Complementary Filter Research Articles

Yawing stability and manipulative approach design for maglev car based on active disturbance rejection control

AbstractIn the present work, to realize the stable static suspension of a new type of electrodynamic wheel (EDW) magnetic levitation (maglev) car without track constraints on the conductor plate. Design and analysis of the active disturbance rejection control and explicit complementary filter (ADRC‐ECF) have been presented to solve the maglev car's yaw angle disturbance rejection under low lateral damping characteristics. Simple and efficient ECF helps to filter the high and low frequency noise generated by EDWs when rotating at high speed, to obtain accurate data in real‐time. Design and build the hardware control system for maglev car, and conduct experimental comparisons with PID controller to verify the effectiveness of suppressing yaw angle disturbances. Based on simulation and experimental results, it is shown that both PID and ADRC‐ECF can improve the stable yaw angle convergence of maglev car under external disturbances. However, ADRC performs better in resisting disturbances than PID and can achieve more accurate fixed angle steering. This paper is the first attempt to control maglev car on a trackless conductor plate for precise steering and anti‐disturbance, which is anticipated to have some reference significance in this field.

Estimation of body segmental orientation for prosthetic gait using a nonlinear autoregressive neural network with exogenous inputs

Assessment of the prosthetic gait is an important clinical approach to evaluate the quality and functionality of the prescribed lower limb prosthesis as well as to monitor rehabilitation progresses following limb amputation. Limited access to quantitative assessment tools generally affects the repeatability and consistency of prosthetic gait assessments in clinical practice. The rapidly developing wearable technology industry provides an alternative to objectively quantify prosthetic gait in the unconstrained environment. This study employs a neural network-based model in estimating three-dimensional body segmental orientation of the lower limb amputees during gait. Using a wearable system with inertial sensors attached to the lower limb segments, thirteen individuals with lower limb amputation performed two-minute walk tests on a robotic foot and a passive foot. The proposed model replicates features of a complementary filter to estimate drift free three-dimensional orientation of the intact and prosthetic limbs. The results indicate minimal estimation biases and high correlation, validating the ability of the proposed model to reproduce the properties of a complementary filter while avoiding the drawbacks, most notably in the transverse plane due to gravitational acceleration and magnetic disturbance. Results of this study also demonstrates the capability of the well-trained model to accurately estimate segmental orientation, regardless of amputation level, in different types of locomotion task.

Attitude measurement of permanent magnet spherical motors based on adaptive mahony complementary filtering

An adaptive attitude measurement algorithm called adaptive mahony complementary filter(AMCF) is proposed to address the issues of drift and noise in gyroscope measurements, as well as the high computational complexity, error accumulation, and sensitivity to noise in the quaternion extended kalman filter(QEKF) within the permanent magnet spherical motor(PMSM) inertial measurement unit. Firstly, this method corrects the gyroscope’s angular velocity bias by utilizing the error between theoretical and actual accelerations. Subsequently, the covariance is adjusted by comparing dynamic accelerations to mitigate disturbances. The fourth-order Runge-Kutta method is employed to continuously update the quaternion, thereby achieving higher accuracy in attitude measurement. Finally, static and dynamic experimental investigations are conducted on the PMSM. The experimental results demonstrate that the AMCF offers faster computation speed compared to the QEKF and higher accuracy than the fast complementary filtering(FCF). This indicates that utilizing the AMCF enables better real-time attitude measurement for three-degree-of-freedom mechanical structures.

Velocity-Aided IMU-Based Tilt and Attitude Estimation

This paper addresses the problem of estimating the tilt and more generally the attitude of a rigid body that is subject to high accelerations and equipped with inertial measurement units (IMU) and a sensor providing the body velocity (expressed in the reference frame attached to the body). In the absence of a magnetometer, tilt estimation is proposed through a two-step observer: a global-exponentially stable pre-estimation given to a manifold-constrained complementary filter. In the presence of a magnetometer, the presented observer allows to reconstruct the full attitude and tune how much the estimation of the tilt is influenced by the magnetometer, depending on the level of confidence given to the measurements of the magnetometer. All state estimators are proposed with proofs of almost global asymptotic stability and local exponential convergence. Finally, these estimators are compared with state-of-the-art solutions in clean and noisy simulations, allowing recommended solutions to be drawn for each case.

An ultra-high timing resolution pulse generator with spur suppression and correction of errors based on real-time computation

In this paper, a novel ultra-high timing resolution pulse generator is proposed. It is based on the waveform real-time computation method. Through real-time computing and filtering of the waveform samples, a pulse with a 0.1 ps timing resolution pulse could be generated at a 2.5 GSPS sampling rate. Based on the waveform real-time computation method, jitters are injected into the waveform time parameter to break the harmonic components caused by non-integer multiples of the sampling rate and waveform frequency. Waveform spurs are further suppressed using this approach. The pulse error correction is achieved by designing digital filters that complement the waveform distortion features. The complementary digital filters are then combined as Farrow filter coefficients by polynomial fitting. Based on the real-time computation method, pulse width modulation, frequency modulation, and amplitude modulation are easy to realize. The implemented pulse generator has four channels, whose minimum pulse width, edge time, frequency range, and amplitude range are 4, 2.5 ns, 1 μHz–120 MHz, and 50 mVpp–5 Vpp, respectively. All timing resolution and timing accuracy of pulse width, edge time, pulse period, and channel delay are 0.1 and 50 ps, respectively. Timing parameters can be changed continuously without glitches.

IMU/UWB Fusion Method Using a Complementary Filter and a Kalman Filter for Hybrid Upper Limb Motion Estimation.

Motion capture systems have enormously benefited the research into human-computer interaction in the aerospace field. Given the high cost and susceptibility to lighting conditions of optical motion capture systems, as well as considering the drift in IMU sensors, this paper utilizes a fusion approach with low-cost wearable sensors for hybrid upper limb motion tracking. We propose a novel algorithm that combines the fourth-order Runge-Kutta (RK4) Madgwick complementary orientation filter and the Kalman filter for motion estimation through the data fusion of an inertial measurement unit (IMU) and an ultrawideband (UWB). The Madgwick RK4 orientation filter is used to compensate gyroscope drift through the optimal fusion of a magnetic, angular rate, and gravity (MARG) system, without requiring knowledge of noise distribution for implementation. Then, considering the error distribution provided by the UWB system, we employ a Kalman filter to estimate and fuse the UWB measurements to further reduce the drift error. Adopting the cube distribution of four anchors, the drift-free position obtained by the UWB localization Kalman filter is used to fuse the position calculated by IMU. The proposed algorithm has been tested by various movements and has demonstrated an average decrease in the RMSE of 1.2 cm from the IMU method to IMU/UWB fusion method. The experimental results represent the high feasibility and stability of our proposed algorithm for accurately tracking the movements of human upper limbs.

A tightly-coupled method of lidar-inertial based on complementary filtering

In the application of small field angle lidar for robot SLAM (simultaneous localization and mapping), livox mapping can provide accurate odometer information and point cloud information of the environment with good precision for the robot in a short time. However, over long periods of motion, the laser odometer calculated by livox mapping will produce a large offset, which will reduce the localization accuracy and mapping accuracy of the robot. To overcome above problem, a lidar-inertial navigation odometer compact fusion method based on the idea of complementary filtering is proposed in this paper. By taking advantage of the good static performance of the accelerometer for a long time, the angle value obtained by the gyroscope integration is corrected. In the back-end optimization, the Jacobian matrix obtained by the residual calculation of the acceleration in the navigation coordinate system obtained by IMU and the gravitational acceleration is tightly coupled with the Jacobian matrix of the lidar residual. Different weights are given to the residual of each part, and the odometer is solved iteratively to further improve the pose accuracy of the whole SLAM system. In this paper, the method is applied to Livox-Mid40. The experimental results show that it can reduce the drift of long time and long distance and improve the accuracy of the system localization and mapping.

A Variable Gain Complementary Filtering Fusion Algorithm Based on Distributed Inertial Network and Flush Air Data Sensing

Aiming at the problem that the accuracy of flight parameters calculated by the traditional flush air data sensing (FADS) and inertial navigation system (INS) complementary filter cannot meet the fine real-time control of the aircraft, a data fusion algorithm based on distributed inertial network and FADS is proposed. This method converts the inertial navigation parameters calculated by the distributed inertial network into flight parameters, and using the least squares fitting theory, the flight parameters are obtained from the pressure data measured by the FADS pressure hole. Then, by adjusting the filter constant of the complementary filtering algorithm, the flight parameters calculated by the inertial network are fused with the flight parameters calculated by the air data sensing to obtain high-precision flight parameters. Finally, the simulation results show that the proposed filtering algorithm can keep the flight parameter estimation error less than 0.01 degrees throughout the flight phase. Compared with the traditional complementary filter, the estimation error of the proposed algorithm is smaller.

Combining Slow and Fast: Complementary Filtering for Dynamics Learning

Modeling an unknown dynamical system is crucial in order to predict the future behavior of the system. A standard approach is training recurrent models on measurement data. While these models typically provide exact short-term predictions, accumulating errors yield deteriorated long-term behavior. In contrast, models with reliable long-term predictions can often be obtained, either by training a robust but less detailed model, or by leveraging physics-based simulations. In both cases, inaccuracies in the models yield a lack of short-time details. Thus, different models with contrastive properties on different time horizons are available. This observation immediately raises the question: Can we obtain predictions that combine the best of both worlds? Inspired by sensor fusion tasks, we interpret the problem in the frequency domain and leverage classical methods from signal processing, in particular complementary filters. This filtering technique combines two signals by applying a high-pass filter to one signal, and low-pass filtering the other. Essentially, the high-pass filter extracts high-frequencies, whereas the low-pass filter extracts low frequencies. Applying this concept to dynamics model learning enables the construction of models that yield accurate long- and short-term predictions. Here, we propose two methods, one being purely learning-based and the other one being a hybrid model that requires an additional physics-based simulator.

Robotic Hummingbird Axial Dynamics and Control near Hovering: A Simulation Model

After a short overview of the COLIBRI project, this paper considers the cycle-averaged flight dynamics of a flapping-wing robot near hovering, taking advantage of the weak coupling between the roll and pitch axes. The system is naturally unstable; it needs to be stabilized actively, which requires an attitude reconstruction. Due to the flapping of the wings, the system is subject to a strong periodic noise at the flapping frequency and its higher harmonics; the resulting axial forces and pitch moments are characterized from experimental data. The flapping noise propagates to the six-axis Inertial Measurement Unit (IMU) consisting of three accelerometers and three gyros. The paper is devoted to attitude reconstruction in the presence of flapping noise representative of flight conditions. Two methods are considered: (i) the complementary filter based on the hovering assumption and (ii) a full-state dynamic observer (Kalman filter). Unlike the complementary filter, the full-state dynamic observer allows the reconstruction of the axial velocity, allowing us to control the hovering without any additional sensor. A numerical simulation is conducted to assess the merit of the two methods using experimental noise data obtained with the COLIBRI robot. The paper discusses the trade-off between noise rejection and stability.

Effect of internal interface layer on dielectric properties of doped Ba0.6Sr0.4TiO3 thin films and its simulation in filters

Effect of the internal interface layer on the dielectric properties of doped Ba0.6Sr0.4TiO3 (BST) films and their simulation research in filters. Based on the interfacial effect in the multi-layer ferroelectric thin film, a different number of internal interface layers was proposed and introduced into the Ba0.6Sr0.4TiO3 thin film. First, Ba0.6Sr0.4Ti0.99Zn0.01O3 (ZBST) sol and Ba0.6Sr0.4Ti0.99Mg0.01O3 (MBST) sols were prepared using the sol-gel method. Ba0.6Sr0.4Ti0.99Zn0.01O3/Ba0.6Sr0.4Ti0.99Mg0.01O3/Ba0.6Sr0.4Ti0.99Zn0.01O3 thin films with 2 layer internal interface layer, 4 layer internal interface layer and 8 layer internal interface layer were designed and prepared (I2, I4, I8). The effects of the internal interface layer on the structure, morphology, dielectric properties, and leakage current behavior of the films were studied. The results showed that all the films were of the cubic perovskite BST phase and had the strongest diffraction peak in the (110) crystal plane. The surface composition of the film was uniform, and there was no cracked layer. When the bias of the applied DC field was 600 kV cm−1, the high-quality factor values of the I8 thin film at 10 MHz and 100 kHz were 111.3 and 108.6, respectively. The introduction of the internal interface layer changed the leakage current of the Ba0.6Sr0.4TiO3 thin film, and the I8 thin film exhibited the minimum leakage current density. The I8 thin-film capacitor was used as the tunable element to design a fourth-step ‘tapped’ complementary bandpass filter. When the permittivity was reduced from 500 to 191, the central frequency-tunable rate of the filter was 5.7%.

MOTION CAPTURE WITH MEMS SENSORS

The object of this article is the registration and analysis of human movements based on sensors. This paper presents a comparison of the basic methods of data processing from inertial micromechanical sensors to collect data a device was implemented that captures movements. As result the device uses the motion data from accelerometer and gyroscope to calculate the motion trajectory: the angle of rotation and acceleration. The data is read by the microcontroller, after which it is filtered and processed by one of the filters (Complementary, Kalman), and finally transferred to a computer for further analysis and display. The purpose of the article is to compare several methods of data processing from microelectromechanical. The results obtained: device was developed, obtained data that can be used to characterize the methods and analyze their work in the system. Conclusions: In the course of the study, a device was developed for collecting and processing data from MEMS sensors, which showed the effectiveness of the complementary filter in comparison with the Kalman filter in real-time systems with limited computing power. Real results confirmed that the results of the complementary method using less computational resources are not far behind the more costly Kalman filter without the use of auxiliary sensors, like a digital compass.

Extended-State-Observer-Based Angular Acceleration Estimation for Supersonic Aircraft Lateral–Directional Control

Large-slenderness-ratio (LSR) aircraft exhibit more severe lateral–directional coupling compared with other aircraft, which poses a significant challenge to their flight safety, especially during high-speed maneuvers. Reliable attitude decoupling control is, therefore, essential for LSR aircraft. In this study, a novel control framework that combines incremental nonlinear dynamic inversion (INDI) and extended state observer (ESO) is proposed for supersonic roll maneuver control of LSR aircraft. The ESO is used to estimate the angular acceleration on the basis of an onboard mathematical model. The acceleration estimator based on ESO achieves superior noise reduction compared with the complementary filter (CF) and reduces the onboard model requirement without significantly sacrificing estimation accuracy. Monte Carlo (MC) simulations and frequency–domain analysis demonstrate the effectiveness and robustness of the proposed controller. The sensitivity of parameter uncertainties is also investigated, revealing that the natural frequency of the actuator is the most critical parameter affecting robustness. Finally, flight tests validate the effectiveness of the proposed control structure.

Robust Attitude and Heading Estimation under Dynamic Motion and Magnetic Disturbance.

Robust and accurate attitude and heading estimation using Micro-Electromechanical System (MEMS) Inertial Measurement Units (IMU) is the most crucial technique that determines the accuracy of various downstream applications, especially pedestrian dead reckoning (PDR), human motion tracking, and Micro Aerial Vehicles (MAVs). However, the accuracy of the Attitude and Heading Reference System (AHRS) is often compromised by the noisy nature of low-cost MEMS-IMUs, dynamic motion-induced large external acceleration, and ubiquitous magnetic disturbance. To address these challenges, we propose a novel data-driven IMU calibration model that employs Temporal Convolutional Networks (TCNs) to model random errors and disturbance terms, providing denoised sensor data. For sensor fusion, we use an open-loop and decoupled version of the Extended Complementary Filter (ECF) to provide accurate and robust attitude estimation. Our proposed method is systematically evaluated using three public datasets, TUM VI, EuRoC MAV, and OxIOD, with different IMU devices, hardware platforms, motion modes, and environmental conditions; and it outperforms the advanced baseline data-driven methods and complementary filter on two metrics, namely absolute attitude error and absolute yaw error, by more than 23.4% and 23.9%. The generalization experiment results demonstrate the robustness of our model on different devices and using patterns.

Data‐Driven Gap Filling and Spatio‐Temporal Filtering of the GRACE and GRACE‐FO Records

AbstractGravity Recovery And Climate Experiment and Follow On (GRACE/‐FO) global monthly measurements of Earth's gravity field have led to significant advances in quantifying mass transfer. However, a significant temporal gap between missions hinders evaluating long‐term mass variations. Moreover, instrumental and processing errors translate into large non‐physical North‐South stripes polluting geophysical signals. We use Multichannel Singular Spectrum Analysis (M‐SSA) to overcome both issues by exploiting spatio‐temporal information of Level‐2 GRACE/‐FO solutions, filtered using the DDK7 decorrelation and a new complementary filter, built based on the residual noise between fully processed data and a parametric fit to observations. Using an iterative M‐SSA on Equivalent Water Height (EWH) time series processed by Center of Space Research, GeoForschungsZentrum, Institute of Geodesy at Graz University of Technology, and Jet Propulsion Laboratory, we replace missing data and outliers to obtain a combined evenly sampled solution. Then, we apply M‐SSA to retrieve common signals between each EWH time series and its same‐latitude neighbors to further reduce residual spatially uncorrelated noise. Comparing GRACE/‐FO M‐SSA solution with Satellite Laser Ranging and Swarm low‐degree Earth's gravity field and hydrological model demonstrates its ability to satisfyingly fill missing observations. Our solution achieves a noise level comparable to mass concentration (mascon) solutions over oceans (3.0 mm EWH), without requiring a priori information nor regularization. While short‐wavelength signals are challenging to capture using highly filtered spherical harmonics or mascons solutions, we show that our technique efficiently recovers localized mass variations using well‐documented mass transfers associated with reservoir impoundments.

Title: Hip and lower limbs 3D motion tracking using a double-stage data fusion algorithm for IMU/MARG-based wearables sensors

This paper presents an algorithm to estimate the relative orientation of body segments during 3D motion tracking, either as multiple individual body segments or as an articulated body chain. For this purpose, a double-stage data fusion algorithm (algorithm-based system) was implemented for inertial measurement units (IMU)/Magnetic Angular Rate and Gravity (MARG)-based wearable sensors during gait. The methodology considers two stages of complementary filters for the data fusion of the IMU/MARG sensors and a Proportional-Integral controller (PI) to incorporate the processed data. Quaternions were employed for the orientation estimation, a Direction Cosine Matrix quaternion-based (DCM) to estimate the relative orientation between the body mobile coordinate system and the inertial reference coordinate system, and Euler angles for the orientation representation. A customized Ambulatory Sensing Motion System (ASMS), consisting of seven monitoring devices was used for the evaluation. The double-stage algorithm-based system was compared with a digital motion processor (DMP) performance. Experimental results of the double-stage algorithm-based system indicated a 0.7° RMSE (M1) and 1° RMSE (M1-M7) with mean values lower than 1° concerning the DMP outcomes. Based on the Bland-Altman analysis, the level of agreement indicated that the double-stage algorithm-based system is neither underestimated nor overestimated and is suitable for the DMP outcome. No singularity conditions nor significant levels of noise or drift were observed in the conducted experiments. The results demonstrate the feasibility of using the proposed method for 3D human motion tracking of multiple body segments, individually or as an articulated body chain. Besides, it suits different IMU/MARG sensor-based wearable sensors.

Perancangan Sendok Makan Parkinson dengan Metode PID berbasis Arduino

Parkinson's disease is a progressive disorder of the nervous system that affects the part of the brain that coordinates body movement. Tremors that often occur in the patient's hands can cause difficulty while eating. One method that can be used as assistive devices for Parkinson's sufferers is to make a spoon that can remain relatively stable. In this study, Parkinson's spoon is made equipped with an MPU6050 sensor which is used to read the rotational movement of the spoon. The read value will be forwarded to the Arduino Nano microcontroller and then calculated using the complementary filter method and the PID (Proportional Integral Derivative). Tuning on the values of Kp, Ki, and Kd in this research was done by trial and error method. In this research, the most optimal PID constant values were obtained, namely Kp = 0.7, Ki = 0.5, and Kd = 20 both on the pitch axis and roll axis. The results of the PID calculation will drive the SG90 servo motor to stabilize the spoon. Testing the percentage error of the MPU6050 sensor was carried out with 6 trials of different angles on the pitch and roll axes. The average error percentage on the pitch axis was 3.23%. and 2.583% on the roll axis. Based on testing the stability of the system against movement, spoon of Parkinson's can stabilize fairly quickly if it is moved slowly despite the initial overshoot, which the highest peak was -21,49 degrees on the pitch axis and -14,89 degrees on the roll axis. However, if the hands vibrate violently, in general the spoon still oscillates between -10 degrees and 10 degrees both on the pitch and roll axis.
 Keywords: Parkinson, MPU6050 Sensor, PID Controller

Attitude Calculation of Quadrotor UAV Based on Extended Kalman Filter and Complementary Filter

Quadrotor UAV obtain the attitude calculation result from inertial measurement unit (IMU), but IMU has the the problems of high noise and low precision, to solve the problems, this paper first introduces the extended Kalman filter (EKF) and complementary filter, and uses them to filter the output of the accelerometer and magnetic sensor. The effects of the two methods are compared by static testing and dynamic testing. The results show that both filtering methods can improve the precision of the attitude angle solutions, but the EKF algorithm performs better.

Hover Dynamics and Flight Control of a UAM-Scale Quadcopter With Hybrid RPM and Collective Pitch Control

Hover analysis is performed on a 1200-lb gross weight UAM-scale quadcopter with both variable rotor speed and collective pitch control. With these redundant controls, the hover performance and flight dynamics are considered at three trim points, where power consumption can be increased to improve authority of the pitch inputs for changes in rotor thrust. An explicit model following control laws is optimized using CONDUITR to meet ADS-33E-PRF handling qualities specifications, with design margin optimization on each axis. The responses of the linearized system are examined with either control type, and pitch control is shown to outperform RPM-control in heave, while the opposite is true for yaw. Trim in axial climb is simulated, where the collective pitch can be scheduled with the climb rate to maintain effective stall margin. Hybrid control mixing is implemented using a complementary filter, allowing the aircraft to use pitch control for short-term responses and RPM control for trim. The benefits of this hybrid control scheme are demonstrated through simulation of hot/high/heavy conditions, where trimming with RPM control allows the pitch actuators to maintain margin for maneuvers. It is concluded that hybrid control allows the aircraft to reap the benefits of pitch control for maneuverability while maintaining stall margin by using RPM control for trim.

Energy-efficient and reconfigurable complementary filter based on analog–digital hybrid computing with SnS2 memtransistor

Sensor fusion is a widely exploited technique that combines data from two or more sensors to improve the accuracy to a level that cannot be achieved using a single sensor alone. Algorithms for sensor fusion are generally executed on conventional digital computing platforms; however, these algorithms impose a burden on small electrical systems with limited battery capacities and computing resources. In this study, we demonstrated an analog–digital hybrid computing platform based on an SnS2 memtransistor for energy-efficient and reconfigurable sensor fusion with a complementary filter algorithm. We experimentally verified that the power consumption of our hybrid computing-based complementary filter is only half that of the traditional software-based complementary filter, even with the same accuracy.