the optimal tuning of the extended Kalman filter covariance matrices is provided. It uses reference data obtained from a stereophotogrammetric system but it has to be tuned only once since it is task-specific only. The improvement of the optimal tuning over classical methods in setting the covariance matrices is shown with a statistical parametric mapping analysis. The proposed approach was tested with six healthy subjects who performed four rehabilitation tasks. The accuracy of joint angle estimates was assessed with a reference stereophotogrammetric system. Even if some joint angles, such as the internal/external rotations, were not well estimated, the proposed optimized algorithm reached a satisfactory average root mean square difference of 9.7 ∘ and a correlation coefficient of 0.8 for all joints. Our results show that an affordable RGB-D sensor can be used for simple in-home rehabilitation when using a constrained biomechanical model.

scholarly journals Pose estimation by extended Kalman filter using noise covariance matrices based on sensor output

2020 ◽  
Author(s):  
AYUKO SAITO ◽  
Satoru Kizawa ◽  
Yoshikazu Kobayashi ◽  
Kazuto Miyawaki
Keyword(s):  
Kalman Filter ◽  
Motion Analysis ◽  
Extended Kalman Filter ◽  
Pose Estimation ◽  
Lower Limb ◽  
Covariance Matrices ◽  
Motion Sensors ◽  
Sensor Output ◽  
Joint Angles ◽  
Noise Covariance

Abstract This paper presents an extended Kalman filter for pose estimation using noise covariance matrices based on sensor output. Compact and lightweight nine-axis motion sensors are used for motion analysis in widely various fields such as medical welfare and sports. A nine-axis motion sensor includes a three-axis gyroscope, a three-axis accelerometer, and a three-axis magnetometer. Information obtained from the three sensors is useful for estimating joint angles using the Kalman filter. The extended Kalman filter is used widely for state estimation because it can estimate the status with a small computational load. However, determining the process and observation noise covariance matrices in the extended Kalman filter is complicated. The noise covariance matrices in the extended Kalman filter were found for this study based on the sensor output. Postural change appears in the gyroscope output because the rotational motion of the joints produces human movement. Therefore, the process noise covariance matrix was determined based on the gyroscope output. An observation noise covariance matrix was determined based on the accelerometer and magnetometer output because the two sensors’ outputs were used as observation values. During a laboratory experiment, the lower limb joint angles of three participants were measured using an optical 3D motion analysis system and nine-axis motion sensors while participants were walking. The lower limb joint angles estimated using the extended Kalman filter with noise covariance matrices based on sensor output were generally consistent with results obtained from the optical 3D motion analysis system. Furthermore, the lower limb joint angles were measured using nine-axis motion sensors while participants were running in place for about 100 seconds. The experiment results demonstrated the effectiveness of the proposed method for human pose estimation.

scholarly journals Pose estimation by extended Kalman filter using noise covariance matrices based on sensor output

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Ayuko Saito ◽  
Satoru Kizawa ◽  
Yoshikazu Kobayashi ◽  
Kazuto Miyawaki
Keyword(s):  
Kalman Filter ◽  
Motion Analysis ◽  
Extended Kalman Filter ◽  
Pose Estimation ◽  
Lower Limb ◽  
Covariance Matrices ◽  
Motion Sensors ◽  
Sensor Output ◽  
Joint Angles ◽  
Noise Covariance

Abstract This paper presents an extended Kalman filter for pose estimation using noise covariance matrices based on sensor output. Compact and lightweight nine-axis motion sensors are used for motion analysis in widely various fields such as medical welfare and sports. A nine-axis motion sensor includes a three-axis gyroscope, a three-axis accelerometer, and a three-axis magnetometer. Information obtained from the three sensors is useful for estimating joint angles using the Kalman filter. The extended Kalman filter is used widely for state estimation because it can estimate the status with a small computational load. However, determining the process and observation noise covariance matrices in the extended Kalman filter is complicated. The noise covariance matrices in the extended Kalman filter were found for this study based on the sensor output. Postural change appears in the gyroscope output because the rotational motion of the joints produces human movement. Therefore, the process noise covariance matrix was determined based on the gyroscope output. An observation noise covariance matrix was determined based on the accelerometer and magnetometer output because the two sensors’ outputs were used as observation values. During a laboratory experiment, the lower limb joint angles of three participants were measured using an optical 3D motion analysis system and nine-axis motion sensors while participants were walking. The lower limb joint angles estimated using the extended Kalman filter with noise covariance matrices based on sensor output were generally consistent with results obtained from the optical 3D motion analysis system. Furthermore, the lower limb joint angles were measured using nine-axis motion sensors while participants were running in place for about 100 s. The experiment results demonstrated the effectiveness of the proposed method for human pose estimation.

scholarly journals Pose estimation by extended Kalman filter using noise covariance matrices based on sensor output

2020 ◽  
Author(s):  
AYUKO SAITO ◽  
Satoru Kizawa ◽  
Yoshikazu Kobayashi ◽  
Kazuto Miyawaki
Keyword(s):  
Kalman Filter ◽  
Motion Analysis ◽  
Extended Kalman Filter ◽  
Pose Estimation ◽  
Lower Limb ◽  
Covariance Matrices ◽  
Motion Sensors ◽  
Sensor Output ◽  
Joint Angles ◽  
Noise Covariance

Abstract This paper presents an extended Kalman filter for pose estimation using noise covariance matrices based on sensor output. Compact and lightweight nine-axis motion sensors are used for motion analysis in widely various fields such as medical welfare and sports. A nine-axis motion sensor includes a three-axis gyroscope, a three-axis accelerometer, and a three-axis magnetometer. Information obtained from the three sensors is useful for estimating joint angles using the Kalman filter. The extended Kalman filter is used widely for state estimation because it can estimate the status with a small computational load. However, determining the process and observation noise covariance matrices in the extended Kalman filter is complicated. The noise covariance matrices in the extended Kalman filter were found for this study based on the sensor output. Postural change appears in the gyroscope output because the rotational motion of the joints produces human movement. Therefore, the process noise covariance matrix was determined based on the gyroscope output. An observation noise covariance matrix was determined based on the accelerometer and magnetometer output because the two sensors’ outputs were used as observation values. During a laboratory experiment, the lower limb joint angles of three participants were measured using an optical 3D motion analysis system and nine-axis motion sensors while participants were walking. The lower limb joint angles estimated using the extended Kalman filter with noise covariance matrices based on sensor output were generally consistent with results obtained from the optical 3D motion analysis system. Furthermore, the lower limb joint angles were measured using nine-axis motion sensors while participants ran on a treadmill for about 90 seconds. The experiment results demonstrated the effectiveness of the proposed method for human pose estimation.

scholarly journals BBO-Based State Optimization for PMSM Machines

2021 ◽  
pp. 1-24
Author(s):  
Hanane Lakehal ◽  
Mouna Ghanai ◽  
Kheireddine Chafaa
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Optimization Technique ◽  
Angular Position ◽  
Covariance Matrices ◽  
Measurement Noise ◽  
Permanent Magnet Synchronous Machine ◽  
Swarm Optimization ◽  
Vector Estimation ◽  
Free Parameters

In this investigation, state vector estimation of the Permanent Magnet Synchronous machine (PMSM) using the nonlinear Kalman estimator (Extended Kalman Filter) is considered. The considered states are the speed of the rotor, its angular position, the torque of the load and the resistance of the stator. Since the extended Kalman filter contains some free parameters, it will be necessary to optimize them in order to obtain a better efficiency. The free parameters of EKF are the covariance matrices of state noise and measurement noise. These later will be auto adjusted by a new metaheuristic optimization technique called Biogeographical-based optimization (BBO). As far as we know, BBO–EKF optimization for PMSM state was not treated in the literature. The suggested estimation tuning approach is demonstrated using a computer simulation of a PMSM. Simulated experimentations show the robustness and effectiveness of the proposed scheme. In addition, a detailed comparative study with conventional methods like Particle Swarm Optimization and Genetic Algorithms will be given.

scholarly journals On the Kalman Filter error covariance collapse into the unstable subspace

2011 ◽  
Vol 18 (2) ◽  
pp. 243-250 ◽  
Author(s):  
A. Trevisan ◽  
L. Palatella
Keyword(s):  
Kalman Filter ◽  
Lyapunov Exponents ◽  
Extended Kalman Filter ◽  
Covariance Matrices ◽  
Reduced Form ◽  
Asymptotic State ◽  
Numerical Verification ◽  
Error Covariance ◽  
Neutral Subspace ◽  
Unstable Subspace

Abstract. When the Extended Kalman Filter is applied to a chaotic system, the rank of the error covariance matrices, after a sufficiently large number of iterations, reduces to N+ + N0 where N+ and N0 are the number of positive and null Lyapunov exponents. This is due to the collapse into the unstable and neutral tangent subspace of the solution of the full Extended Kalman Filter. Therefore the solution is the same as the solution obtained by confining the assimilation to the space spanned by the Lyapunov vectors with non-negative Lyapunov exponents. Theoretical arguments and numerical verification are provided to show that the asymptotic state and covariance estimates of the full EKF and of its reduced form, with assimilation in the unstable and neutral subspace (EKF-AUS) are the same. The consequences of these findings on applications of Kalman type Filters to chaotic models are discussed.

Navigation of an Underwater Remotely Operated Vehicle Based on Extended Kalman Filter

2013 ◽  
Author(s):  
Blanca V. Martínez ◽  
Daniel A. Sierra ◽  
Rodolfo Villamizar
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Inertial Measurement Unit ◽  
Dynamic Models ◽  
Estimation Error ◽  
Covariance Matrices ◽  
Measurement Unit ◽  
Remotely Operated Vehicle ◽  
Filter Performance ◽  
Order Of Magnitude

An algorithm to estimate positions, orientations, linear velocities and angular rates of an Underwater Remotely Operated Vehicle (UROV), based on the Extended Kalman Filter (EKF), is presented. The complete UROV kinematic and dynamic models are combined to obtain the process equation, and measurements correspond to linear accelerations and angular rates provided by an Inertial Measurement Unit (IMU). The proposed algorithm is numerically validated and its results are compared with simulated UROV states. A discussion about the influence of the covariance matrices on the estimation error and overall filter performance is also included. As a conclusion, the proposed algorithm estimates properly the UROV linear velocities and angular rates from IMU measurements, and the noise in estimated states is reduced in about one order of magnitude.

scholarly journals An Extended Kalman Filter, with pre-adjusted covariance matrices, applied to the sensorless speed control of three-phase induction motors

2020 ◽  
pp. 109-126
Author(s):  
Leonardo de Magalhães Lopes ◽  
Zélia Myriam Assis Peixoto
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Induction Motors ◽  
Sensorless Control ◽  
Speed Control ◽  
Covariance Matrices ◽  
Operating Conditions ◽  
Control Technique ◽  
State Variables ◽  
Three Phase

With the emergence of sensorless control methods, there was a need for the use of estimators and/or state observers to give it the robustness and precision required in the drive of induction motors. This work deals with the application of the Extended Kalman Filter (EKF) in the estimation of rotor speed and position, aiming at the implementation of the indirect vector control technique in a sensorless speed control system for three-phase induction motors. The mathematical development of the system state variables associated with the EKF stochastic process is presented in this study, and point out its application under variable speed and load conditions, which are imposed on these motors in everyday life. The sensorless control strategy was tested through routine lines in the Matlab® software, simulating operating conditions of this type of engine, being proven its performance, as well as the convergence times consistent with the usual requirements of high performance systems. The main contributions of this work are the use of a reduced-order EKF (ROEKF) and the preset of covariance matrices to accelerate convergence in speed and position estimates for future implementations in currently accessible digital signal processors.

scholarly journals Simulation Analysis of Extended Kalman Filter Applied for Estimating Position and Speed of a Brushless DC Motor

2018 ◽  
Vol 3 (1) ◽  
pp. 145-155
Author(s):  
Maciej Chojowski
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Simulation Analysis ◽  
Covariance Matrices ◽  
Brushless Dc Motor ◽  
Bldc Motor ◽  
Rotor Speed ◽  
State Equations ◽  
Brushless Dc ◽  
Noise Covariance

Abstract The purpose of this paper was to present a method for the estimation of the rotor speed and position of brushless DC (BLDC) motor. The BLDC motor state equations were developed, and the model was discretised. Extended Kalman filter has been designed to observe specific states from the state vector, needed for the sensorless control (rotor position) and to determine the speed, which may be useful to use as a feedback for the controller. A test was carried out to determine the noise covariance matrices in a simulation manner.

Self-Tuning Extended Kalman Filter Parameters to Identify Ankle's Third-Order Mechanics

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
E. Coronado ◽  
A. González ◽  
A. Cárdenas ◽  
M. Maya ◽  
E. Chiovetto ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Influencing Factor ◽  
Simulated Data ◽  
Biomechanical Model ◽  
Mechanical Impedance ◽  
Quiet Standing ◽  
Third Order ◽  
Human Balance

Abstract The estimation of human ankle's mechanical impedance is an important tool for modeling human balance. This work presents the implementation of a parameter-estimation approach based on a state-augmented extended Kalman filter (AEKF) to infer the ankle's mechanical impedance during quiet standing. However, the AEKF filter is sensitive to the initialization of the noise covariance matrices. In order to avoid a time-consuming trial-and-error method and to obtain a better estimation performance, a genetic algorithm (GA) is proposed to best tune the measurement noise (Rk) and process noise covariances (Q) of the extended Kalman filter (EKF). Results using simulated data show the efficacy of the proposed algorithm for parameter-estimation of a third-order biomechanical model. Experimental validation of these results is also presented. They suggest that age is an influencing factor in the human balance.

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