Airship aerodynamic model estimation using unscented Kalman filter

doi:10.23919/JSEE.2020.000102

Abstract

Abstract:

An airship model is made-up of aerostatic, aerodynamic, dynamic, and propulsive forces and torques. Besides others, the computation of aerodynamic forces and torques is difficult. Usually, wind tunnel experimentation and potential flow theory are used for their calculations. However, the limitations of these methods pose difficulties in their accurate calculation. In this work, an online estimation scheme based on unscented Kalman filter (UKF) is proposed for their calculation. The proposed method introduces six auxiliary states for the complete aerodynamic model. UKF uses an extended model and provides an estimate of a complete state vector along with auxiliary states. The proposed method uses the minimum auxiliary state variables for the approximation of the complete aerodynamic model that makes it computationally less intensive. UKF estimation performance is evaluated by developing a nonlinear simulation environment for University of Engineering and Technology, Taxila (UETT) airship. Estimator performance is validated by performing the error analysis based on estimation error and 2- $ \sigma $ uncertainty bound. For the same problem, the extended Kalman filter (EKF) is also implemented and its results are compared with UKF. The simulation results show that UKF successfully estimates the forces and torques due to the aerodynamic model with small estimation error and the comparative analysis with EKF shows that UKF improves the estimation results and also it is more suitable for the under-consideration problem.

Key words: airship, unscented Kalman filter (UKF), extend Kalman filter (EKF), state estimation, aerodynamic model estimation

Muhammad WASIM, Ahsan ALI. Airship aerodynamic model estimation using unscented Kalman filter[J]. Journal of Systems Engineering and Electronics, 2020, 31(6): 1318-1329.

Figures/Tables 7

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Parameter	Symbol	Value
Length	L/m	9
Diameter	D/m	2.2
Volume of hull	V/m³	25
Mass	m/kg	24.073
Moment of inertia about x-axis	$ {I}_{x} $ /kg·m²	2.842
Moment of inertia about y-axis	$ {I}_{y} $ /kg·m²	26.769
Moment of inertia about z-axis	$ {I}_{z} $ /kg·m²	26.769
Product of inertia	$ {I}_{xz} $ /kg·m²	0.001166
Maximum radius	b/m	1.1
x-distance from nose to CV	$ {a}_{1} $ /m	3.9
x-distance from CV to tail	$ {a}_{2} $ /m	5.1
Distance of CV from airship nose on x-axis	x_cv/m	4.34
Length of the hull up to the leading edge of the fins	$ {l}_{h} $ /m	6.43
x-distance from origin to aerodynamic center of fins	l_f1/m	2.41
z-distance from origin to aerodynamic center of fins	l_f3/m	1.04
x-distance from origin to geometric center of fins	l_f2/m	2.62
Fin reference area	S_f /m²	9
Gondola reference area	S_g /m²	1

State	Mean estimation error
State	EKF	UKF
u	0.0136	0.0128
v	?2.278 0×10^?5	?2.521 0×10^?5
w	0.0017	0.0014
P	0.0036	0.0035
q	0.0045	0.0041
r	6.707 0×10^?5	6.208 0×10^?5
$ {F}_{Ax} $	?0.1123	?0.034
$ {F}_{Ay} $	0.0092	?0.0040
$ {F}_{Az} $	?0.0055	0.0022
$ {\tau }_{Al} $	?0.0020	0.0012
$ {\tau }_{Am} $	?0.2501	?0.0645
$ {\tau }_{An} $	0.0130	0.0153

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