Robust UAV Attitude Estimation Using a Cascade of Nonlinear Observer and Linearized Kalman Filter

2018 ◽  
Author(s):  
Valthor Gudmundsson ◽  
Haukur Kristinsson ◽  
Soren Petersen ◽  
Agus Hasan
Keyword(s):  
Kalman Filter ◽  
Nonlinear Model ◽  
Attitude Estimation ◽  
Nonlinear Observer ◽  
Linear Matrix ◽  
Globally Asymptotically Stable ◽  
New Approach ◽  
Locally Lipschitz ◽  
Aerial Vehicle ◽  
Linearized Model

This paper presents a new approach for Unmanned Aerial Vehicle (UAV) attitude estimation using a cascade of nonlinear observer and linearized Kalman filter. The nonlinear observer is globally asymptotically stable and is designed using linear matrix inequalities (LMI). The exogenous signal from the nonlinear observer is used to generate a linearized model for the Kalman filter. The method is implemented for attitude estimation of a quadcopter. The nonlinear model is derived from the Newton-Euler equations. The nonlinear model is locally Lipschitz due to the cross and dot products between the angular and linear velocity vectors. The attitude estimation from the dynamical system presented in this paper can be used as a module for fault detection. Simulations in Gazebo on a PX4 using Software In The Loop (SITL) shows the proposed method is able to estimate the attitude of a quadcopter accurately.

scholarly journals A Nonlinear Observer to Estimate the Effective Reproduction Number of Infectious Diseases

2021 ◽  
Vol 4 (1) ◽  
pp. 39-45
Author(s):  
Agus Hasan
Keyword(s):  
Kalman Filter ◽  
Infectious Diseases ◽  
Extended Kalman Filter ◽  
Discrete Time ◽  
Reproduction Number ◽  
Epidemiological Data ◽  
Sir Model ◽  
Nonlinear Observer ◽  
Linear Matrix ◽  
Matrix Inequality

In this paper, we design a Nonlinear Observer (NLO) to estimate the effective reproduction number (Rt) of infectious diseases. The NLO is designed from a discrete-time augmented Susceptible-Infectious-Removed (SIR) model. The observer gain is obtained by solving a Linear Matrix Inequality (LMI). The method is used to estimate Rt in Jakarta using epidemiological data during COVID-19 pandemic. If the observer gain is tuned properly, this approach produces similar result compared to existing approach such as Extended Kalman filter (EKF).

scholarly journals Attitude estimation for collision recovery of a quadcopter unmanned aerial vehicle

2019 ◽  
Vol 38 (10-11) ◽  
pp. 1286-1306 ◽  
Author(s):  
Adrian Battiston ◽  
Inna Sharf ◽  
Meyer Nahon
Keyword(s):  
Kalman Filter ◽  
Unmanned Aerial Vehicle ◽  
Unscented Kalman Filter ◽  
Real Data ◽  
Attitude Estimation ◽  
Sensor Data ◽  
Measurement Unit ◽  
Post Processing ◽  
Extensive Evaluation ◽  
Aerial Vehicle

An extensive evaluation of attitude estimation algorithms in simulation and experiments is performed to determine their suitability for a collision recovery pipeline of a quadcopter unmanned aerial vehicle. A multiplicative extended Kalman filter (MEKF), unscented Kalman filter (UKF), complementary filter, [Formula: see text] filter, and novel adaptive varieties of the selected filters are compared. The experimental quadcopter uses a PixHawk flight controller, and the algorithms are implemented using data from only the PixHawk inertial measurement unit (IMU). Performance of the aforementioned filters is first evaluated in a simulation environment using modified sensor models to capture the effects of collision on inertial measurements. Simulation results help define the efficacy and use cases of the conventional and novel algorithms in a quadcopter collision scenario. An analogous evaluation is then conducted by post-processing logged sensor data from collision flight tests, to gain new insights into algorithms’ performance in the transition from simulated to real data. The post-processing evaluation compares each algorithm’s attitude estimate, including the stock attitude estimator of the PixHawk controller, to data collected by an offboard infrared motion capture system. Based on this evaluation, two promising algorithms, the MEKF and an adaptive [Formula: see text] filter, are selected for implementation on the physical quadcopter in the control loop of the collision recovery pipeline. Experimental results show an improvement in the metric used to evaluate experimental performance, the time taken to recover from the collision, when compared with the stock attitude estimator on the PixHawk (PX4) software.

scholarly journals Attitude heading reference algorithm based on transformed cubature Kalman filter

2020 ◽  
Vol 53 (7-8) ◽  
pp. 1446-1453
Author(s):  
Yong-jun Yu ◽  
Xiang Zhang ◽  
M Sadiq Ali Khan
Keyword(s):  
Kalman Filter ◽  
Unmanned Aerial Vehicle ◽  
Reference System ◽  
Orthogonal Transformation ◽  
Estimation Algorithm ◽  
Attitude Estimation ◽  
Measurement Unit ◽  
Sampling Point ◽  
Cubature Kalman Filter ◽  
Aerial Vehicle

Stable and accurate attitude estimation is the key to the autonomous control of unmanned aerial vehicle. The Attitude Heading Reference System using micro-electro-mechanical system inertial measurement unit and magnetic sensor as measurement sensors is an indispensable system for attitude estimation of the unmanned aerial vehicle. Aiming at the problem of low precision of the Attitude Heading Reference System caused by the nonlinear attitude model of the micro unmanned aerial vehicle, an attitude heading reference algorithm based on cubature Kalman filter is proposed. Aiming at the nonlocal sampling problem of cubature Kalman filter, the transformed cubature Kalman filter using orthogonal transformation of the sampling point is presented. Meanwhile, an adaptive estimation algorithm of motion acceleration using Kalman filter is proposed, which realizes the online estimation of motion acceleration. The car-based tests show that the algorithm proposed in this paper can accurately estimate the carrier’s motion attitude and motion acceleration without global positioning system. The accuracy of acceleration reaches 0.2 m/s2, and the accuracy of attitude reaches 1°.

scholarly journals A Nonlinear Observer to Estimate the Effective Reproduction Number of Infectious Diseases

2021 ◽  
Author(s):  
Agus Hasan
Keyword(s):  
Kalman Filter ◽  
Infectious Diseases ◽  
Extended Kalman Filter ◽  
Discrete Time ◽  
Reproduction Number ◽  
Epidemiological Data ◽  
Sir Model ◽  
Nonlinear Observer ◽  
Linear Matrix ◽  
Matrix Inequality

AbstractIn this paper, we design a Nonlinear Observer (NLO) to estimate the effective reproduction number (ℛt) of infectious diseases. The NLO is designed from a discrete-time augmented Susceptible-Infectious-Removed (SIR) model. The observer gain is obtained by solving a Linear Matrix Inequality (LMI). The method is used to estimate ℛt in Jakarta using epidemiological data during COVID-19 pandemic. If the observer gain is tuned properly, this approach produces similar result compared to existing approach such as Extended Kalman filter (EKF).

scholarly journals Robust Tracker of Hybrid Microgrids by the Invariant-Ellipsoid Set

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1794
Author(s):  
Hilmy Awad ◽  
Ehab H. E. Bayoumi ◽  
Hisham M. Soliman ◽  
Michele De Santis
Keyword(s):  
Sliding Mode ◽  
Tracking Error ◽  
Nonlinear Dynamical System ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Nonlinear Dynamical ◽  
Load Variations ◽  
Invariant Ellipsoid ◽  
Steady State Responses ◽  
Linearized Model

This paper introduces a new ellipsoidal-based tracker design to control a grid-connected hybrid direct current/alternating current (DC/AC) microgrid (MG). The proposed controller is robust against both parameters and load variations. The studied hybrid MG is modelled as a nonlinear dynamical system. A linearized model around an operating point is developed. The parameter changes are modelled as norm-bounded uncertainties. We apply the new extended version of the attractive (or invariant) ellipsoid for this tracking problem. Convex optimization is used to obtain the region’s minimal size where the tracking error between the state trajectories and the reference states converges. The sufficient conditions for stability are derived and solved based on linear matrix inequalities (LMIs). The proposed controller’s validity is shown via simulating the hybrid MG with various operational scenarios. In each scenario, the performance of the controller is compared with a recently proposed sliding mode controller. The comparison clearly illustrates the superiority of the developed controller in terms of transient and steady-state responses.

A Unified Approach to H∞ Control of Singular Markovian Jump Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Guoliang Wang ◽  
Hongyi Li
Keyword(s):  
Transition Probability ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
New Approach ◽  
Control Approach ◽  
Singular Markovian Jump Systems ◽  
Jump Systems ◽  
Bounded Uncertainties ◽  
The Given

This paper considers the H∞ control problem for a class of singular Markovian jump systems (SMJSs), where the jumping signal is not always available. The main contribution of this paper introduces a new approach to a mode-independent (MI) H∞ controller by exploiting the nonfragile method. Based on the given method, a unified control approach establishing a direct connection between mode-dependent (MD) and mode-independent controllers is presented, where both existence conditions are given in terms of linear matrix inequalities. Moreover, another three cases of transition probability rate matrix (TRPM) with elementwise bounded uncertainties, being partially unknown and to be designed are analyzed, respectively. Numerical examples are used to demonstrate the effectiveness of the proposed methods.

Integral based sliding mode stabilizing a camera platform using Kalman filter attitude estimation

Mechatronics ◽  
2017 ◽  
Vol 44 ◽  
pp. 42-51 ◽  
Author(s):  
Mohammad Sheikh Sofla ◽  
Mohammad Zareinejad ◽  
Mohsen Parsa ◽  
Hassan Sheibani
Keyword(s):  
Kalman Filter ◽  
Sliding Mode ◽  
Attitude Estimation

scholarly journals Evaluation of Matrix Square Root Operations for UKF within a UAV GPS/INS Sensor Fusion Application

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Matthew Rhudy ◽  
Yu Gu ◽  
Jason Gross ◽  
Marcello R. Napolitano
Keyword(s):  
Sensor Fusion ◽  
Unscented Kalman Filter ◽  
Attitude Estimation ◽  
Square Root ◽  
Fusion Algorithm ◽  
Matrix Square Root ◽  
Global Positioning ◽  
The Matrix ◽  
Aerial Vehicle ◽  
Diagonalization Method

Using an Unscented Kalman Filter (UKF) as the nonlinear estimator within a Global Positioning System/Inertial Navigation System (GPS/INS) sensor fusion algorithm for attitude estimation, various methods of calculating the matrix square root were discussed and compared. Specifically, the diagonalization method, Schur method, Cholesky method, and five different iterative methods were compared. Additionally, a different method of handling the matrix square root requirement, the square-root UKF (SR-UKF), was evaluated. The different matrix square root calculations were compared based on computational requirements and the sensor fusion attitude estimation performance, which was evaluated using flight data from an Unmanned Aerial Vehicle (UAV). The roll and pitch angle estimates were compared with independently measured values from a high quality mechanical vertical gyroscope. This manuscript represents the first comprehensive analysis of the matrix square root calculations in the context of UKF. From this analysis, it was determined that the best overall matrix square root calculation for UKF applications in terms of performance and execution time is the Cholesky method.

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