Digital Twin Concept for Aircraft System Failure Detection and Correction

Full text

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Digital Twin Concept for Aircraft System
Failure Detection and Correction
Omar Hazbon Alvarez1 and Luis B. Gutierrez Zea2
Universidad Pontificia Bolivariana, School of Aeronautical Engineering, Medellin,
Colombia.
Cees Bil3
RMIT University, School of Engineering, Melbourne, Australia.
Mario L. Fravolini4
University of Perugia, Department of Engineering, Perugia, Italy.
Marcello Napolitano5
West Virginia University, School of Mechanical and Aerospace Engineering,
Morgantown, USA.
The air data system estimates vital flight parameters for correct and safe aircraft operation.
One of the main components in this system is the Pitot tube sensor for measuring the total
pressure and static pressure to estimate altitude, air speed, vertical speed and Mach number.
The Pitot tube can supply incorrect measurement readings when its orifices are blocked by ice,
dust or even insects. This paper describes the results of an ongoing research project to develop
a solution to aircraft loss of control caused by an unreliable airspeed indication by
incorporating the concept of an aircraft digital twin.
I. Nomenclature
_____________________________________
1 Professor, School of Aeronautical Engineering, Universidad Pontificia Bolivariana, Medellin, Colombia, AIAA
Senior Member.
2 Professor, School of Aeronautical Engineering, Universidad Pontificia Bolivariana, Medellin, Colombia.
3 Professor, School of Engineering, RMIT University, Melbourne, Australia, AIAA Associate Fellow.
4 Associate Professor, Department of Engineering, University of Perugia, Perugia, Italy.
5 Professor, School of Mechanical and Aerospace Engineering, West Virginia University, Morgantown, USA, AIAA
Senior Member
 =accelerometer
measurement
Ω = angular velocity
 = angular acceleration
 = direction cosine matrix
 = velocity
 = acceleration
 = position
 = attitude quaternion
 = attitude quaternion rate
 = instrument bias
 = angle of attack
 = angle of sideslip
 = thrust force
 = thrust moment
 = aerodynamic force
 = aerodynamic moment
 = aircraft mass
 = center of gravity
 = aircraft inertia
 = bandwidth
Subscripts or Superscripts
 = body frame
 = navigation frame
 = measurement
 = accelerometer
 = gyroscope
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II. Introduction
The Air Data System (ADS) plays a vital role in aircraft operation. The information provided by this device is used
by the pilot and other aircraft subsystems for maneuvering and navigating within safe performance boundaries. Aircraft
state parameters like pressure altitude, vertical speed, calibrated airspeed, Mach number, true airspeed, static air
temperature, air density ratio, angle of attack and angle of sideslip are calculated by the Air Data Computer (ADC)
from the information provided by the ADS Sensors. The basic air data sensors are the Pitot tube that provides
information to the ADC about total pressure, the static port that provides information of the static pressure and the
temperature probe that provides information of the total air temperature. For some applications, were the aircraft can
reach angles of attack near the stall region or fly-by-wire flight control system applications, the ADS is provided with
angle of attack and sideslip vanes.
There is a history of aircraft accidents caused by the failure of one of the ADS sensors: the Pitot tube. The most
controversial accidents were AeroPerú flight 603 in October 1996 and Air France flight 447 in June 2009. In 2018
two accidents are suspected to be caused by the Pitot tube failure, Saratov Airlines flight 6W703 and Lion Air flight
610. Table 1 shows a list of some selected non-military aircraft accidents caused by Pitot tube failure since 1973 [1-
15].
Table 1 Some non-military aircraft accidents caused by Pitot tube Failure or ADS sensors since 1973.
There are also cases were angle of attack vane failure caused aircraft accidents. This was the case for XL Airways
flight 888T on November 2008 and it is also a presumed the cause for the Ethiopian Airways flight 302 accident on
March 2019.
It has been observed that the Pitot-static system fails under certain atmospheric conditions of low temperature and
high humidity. The sensor orifices or internal ducts are blocked with ice preventing actual pressure readings to be
sensed by its transducer and as a result, the computed airspeed become erratic and unreliable. There are other possible
causes of Pitot blockage like dirt, insects or even ground protection devices. The Pitot tube failure affects air safety as
pilots may not be able to identify the failure and become confused due to unreliable and conflicting warnings. In
unmanned air vehicles the situation is also critical because the autopilot is receiving erratic information from the ADS
system causing a total loss of control.
To overcome the consequences of ADS sensor failures, aircraft manufacturers have implemented sensor
redundancy with a voting scheme that detects and isolate faulty air data sensor signals, however under certain
atmospheric circumstances all sensors fail at the same time and is known as common mode failure. Airbus equipped
the A320, A330 and A340 with a Backup Speed Scale (BUSS) were a theoretical airspeed is estimated from pitch and
thrust tables, however the system failed on Air France 447 [16]. The Airbus A350, a state of the art airliner, is using
an extra air pressure information from the sensors of the engine nacelles that helps alleviating the effects of corrupted
ADS sensor signals [17]. On the other hand, Boeing’s approach to this problem was to equip the 787 Dreamliner with
an airspeed estimation using information of angle of attack and inertial data called “Synthetic Air Speed”, however
this system failed on Jetstar flight JQ 07 [18].
Date
Model
Aircraft Damage
Cause
Passengers
and
Crew
Casualties
/ Injured
January 30 1973
DC-9-21
Aircraft total Loss
Ice in Pitot tubes
33
0
December 01
1974
Boeing 727 - 251
Aircraft total Loss
Ice in Pitot tubes
3
3
July 28 1984
Learjet 25B
Aircraft total Loss
Pitot tube covers not removed
3
0
May 21 1986
Tupolev 154B-2
Aircraft total Loss
Ice on Pitot tubes
176
0
March 02 1994
MD-82
Structural
damage
Ice on Pitot tubes
116
0
February 06 1996
Boeing 757 - 225
Aircraft total loss
Dust or insect debris blocking Pitot tubes
orifices
189
189
October 02 1996
Boeing 757-23A
Aircraft total loss
Adhesive tape blocking ADS static port orifice
70
70
October 10 1997
DC-9-32
Aircraft total loss
Ice on Pitot tubes
74
74
April 7 1999
Boeing 737 4Q8
Aircraft total loss
Ice on Pitot tubes
6
6
October 17 1999
MD-11F
Aircraft total loss
Ice blocking Pitot tube drain orifices
2
0
June 3 2006
Dornier 328Jet-
300
Aircraft total loss
Obstruction of Pitot tube orifices
8
0
June 01 2009
Airbus A330 - 202
Aircraft total loss
Obstruction of Pitot tube orifices
228
228
Feb 11 2018
Antonov 148
Aircraft total loss
Possible Ice on Pitot Tubes
71
71
Oct 29 2018
Boeing 737
Aircraft total loss
Possible ADS Failure
189
189
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The goal of this research is to develop an ADS tolerant to the Pitot-static sensor failure by means of a real time
numerical estimation of the airspeed, using information from other airborne sensors and supported by a high-fidelity
aircraft dynamic model called digital twin that will act as a virtual sensor. The digital twin concept is illustrated in Fig.
1. Fig. 1 Aircraft digital twin concept.
III. Literature review
The airspeed sensor failure problem has been worked out by means of a Sensor failure detection identification and
accommodation (SFDIA) task. SFDIA has been traditionally divided in two steps. The first step involves the detection
of the sensor failure and identification (SFDI) of the sensor that is generating the unhealthy signal so the corrupted
hardware can be isolated. Sensor failure accommodation (SFA), the second task, consist in the numerical estimation
of the airspeed by means of a virtual sensor and the statistical comparison of this value with the sensor (or sensors)
signal so the healthy parameter can be selected and used in the flight control system.
A. Sensor Failure and Identification
Napolitano et al [19] used three approaches for SFDI purposes based in statistical fault detection filters. The first
approach analyses the sensor signal residual by means of a fixed failure detection threshold that uses a Cumulative
Sum filter – CUSUM. The second approach tries to minimize the number of false detections or undetected corrupted
signals by using adaptive signal residual thresholds and calling this algorithm the “floating limiter”. The third approach
is based on the analysis of the residual signals by using the statistical generalized likelihood ratio test method – GLRT.
In either approach, the difference between the sensor measurement and the analytically estimated value, so called the
residual, is compared with the computed threshold and the failure will be identified when the residual exceeds a
particular threshold value thus triggering failure detection. Recent research efforts focus on giving robustness to the
statistical fault detection algorithm to the previous approaches by using the exponentially weighted moving averaged
– EWMA filter that can detect small shifts in the mean and standard deviation of the residual signals [20]. The EWMA
filter tracks the EWMA mean of all previous samples so that the most recent are weighted more heavily than the older
ones, preventing that the faults in previous time steps affect the current residual. These fault tolerant techniques can be
extended to as many sensors as needed in conjunction with a bank of residual monitors to isolate the faulty sensor.
B. Model-Based Sensor Failure Accommodation
The model-based current airspeed estimation approaches take advantage of the well-known aircraft non-linear
model [21, 22] and redundant measurements from the sensors onboard. The commonly used model state variables are
the true airspeed, angle of attack, angle of sideslip, angular rates, Euler attitude angles and the aircraft position. The
state control variables rely on the thrust force and the elevator, rudder and aileron deflections. The airspeed is implicit
in all the twelve equations of the aircraft nonlinear model, however in Napolitano’s early research it is stated that the
airspeed is strongly correlated with the angle of attack equation and it suffices for the estimation of the airspeed. The
researchers expressed this equation in a form that is suitable for parameter identification with a linear combination of
unknown coefficients and known nonlinear functions of measured signals. The equation is evaluated at several instants
on a time window to set up a linear system of equations that is solved for the unknown equation coefficients by means
of least squares and taking advantage of previously recorded flight test data. The online estimates of the airspeed at a
particular time are based on the online solution of the quadratic equation were the unknown coefficients are substituted
by the LS estimate and only the positive value of the airspeed is selected.
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C. Model-Independent Sensor Failure Accommodation
The model-independent virtual sensors are of great interest because the estimation method can be applied
conveniently to any aircraft without information of the vehicle dynamics which most of the time is difficult to obtain.
Researchers had tried several types of state estimators to predict the aircraft airspeed. The nonlinear behavior of the
aircraft dynamics has caused the researchers to use Kalman filter based estimation methods in the form of Extended
and Unscented Kalman filter. These estimation methods use information from the other airborne sensors to estimate
the airspeed, particularly the three axis accelerations and angular rates from the IMU, roll and pitch angle measurements
from the vertical gyro and angle of attack and sideslip from the ADS as stated by Napolitano et al [23].
A second type of model independent SFA methods tried by researchers in the aircraft airspeed estimation are based
in flight test data correlations in the form of Neural Networks - NN. The NN is trained to learn the functional
relationship between the airspeed and a set of correlated measurements provided by the other aircraft sensors. Different
type of NN has been tested in simulation. Napolitano et al [24] and Turkmen et al [25], developed airspeed estimators
using Multi-Layer Perceptron – MLP NN to take advantage of its flexibility for several applications, including function
fitting and pattern recognition. The MLP is usually trained to learn the functional relationship between the airspeed
and a set of correlated measurements provided by the other aircraft sensors. To reduce the real-time computational
requirements of the MLP NN, Napolitano et al [24] used the Extended Minimal Resource Allocating Networks –
EMRAN NNs that allows only the parameters of the most active neurons to be updated, while all the others are left
unchanged. Some other types ANNs had been used in aircraft airspeed estimation. Husain [26] used a fully connected
cascade ANN for estimation arguing that it requires lower computational effort that MLP and EMRAN ANNs.
The NN estimation methods described above require tailored time-consuming tuning procedures that usually
produce unreliable performance when validated with actual flight data. To overcome this problem current research
effort is being conducted by Balzano et al [27] based on a semiautomatic data driven approach to select model
regressors and identify Nonlinear Autoregressive Exogenous – NARX input-output neural network prediction models.
This approach provides online model adaption mechanisms to cope with time dependent and flight dependent levels
of uncertainties. The drawback of the NARX estimation model is that being an autoregressive model, its prediction is
influenced by the fault. Trying to unlink the estimation result from the fault the researcher’s tried a feed-forward non-
autoregressive MLP NN modelled which can provide a reliable multi-step ahead estimation independently of the
occurrence of the fault.
D. Modelling Pitot tube faults
The fault on the airspeed sensor is usually modeled by different authors like in Napolitano [23] as an additive bias.
Two suddenly fault scenarios commonly used in fault detection and identification practice are usually implemented: a
sudden bias (SB) failure and a slow ramp bias (SRB) failure as shown in Fig. 2 and Fig. 3 respectively as shown in
Ref. [28]. The residual signal used for SFD is defined as the difference between the measured airspeed from the ADS
and the estimated airspeed as shown in Fig. 4 and published in Ref. [28].
Fig. 2 SB failure. Fig. 3 SRB failure. Fig. 4 Residual signal.
Theoretically the residual signal should approach to zero in the fault free condition scenario, but in the real world,
due to modelling uncertainties and noise, the residual signal is different from zero. It is found in experiments that the
raw residual signal has a significant autocorrelated length that is introduced mainly by uncertainties in the low
frequency range. Since statistical detectors perform optimally when residual signals are completely uncorrelated, a
whitening filter is usually designed to remove the residual signal correlation.
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IV. Proposed Methodology
The objective of the project is to develop a new approach to perform SFDIA in case of ADS sensor failure. The
SFDIA algorithm estimates the aircraft airspeed and other aircraft parameters using information from gyroscopes and
accelerometers. A Global Positioning System - GPS, a magnetometer and a barometric altimeter are used as aiding
sensors for estimation purposes. The sensor data fusion and estimation are done by a Kalman Filter based algorithm
with the help of an accurate aircraft dynamic model acting as a virtual sensor referred to as the “Aircraft Digital Twin”.
FDI will be carried out automatically by statistical evaluation of the sensor residual signal and accommodation will be
done automatically by modulating the faulty sensors covariance, giving less weight during the estimation process. The
proposed system concept is shown in Fig. 5.
Fig. 5 Proposed airspeed estimation scheme.
A. Simulation Tools
The development of the estimator requires an aircraft flight simulation that provides information of the aircraft state
to the sensor models and two approaches are being used. The first simulation approach is used for development
purposes and consist in a Simulink® model of a Ryan Navion aircraft constructed from geometric, aerodynamic and
propulsion data published by Seckel [29] and featuring an automatic flight control to generate cruise, turn and climb
maneuvers during a 200 second flight time. The second simulation approach consist in an XPlane-11 based flight
simulation that communicates in real time via UDP port with the estimation algorithm in Simulink and it will allow to
use a human pilot to test the estimation algorithm at RMIT’s FlyThisSIM Touch Trainer© flight simulator.
B. Sensor Simulink Models
The aircraft flight simulation provides true state data to the sensor models: latitude, longitude, altitude, velocity,
angular velocity, linear accelerations, dynamic pressure, angle of attack, angle of sideslip, static pressure and static
temperature. Sensor models will add noise, bias and dynamics to the true aircraft state variable signals so its behavior
mimics the actual sensors. The following instruments were used:
• Xsens MTi G 700 Series sensor suit which contains an IMU (Gyroscopes and Accelerometers), GPS and a
Magnetometer.
• Aeroprobe Micro Air Data System V2.0 wich contains the Pitot-static probe, and provides measurements of
angle of attack and angle of Sideslip. This instrument come with an air data computer.
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• Honeywell Linear Position Transducers are used to read the position of Flaps, Ailerons, Elevator, Rudder and
Throttle.
Fig. 6 Instrumentation for real-time inflight state estimation.
The sensor signals are processed in Fit PC - IPC2 computer with an Intel core i7 processor, solid state disk of
512GB, 16 GB RAM. Fig. 6 shows the developed instrumentation suite. The instrument signals were registered during
a period of 20 minutes to compute its statistics as shown in table 2.
Table 2 Sensor Data.
Instrument
Sensor
Bias
Bias Standard
Deviation
Noise Standard
Deviation
Bandwidth
[rad/s]
Sample
Time
[s]
ADS
Pitot
0
-
0.1
2*pi*100
0.02
Alpha Vane
0
-
0.0001
2*pi*10
Beta Vane
0
-
Barometric
Altimeter
0
-
0.1
2*pi*10
Thermocouple
0
-
0.1
2*pi*0.1
IMU
Accelerometer
0
X:
0.0000166278915096521
X:
0.0166278915096521
2*pi*40
0.01
Y:
0.0000210908739381218
Y:
0.0210908739381218
Z:
0.000098348406709339
Z:
0.0098348406709339
Gyroscope
0
X:
0.00000144095816668194
X:
0.00144095816668194
Y:
0.0000015453608741964
Y:
0.0015453608741964
Z:
0.00000158938163186551
Z:
0.00158938163186551
Aiding
Sensors
Magnetometer
0
Latitude:
0
Latitude:
0.0041428199321538
2*Pi*40
0.02
0
Longitude:
0
Longitude:
0.0069532526571309
0
Altitude:
0
Altitude:
0.00947124844151009
GPS
Position
0
Horizontal:
6.45060790039193e-11
-
-
0.25
0
Vertical:
0.000764384712305632
Speed
0
Horizontal:
0.0419758512436594
0
Vertical:
0.0194447270856484
The sensor dynamics was modelled as a first order model in state space form as shown in Fig. 7. For
each sensor signal component “”, the state space dynamic model was written as:
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 (1)
 (2)
Where:
  
  
  ,  
 
  ,  
  
  ,  
  
  
Fig. 7 Sensor dynamics in state space form.
C. Air Data System
The ADS models use the dynamic pressure, angle of attack, angle of sideslip, atmospheric pressure and temperature
as input signals and it will add noise and bias were necessary in each sensor model to return the measured values of
the dynamic pressure, angle of attack, and angle of sideslip, atmospheric pressure and atmospheric temperature. Figure
8 shows the Simulink block diagram of the ADS.
Fig. 8 Simulink model of Air Data System.
The Pitot was modelled using as input signal the dynamic pressure trough a zero-order hold to convert the
continuous signal to discrete time. The sensor dynamics was modelled using the discrete state space model to which a
white noise and a bias modelled as a random walk was added to obtain the dynamic pressure measured signal. Fig. 9
shows the Simulink block diagram for this sensor.
Fig. 9 Simulink model of the Pitot sensor.
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The angle of attack vane sensor was modelled using as input signal the angle of attack to which a white noise and
a bias modelled as a random walk is added. The sensor dynamics is modelled as a first order state space model. The
signal enters a zero-order hold so a conversion from continuous system to discrete time is carried out before giving as
output the measured angle of attack. A similar model is applied to the sideslip angle vane, the barometric altimeter and
the temperature probe sensors but using as inputs signals the sideslip angle, the ambient static pressure and the ambient
air temperature respectively. Fig. 10 shows the Simulink block diagram for these sensors.
Fig. 10 Simulink model of the angle of attack, sideslip, barometric altimeter and temperature sensors.
D. Inertial Measurement Unit (IMU)
The IMU is composed of a 3-axis accelerometers and gyroscopes with angular velocity and linear acceleration as
inputs respectively. To each signal a white noise and a bias is added, modelled as a random walk. The noisy and biased
signal of each sensor is subjected to a first-order model dynamics in state space form and a zero-order hold to convert
the continuous time signal to discrete time before it outputs the measured acceleration and angular velocity. True
accelerometer and gyroscope bias signals are taken directly from the random walk. Figures 11 and 12 show the IMU
Simulink© block diagram and each sensor model respectively.
Fig. 11 IMU Simulink model.
Fig. 12 Accelerometers and Gyroscopes Simulink model.
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E. Magnetometer
The magnetometer was modelled using latitude, longitude, altitude and 
 as inputs and returning the Earth’s
magnetic field vector in the aircraft position and its true bias. The Simulink model was constructed using a Matlab
embedded function block that runs the wrldmagm function. White noise and a bias modelled as random walks are
added to the wrldmagm output signal. Finally, the noisy and biased signal passes thru a first order state space model to
mimic its dynamics and a zero-order hold to convert from continuous to discrete time. Figure 13 and Fig. 14 shows the
magnetometer Simulink© block diagram with the embedded Matlab function and the sensor model respectively.
Fig. 13 Magnetometer Simulink model – World Magnetic Model embedded function.
Fig. 14 Magnetometer Simulink model.
F. Global Positioning System (GPS)
The GPS model takes the simulation values of latitude, longitude, altitude and velocity as inputs. A bias modelled
as a random walk that passes through an integrator is added to each position component. A zero-order hold and a unit
delay is applied to the biased signal before the output of the GPS measured position. Figures 15 and 16 show the GPS
position Simulink© block diagram and its sensor model respectively.
Fig. 15 GPS Simulink model (position). Fig. 16 GPS Simulink model (position).
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The GPS velocity is modelled by adding a bias to each component of the simulation velocity. Then the biased
velocity signal is passes through a zero-order hold and a unit delay before giving the GPS measured velocity as output.
Figures 17 and 18 show the GPS velocity Simulink© block diagram and its sensor model respectively.
Fig. 17 GPS Simulink model (velocity). Fig. 18 GPS Simulink model (velocity).
V. Navigation System Extended Kalman Filter
The navigation system fuses sensor information from the IMU (gyroscopes and accelerometers), global positioning
system GPS, a 3-axis magnetometer and a barometric altimeter in a framework of Extended Kalman Filter with
sequential measurement update (SMU-EKF). In this estimation method, the sensor measurements can be easily fused
together regardless of the number of sensors, sensor update rates, and sensor data dimensions as stated and well
documented by Oh and Johnson [30].
Fig. 19 Navigation System Extended Kalman Filter.
The core sensor in the estimation algorithm is the IMU, however to increase the accuracy of the estimation a GPS,
a 3-axis magnetometer and a barometric altimeter are used as aiding sensors. The filter´s estimated state includes the
aircraft position, velocity, attitude, accelerometer bias and gyroscope bias. The IMU provides information of the
measured linear acceleration 
 and measured angular velocity
. The navigation EKF algorithm estimates the IMU
sensor bias to correct each measured signal and obtain the unbiased aircraft’s linear acceleration  and angular
velocity. The aircraft’s acceleration has to be transformed from the body axis to the navigation frame using the
direction cosine matrix
 to obtain. Since  is a specific force, gravity must be added to obtain the aircraft
acceleration in the navigation frame. By integrating twice, the aircraft speed and position  in the navigation
frame are obtained. As shown in fig. 19,  is used in conjunction with the world gravitation model to compute the
gravity vector. The aircraft attitude  is obtained by integration of the attitude rate  which is computed when the
angular velocity feeds the quaternion kinematical equations.
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Figure 20 shows the aircraft velocity estimation results. The aircraft start flying to the north and at 20 second flight
time the aircraft turns to the east 45 degrees and continue level flight. At 120 seconds of flight time the aircraft start
climbing until 180 seconds of flight time where it levels and start cruise flight. The estimated velocity follows the true
velocity accurately during all aircraft maneuvers. The estimated downward component of the aircraft velocity deviates
in one m/s during climb, in the rest maneuvers the airspeed components deviate in 0.15 m/s.
Fig. 20 Aircraft velocity estimation.
Figure 21 shows the aircraft attitude estimation. The estimation accurately follows the aircraft attitude true value
in all maneuvers, particularly in roll and yaw. The pitch estimation accurately follows the true value. At the beginning
of the climb there is a deviation from the estimation of one degree and at the end of the climb when the aircraft is
leveling for cruise there is a deviation of two degrees, however in both cases the estimation in pitch converges to the
true value in 20 seconds.
Fig. 21 Aircraft attitude estimation.
true aircraft velocity
EKF estimation
true aircraft attitude
EKF estimation
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Figure 22 shows the aircraft position estimation. The estimated altitude at the beginning of the flight reaches a
deviation of 100 meters from the true altitude value. The estimated altitude starts to converge at 40 seconds of flight
and it reaches a good accuracy during the climb. This behavior can be caused by the low sampling time of the GPS
used. A second reason is that this simulation was performed without including the barometric altimeter as an aiding
sensor. In contrast the latitude and longitude estimation is very accurate, the deviations are in the order of degrees.
Fig. 22 Aircraft position estimation – Latitude, Longitude, and Altitude.
This simulation was repeated three times by varying the sensors bias and noise parameters without noticing an
effect on the estimation accuracy.
VI. Current research on EKF navigation filter
The estimation results described in the previous section were computed without the implementation of the aircraft
digital twin. Current research efforts are focused on the integration of the aircraft digital twin with the estimation
algorithm described above. Figure 23 shows the integrated navigation system with the aircraft digital twin.
Fig. 23 Proposed estimation filter.
true aircraft position
EKF estimation
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The estimation algorithm described in previous section provide accurate information of  and. This values
will pass through a first-order filter to simulate its dynamics. In the case of the value of its derivative can be
extracted. These values can be used together with the propulsion force  and moment, the aircraft’s controls,
inertia matrix, mass  and CG location to feed the equations of motion (3) and (4) to obtain the measured aircraft’s
aerodynamic force  and moment
.

 (3)
 (4)
The values of  and 
 will be used for two tasks. The first task will be to feed a second Kalman based estimation
algorithm in conjunction with the attitude estimated in the navigation EKF filter and the measured values of airspeed,
angle of attack and sideslip from the ADS. The second task will be to train the aircraft digital twin model that will act
as a virtual sensor and that it will also provide virtual values of  and 
 to the second EKF, aiding in the estimation
of the airspeed, angle of attack, angle of sideslip and  in the case of an ADS failure.
VI. Conclusion
This paper discusses different methods to estimate the aircraft airspeed and other state variables in case of a Pitot
tube failure. The EKF navigation filter with sequential measurement update has shown to be a promising tool in the
estimation of the airspeed, attitude and position with enough accuracy and low computational effort. The addition of
adding sensors like the barometric altimeter to the estimation and the digital twin virtual sensor will increase the
accuracy of the estimation filter especially in the estimation of the downward component of the velocity and the
altitude. Higher GPS sample rates are desirable to decrease the time of the altitude estimation convergence. In addition
a parametric study on the EKF estimation performance must be carried out varying the sensor parameters and noise.
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