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International Forum on Aeroelasticity and Structural Dynamics
IFASD 2022
13-17 June 2022, Madrid, Spain
1
Comparison of EKF and Neural Network based wing
shape estimation of a flexible wing demonstrator
Bence Zs. Hadlaczky1, Noémi Friedman1, Béla Takarics1 and Bálint Vanek1
1 Institute for Computer Science and Control
Eötvös Lóránd Research Network
Kende u. 13-17. 1111, Budapest, Hungary
hadlaczky.bence.zsombor@sztaki.hu
friedman.noemi@sztaki.hu
takarics.bela@sztaki.hu
vanek@sztaki.hu
Keywords: aeroelasticity, structural dynamics, LPV, Kalman filtering, neural network,
KalmanNet.
Abstract: Structural flexibility of advanced, large-wingspan aircrafts is a crucial factor which
has huge influence on the dynamics and stability of these vehicles. In case of a highly flexible
wing structure, there is a need for an efficient observer to measure and predict the structural
changes and dynamics of the wing. However, the modal coordinates of the wing cannot be
measured directly so designing a state observer is necessary. Since the flexible aircraft model
is nonlinear, the classical Kalman filter approach can have limited performance. Instead, two
state observer approaches are investigated in the paper. First, we present a model-based method
for designing an extended Kalman filter (EKF) when only a linear parameter-varying model
(LPV) is available to describe the behaviour of the real aircraft. Second, we present a data-
driven approach for this problem which is based on the new KalmanNet architecture. Finally,
the results of the two methods are evaluated on the T-Flex model of the FLiPASED H2020
project.
1 INTRODUCTION
In the recent years, research and development trends in the aerospace industry placed more
emphasis on increasing fuel efficiency [1]. The greatest portion of the operating costs of an
aircraft today comes from fuel consumption, so achieving better fuel economy is a key aspect
for cost reduction. To achieve these goals the decrease of structural mass and use of more
flexible components are the most widely investigated solutions. The use of flexible components
can mean the utilization of highly flexible wings [2]. However, this approach is not without its
difficulties. First, the fuel consumption of the aircraft is largely dependent on the aerodynamic
drag acting on the wings, so reducing drag with a suitable wing shape controller results better
fuel economy. The other difficulty is - for one - the aeroelastic flutter which can cause serious
structural damage to the wings, and the occurring instability and handling quality issues of the
flight controller caused by the flexible structure dynamics of the vehicle [3]. So, supressing
these effects with a flutter controller is a must to ensure safe flights. Control based active flutter
suppression is investigated in several recent research projects. These are the Performance
Adaptive Aeroelastic Wing (PAAW) project [4] and the X-56 program in the USA. However,
both the controller for drag reduction and the flutter controller [5] requires some information
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about the flexible dynamics of the wings, which is not possible with direct measurements. As a
result, a state observer/estimator is required to acquire information about the states which
determine the flexible behaviour of the wings. This paper presents results from the ongoing
Flight Phase Adaptive Aero-Servo-Elastic Aircraft Design Methods (FLiPASED) [6] project
which is the continuation of the Flutter Free Flight Envelope Expansion for Economical
Performance Improvement (FLEXOP) project. The FLEXOP [1] project’s main goal was to
develop an effective flutter suppression system. Therefore, one of the main goals of the
FLiPASED project is to develop drag reducing control for aircrafts with highly flexible wings.
The main motivation of this paper is to present 2 different approaches to estimate the flexible
dynamics of the T-Flex demonstrator which can be then used for the design of a wing shape
controller for drag reduction purposes.
The most straightforward solution for designing a state predictor is the Kalman filter [7] for
linear systems and the extended Kalman filter (EKF) in the case of nonlinear systems. The EKF
is proved to be useful in inertial estimation of wing shape [8]. However, it has two main
drawbacks. First, the EKF requires the exact mathematical state-space description of the
nonlinear system, which might not be available or simply it is too complex to be efficiently
used in calculations. The second drawback is that the knowledge of the noises and disturbances
related to observations and states is necessary. Defining observation noise is the less
challenging task but giving an accurate estimation about the uncertainties and disturbances
related to the model states might not be possible.
To solve the first issue, the approximation of the full, nonlinear system with a Linear Parameter
Varying (LPV) model [9] can be considered. Using an LPV model can be less computation
heavy and implementing an LPV-based EKF for predicting states is a feasible solution [10].
However, this solution still requires noise information. Data-driven approaches have the great
advantage that they can be used for inertial odometry [11] and inertial aided navigation [12]
problems without needing any specific information about model or observation uncertainties.
However, estimating flexible states is a more complex problem. This is where the new
KalmanNet architecture can be useful [13]. The KalmanNet is based on Kalman filtering
however it uses a Recurrent Neural Network (RNN) to estimate a Kalman gain. So as a result,
it does not need any information about the noises and model uncertainties present.
This paper presents the working of the LPV-based EKF and the KalmanNet for predicting the
modal coordinates and aerodynamic lag states of the nonlinear model of an Unmanned Aerial
Vehicle (UAV) T-Flex, which was created during the FLEXOP project for demonstrator
purposes. [2] The testing was carried out with MATLAB, Simulink simulations where the
model received square wave, doublet control surface inputs to excite the flexible dynamics of
the aircraft. The LPV-based EKF was also tested with the baseline controller of the aircraft
which keeps the vehicle on an oval shaped track. The paper is organized as follows. In Section
2., the dynamic model of the FLEXOP demonstrator is presented. Section 3. introduces the
reduced, LPV model of the original nonlinear system, while also discussing the working of the
LPV-based EKF. In Section 4. the KalmanNet’s basic structure is summarized with the chosen
training hyperparameters. Section 5. contains the presentation of the results of the modal
coordinate and lag state estimations. The accuracy of the LPV-based EKF and the KalmanNet
is compared, while for the filter a real-life application is also presented. Conclusions are drawn
in Section 6.
2 FLEXOP DEMONSTRATOR DYNAMIC MODEL
The chosen system for our research is the nonlinear, state space representation of the FLEXOP
demonstrator aircraft. The model consists of 3 main parts: states that are responsible for the
description of the rigid body dynamics; states related to flexible dynamics and aerodynamics,
and finally, states that represent the control surface inputs and their first derivatives. The
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interconnection of these subsystems forms the nonlinear aeroservoelastic model of the aircraft
as seen in Figure 1.
Figure 1: Aeroservoelastic subsystem interconnection
The structural dynamics of the demonstrator was represented with the use of a finite element
(FE) complemented by Guyan reduction to reduce the number of degrees of freedom (DOF).
Based on this model the equations of motion were formulated both for the rigid and the flexible
aircraft motion. The aerodynamic model is based on a set of trapezoidal aerodynamic boxes
which represent the lifting surfaces. The flow field of the demonstrator is approximated either
with vortices or doublets applied to the aerodynamic boxes. The first method is called vortex
lattice method (VLM) while the second is the doublet lattice method (DLM). VLM represents
the steady aerodynamics, DLM incorporates the unsteady aerodynamics as well which results
in extra – so called – aerodynamic lag states. The complete aeroelastic model was created with
connecting the structural dynamics and the aerodynamics using splining. The details of the
modelling can be found in [2]. Since the aeroelastic model is of very high order, first model
order reduction needs to be carried out. The model order reduction is based on the bottom-up
modelling approach and the details are given in [14]-[15].
The rigid body motion is represented with a 6-DOF model with 12 states: states of translational
and angular velocities, position, and orientation. All of these are defined in the body coordinate
system of the aircraft.
(1)
The states which describe the flexible dynamics are the modal coordinates and their first
derivatives. Due to the reduced order modelling only the 6 most significant modal coordinates
and 2 aerodynamic lag states were considered.
(2)
The T-Flex aircraft model has 19 inputs (Figure 2): 2 landing gears (GearR/L), 2 landing gear
wheel brakes (WheelbrakeR/L), 2 airbrakes located on the aircraft’s fuselage (AirbrakeR/L) and
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1 turbofan engine (Throttle). The demonstrator has 12 control surfaces: 4-4 ailerons
(AileronR/L) on each wing and on the V-tail 2-2 ‘ruddervators’. From the inputs, the landing
gear related ones are insignificant in our research since the estimation of the structural dynamics
only conducted during airborne operations.
Figure 2: Demonstrator input and control surfaces
The model has 23 rigid body related outputs, which provide information about the aircraft’s
position (xE, yE, zE), orientation (Φ, Θ, ψ), translational (vN, vE, vD) and angular velocity (p, q,
r), and acceleration (axB, ayB, azB). Furthermore, the course angle (χ), angle of attack (α), sideslip
angle (β), air (pa) and total pressure (pT), barometric altitude (hbaro), indicated (vIAS) and the true
airspeeds (vTAS) are measured as well.
Each wing of the demonstrator has 6-6 inertial measurement units (IMUs). An IMU provides
acceleration and angular velocity data around the x-, y- and z-axis of its coordinate system. The
IMUs communicate with the flight control computer (FCC) via CAN. However, as the
bandwidth of the CAN-bus is limited and other sensors use the CAN as well, one IMU can only
provide 3 measurement data. We opted for such an IMU configuration, where the IMUs on the
leading-edge measure accelerations in the x, y, and z directions. The IMUs on the trailing-edge
provide angular velocity data around the x- and y-axis, and acceleration data in the z direction.
The exact location of the IMUs can be seen in Figure 3. So, in total, the 12 IMU measurements
add up as 36 additional outputs.
Figure 3: IMU configuration
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In addition – in the light of the recent research conducted by the Technical University of Munich
(TUM) – we assumed, that the wingtip coordinates can be measured with a mono camera. On
each wing, the coordinates of 4 wingtip points are measured in each direction which results 12
additional outputs. This is useful for preventing acceleration-based estimation errors from
diverging in time [8].
3 MODEL BASED ESTIMATION OF FLEXIBLE DYNAMICS
3.1 LPV model
The linear parameter varying (LPV) model is an approximation to describe the behaviour of a
nonlinear system [9]. It is essentially a pointwise linearization of a state-space system: the
nonlinear system is linearized at different trim points. These trim points are defined by – so
called – scheduling parameters. The scheduling parameters create a multidimensional grid, and
a linear, state-space model is assigned to every grid point. The state-space description of a
discrete time LPV system can be written as:
(3)
where ρ[k] is the time varying vector of the scheduling parameters.
In our work, we created an LPV approximation of the nonlinear bottom-up model of the T-Flex
demonstrator aircraft with 2 scheduling parameters: the true airspeed (vTAS) and the roll angle
(Φ) sensor outputs. The grid for the LPV model consisted of airspeed values form 30 m/s to 50
m/s with a 1 m/s resolution while the roll angles from 0° to 40° with 10° resolution. Then the
nonlinear model was trimmed at each grid-point. The resulting LPV model structure was then
further refined to 0.1 m/s and 1° resolution with the spline interpolation method of the
LPVTools MATLAB toolbox [16].
3.2 LPV-based Kalman filtering
For the model-based wing-shape estimation, an extended Kalman filter (EKF) was used. The
EKF pipeline requires the full, nonlinear state-space description of the system as well as
information about the model noise and observation noise in the form of noise covariance
matrices. The nonlinear system’s state-space representation in discrete time is written as:
(4)
where x[k] is the state vector, u[k] is the input vector, y[k] is the output vector at timestep k.
Nonlinear function f(.) is called state-transition function, while h(.) is called state-observation
function. The w[k] and v[k] vectors are the model noise and observation noise vectors
respectively. However, the explicit mathematical description – the nonlinear state-transition
and state-observation functions – of the T-Flex demonstrator was not available for us, therefore
a unique approach was necessary for designing the EKF.
The general workings of the EKF consists of 2 main steps: prediction and update. In these steps,
pointwise linearization is used to approximate the behaviour of the nonlinear system. More
precisely the Jacobians of the nonlinear state-transition and state-observation functions are
calculated to get the linear, state-space matrices A, B, C and D at each timestep.
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(5)
In the prediction step the prior state estimation and the prior state estimation covariance is
calculated using the inputs of the current timestep and the estimations from the previous
timestep.
(6)
(7)
In the update step, first the so-called innovation and innovation covariance is calculated which
is used directly to get the near-optimal Kalman gain. With the help of the Kalman gain, the
posterior state vector and state prediction covariance is computed.
(8)
(9)
(10)
(11)
(12)
In the equations, the Q and R matrices are the model and the observation noise covariance
matrices respectively.
To obtain an appropriate pointwise linearization we used our LPV model. During simulation
the true airspeed and roll angle is measured at each timestep which then can be used to select
an approximating linear system from the LPV model. The selected model’s state-space matrices
are fed to the EKF as the current A, B, C and D matrices. Then the EKF conducts the prediction
and update steps. Acquiring model and observation noise covariance matrices the following
was done. Both the nonlinear and the LPV model was simulated with doublet inputs on the
control surfaces and then the measured outputs and states were compared. The trim values in
case of the states, inputs and outputs were subtracted thus only changes in these quantities were
taken into account. The variance of the output and state differences were taken between the
models and ordered into observation and model noise (co)variance matrices respectively. In the
observation covariance matrix, the T-Flex’s onboard sensors’ noise variances were
incorporated as well. These were specified based on the sensors’ datasheets. Note that we used
the assumption that both noises have 0 mean, normal distributions, and the noise vectors at each
timestep are mutually independent.
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4 DATA-DRIVEN ESTIMATION OF FLEXIBLE DYNAMICS
4.1 KalmanNet architecture
The other approach for estimating the flexible dynamics of the demonstrator is to use artificial
intelligence, more precisely a neural network. Our choice was to use the relatively new
KalmanNet architecture. [13]
KalmanNet – as its name suggests – combines Kalman filtering with a neural network. It still
uses the current inputs and observations for giving state estimations, however the near optimal
Kalman gain is provided by a trained recurrent neural network. The main advantage of this is
that KalmanNet does not require neither the model (Q) nor the observation noise covariance
matrices (R) and it can effectively overcome any uncertainties or errors in the model of the
dynamic system, but it still retains engineering insight about the physical system, so it is not a
black-box end-to-end neural network.
The KalmanNet pipeline is the following. It still consists of a prediction and an update step just
like a Kalman filter. In the prediction step however only the prior state prediction is calculated,
the state prediction covariance (P) is not.
(13)
In the update step, first the innovation difference (Δy[k]) and the forward update difference
(Δx[k]) are computed:
(14)
(15)
These act as the input features for the recurrent neural network. The RNN uses Fully Connected
Layers with Rectified Linear Units (ReLU) and a Gated Recurrent Unit (GRU) to provide the
actual Kalman gain. The network architecture can be seen in Figure 4. with each layer's input
and output dimensions where m denotes the number of states (in our case 50) and n denotes the
number of outputs/observations (in our case 64).
Figure 4: KalmanNet architecture
With the Kalman gain and using the innovation, the a posteriori state prediction vector is
calculated.
(16)
(17)
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The whole pipeline for the KalmanNet is presented at Figure 5.
Figure 5: KalmanNet pipeline
As it can be seen, since neither the state estimation covariance (P) nor the innovation covariance
(S) is used, the noise covariance matrices are not required. The whole pipeline works without
any information about the model or observation noises.
4.2 Training parameters
The hyperparameters for training were set with the following values. The learning rate value
was 5*10-7 with ‘on plateau’ learning rate scheduler. This method reduces the learning rate with
a predefined factor if the validation accuracy hasn’t changed for a given number of ‘patience’
epochs. The reduction factor was set to 0.5 and the ‘patience’ epoch number was 3. The chosen
optimizer for training was the ADAM algorithm [17] with a weight decay value of 10-5. The
prediction accuracy was calculated with mean squared error (MSE) function. However –
although the linearized aircraft model is a stable system, the system’s poles are relatively close
to the unstable region. So, a stability criterion was added to the MSE loss function.
It is possible to describe the complex system of the aircraft model joined with the Kalman filter
with an error system:
,
(18)
where K is the Kalman gain, e[k] is the state prediction difference at timestep k. If the error
system’s state transition matrix (A-KC) has any unstable poles, then the whole system is
unstable. So, the MSE loss was extended with the distance of the error system poles from the
boundary of stability if it is larger than 0, thus making the loss value larger if the computed
Kalman gain results an unstable error system. This is especially useful during the convergence
of the training.
As for weights initialization, both the linear layers’ and the GRU cell’s weights were initialized
with 0 mean, 10-5 standard deviation normal distribution. The reason for having such a small
standard deviation is the fact that if the initialized weights of the layers are too large, the newly
initialized network produces such Kalman gains that makes the whole system so unstable, that
the gradients explode because of the huge prediction error values.
5 RESULTS
5.1 LPV-based EKF
The behaviour of the LPV-based EKF was tested with 2 different control signal configurations.
The first configuration was 2.6 seconds long square-wave doublet inputs on each control surface
with an amplitude of 6.6° (0.12 rad) while there was a 3-second-long throttle input with an
amplitude of 10%, which accelerated the aircraft. For constructing the LPV model, the linear
models were discretized with Ts = 5 ms sampling time. The used control surface inputs and a
single control surface input is shown at Figure 6.
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Figure 6: Single aileron input (left) and all control surface inputs (right)
The simulation lasted for 6 seconds which adds up to 1200 samples in total. The initial flight
conditions of the aircraft model were 42 m/s true airspeed at 800 m altitude with an initial course
angle of 2°. The initial vertical speed and the roll angle were set to 0.
The results for the doublet inputs are shown in Figure 7., where the data with the ground truth
label show the states of the nonlinear model, while the predictions show the states estimated by
the filter. Since the main purpose of the observer design is to observe the flexible dynamics of
the states, only the results for these states are presented. The first 4 modal coordinates are
plotted where Uf1 is the 1st symmetric bending and Uf2 the 1st asymmetric bending mode. Uf3
denotes the 1st symmetric torsion mode and Uf4 is the 1st asymmetric torsion mode. The 2
aerodynamic lag states are plotted as well.
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Figure 7: LPV-based EKF with doublet inputs
It can be seen, that the LPV-based EKF provides good estimations on the considered state
dynamics. However, it is important to highlight that the predictions of Uf4 and lag1 have
inaccuracies and small spikes can be seen around those timesteps where the doublet, square-
wave signal was given on a control surface.
The second input configuration was provided by a baseline controller which keeps the aircraft
at an oval – the so-called ‘horserace’ – track (Figure 8).
Figure 8: Horserace track
This controller is used during real-life flight tests on the T-Flex demonstrator. The LPV model
was specifically designed for this application that is why the roll angle was selected as a
scheduling parameter in addition to the true airspeed since during a turning manoeuvre the
aircraft rotates around its longitudinal axis.
The initial conditions were the same as in the previous case: 42 m/s flight speed at 800 m
altitude, with 2° course angle. The whole simulation lasted for 120 seconds which corresponds
to 1 full lap around the track.
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Figure 9: LPV-based EKF with baseline controller
From the results (Figure 7) it can be concluded that the designed filter accurately predicts the
modal coordinates and the aerodynamic lag states. Minor errors occur only during turning
manoeuvres in Uf3 and lag1 states. The reason behind these is that the LPV model is still just an
approximation of the real, nonlinear system. However, these inaccuracies are inside the error
tolerance for this problem.
5.2 KalmanNet
For training, 20 batches of 1200 sample long trajectories were created with a sampling time of
5 ms. For generating the training, validation and test data, the reduced, nonlinear model of the
T-Flex was used in Simulink. The inputs for the neural network were the observations and
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control surface and throttle inputs of the nonlinear model. The target for the network were the
nonlinear model’s states.
During training, validation and testing the KalmanNet used the linear, state-space matrices of
the nonlinear model trimmed at 42 m/s true airspeed at 800 m altitude with initial course angle
of 2°.
In each trajectory, similar doublet and throttle inputs were given to the model as in the case of
the LPV model. However, the doublet amplitudes were randomly generated between [6°; 10°],
the length of a doublet from [1.5 s; 2 s]. The exact start time of a doublet was also randomly
picked to make the training, validation, and testing data more diverse. Also, observation and
model noise were also incorporated into the data. The noise samples were taken from random
normal distributions with 0 mean and R and Q covariance matrices respectively.
The whole training procedure lasted for 100 epochs. In each epoch 5-5 batches were randomly
selected from the total 20 for training and validation. The error metrics were defined in decibels
for the sake of convenience during plotting, because the freshly initialized network tends to
produce large errors. It is simply calculated with the following formula:
(19)
Before the training procedure, a simple Kalman filter was designed to the linear state-space
model used by the KalmanNet as a reference. The summary of the training is presented at Figure
10.
Figure 10: Training graph (Kalman filter included for reference)
The initial flight conditions for testing were set to 42 m/s true airspeed at 800 m altitude with
initial course angle of 2° in the T-Flex nonlinear model. The results are shown in Figure 11.
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Figure 11: KalmanNet predictions with doublet inputs
The results indicate the following: the network manages to give better predictions in the case
of Uf1, Uf4 and lag1 than the LPV-based filter. However, in the case of the other states, the
accuracy of the predictions is worse than the EKF. The reason for this is that the KalmanNet
only uses the linear state space model, corresponding to the initial flight conditions, but as the
inputs are given on the control surfaces, the behaviour of the nonlinear model starts to differ
more and more form the initial linear model. However, even with this handicap, it still manages
to perform better than a standard Kalman filter designed for the initial flight condition’s linear
model. The KalmanNet had -23 dB test error compared to -11.3 dB of the Kalman filter. This
suggests that it can alleviate some of the inaccuracies caused by the discrepancies between the
linearized and the nonlinear model.
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The training of the neural network was carried out with a Nvidia Tesla V100 GPU with 32 GB
RAM. Using this setup, the training lasted for approximately 4 - 4.5 hours.
Considering the results, we can conclude that only using a simple Kalman filter fitted to a
linearized/trimmed model is a suboptimal solution to accurately predict the flexible dynamics
of the nonlinear system. However, using an LPV-based EKF can provide good estimations. The
use of the new KalmanNet architecture shows that even when it only has access to the linearized
model while seeing data from the nonlinear model, it can overcome some of the inaccuracies
coming from the differences between the models while not using any information about these
model uncertainties. In order to give quantitative comparison of the performance of the 2
proposed architecture estimating the modal coordinates and lag states the previously mentioned
logarithmic error metric was used. This is presented in Table 1.
Table 1: Prediction errors
Description
lossdBMSE, dB
Kalman filter (as a
reference)
-11.3
LPV-based EKF
-29.5
KalmanNet
-23
In case of the KalmanNet-based flexible dynamics estimation further research is needed in
which the network will use the LPV model as the representation of the dynamic system.
6 CONCLUSION
To summarize, in this work we propose a model-based and a data-driven approach to estimate
the flexible dynamics of a UAV with large wingspan and highly flexible wings. The model-
based approach uses an LPV-based EKF while the data-driven solution utilizes the KalmanNet
architecture. We show that the EKF-based estimator is able to predict the flexible and
aerodynamic lag states both for doublet ‘test’ control surface inputs and for baseline controller
inputs. The neural network-based approach is also capable of estimating the above-mentioned
states, however, to obtain better, more accurate results, further research is needed. Our long-
term goals include extending the KalmanNet architecture with the LPV system model to have
a better approximation of the original, nonlinear system and conduct training with this
modification. It is also a prospective goal to test both architectures in real life flight data and
then incorporate them in the T-Flex’s FCC for real-time, airborne operations. With this, it will
be possible to design a wing shape controller to minimize aerodynamic drag during flights.
7 ACKNOWLEDGEMENT
The research leading to these results is part of the FLiPASED project. This project has received
funding from the Horizon 2020 research and innovation programme of the European Union
under grant agreement No 815058.
The research was supported by the Ministry of Innovation and Technology NRDI Office within
the framework of the Autonomous Systems National Laboratory Program.
Supported by the ÚNKP-21-5 New National Excellence Program of the Ministry for Innovation
and Technology from the source of the National Research, Development and Innovation Fund.
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This paper was supported by the János Bolyai Research Scholarship of the Hungarian Academy
of Sciences.
8 REFERENCES
[1] FLEXOP, “Flutter Free FLight Envelope eXpansion for ecOnomical Performance
improvement (FLEXOP),” Project of the European Union, Project ID: 636307, 2015-2018.
[2] Wüstenhagen, M., Kier, T., Pusch, M., Ossmann, D., Meddaikar M. Y., Hermanutz, A.
(2018). Aeroservoelastic Modeling and Analysis of a Highly Flexible Flutter
Demonstrator, AIAA AVIATION Forum, Atmospheric Flight Mechanics Conference
June 25-29, 2018, Atlanta, Georgia
[3] Robles, R. R. (2022). A Novel Adaptive Aeroservoelastic Coupling Supprerssion
Algorithm for the A330 SMART MRTT Flying Boom Control Laws, Conference on
Guidance, Navigation and Control, 2022
[4] PAAW, Performance Adaptive Aeroelastic Wing Program, Supported by NASA NRA
"Lightweight Adaptive Aeroelastic Wing for Enhanced Performance Across the Flight
Envelope", 2014-2019.
[5] Patartics, B., Luspay, T., Péni, T., Takarics, B., Vanek, B., Kier, T. (2017). Parameter
varying flutter suppression control for the BAH jet transport wing, International
Federation of Automatic Control Conference, 2017.
[6] FLiPASED, “Flight Phase Adaptive Aero-Servo-Elastic Aircraft Design Methods
(FLiPASED)”, Project of the European Union, Project ID: 815058, 2019-2022.
[7] Kotikalpudi, A., Danowsky, B. P., Schmidt, D. K., Gupta, A., Regan, C. (2019). Real-
Time Shape Estimation for a Small Flexible Flying-Wing Aircraft, AIAA SciTech Forum,
7-11 January 2019, San Diego, California
[8] Lustosa, L. R., Kolmanovsky, I., Cesnik, C. E. S., Vetrano, F. (2021). Aided Inertial
Estimation of Wing Shape. Journal of Guidance, Control and Dynamics, American
Institute of Aeronautics and Astronautics, 2021, 44 (2), pp.210-219.
[9] Takarics, B., Vanek, B. (2021). Robust Control Design for the FLEXOP Demonstrator
Aircraft via Tensor Product Models, ASIAN JOURNAL OF CONTROL, 23 (3). pp. 1290-
1300. ISSN 1561-8625
[10] Shereen, M. K., Khan, M. I., Khan, N., Ullah, W. (2016). By the Design and
Implementation of Modified Kalman Filter for LPV Systems, International Journal of
Engineering Works, Vol. 3, Issue 4, PP. 26-31
[11] Dugne-Hennequin, Q. A., Hideaki, U., do Monte Lima, J. P. (2021). Understanding the
Behaviour of Data-Driven Inertial Odometry with Kinematics-Mimicking Deep Neural
Network, IEEE Access, vol. 9, pp. 36589-36619, 2021, doi:
10.1109/ACCESS.2021.3062817.
[12] Zhang, M., Zhang, M., Chen, Y., Li, M. (2021). IMU Data Processing for Inertial Aided
Navigation: A Recurrent Neural Network Based Approach, arXiv: 2103.14286 v1, 26 Mar
2021
[13] Revach, G., Schlezinger, N., Ni, X., Escorzia, A. L., van Sloun, R. J. G., Eldar, Y. C.
(2021). KalmanNet: Neural Network Aided Kalman Filtering for Partially Known
Dynamics. arXiv 2107.10043 v1
[14] Takarics, B., Vanek, B., Kotikalpudi, A., Seiler, P. (2018). Flight Control Oriented
Bottom-up Nonlinear Modeling of Aeroelastic Vehicles, 2018. IEEE Aerospace
Conference
IFASD-2022-111
16
[15] M. Meddaikar et al. (2019). Aircraft aeroservoelastic modelling of the FLEXOP
unmanned flying demonstrator, AIAA Scitech 2019 Forum, AIAA, 2019–1815.
[16] Balas, G., Packard, A., Seiler, P., Hjartarson, A. (2015) LPVTools - A Toolbox for
Modeling, Analysis, and Synthesis of Parameter Varying Control Systems, MUSYN Inc.
2015
[17] D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, preprint
arXiv:1412.6980, 2014.
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