An innovative calibration method for the wind speed measurement using
a boom-mounted Rosemount model 858 AJ air velocity probe is introduced. The
method is demonstrated for a sensor system installed on a medium-size
research aircraft which is used for measurements in the atmospheric boundary
layer. The method encounters a series of coordinated flight manoeuvres to
directly estimate the aerodynamic influences on the probe and to calculate
the measurement uncertainties. The introduction of a differential Global
Positioning System (DGPS) combined with a high-accuracy inertial reference
system (IRS) has brought major advances to airborne measurement techniques.
The exact determination of geometrical height allows the use of the pressure
signal as an independent parameter. Furthermore, the exact height information
and the stepwise calibration process lead to maximum accuracy. The results
show a measurement uncertainty for the aerodynamic influence of the dynamic
and static pressures of 0.1

The three-dimensional (3-D) wind vector from an aircraft is measured as the
difference between the ground speed (

Traditionally the basic calibration starts with the determination of the
static pressure error

This new technology is available for a meteorological sensor package on
a Cessna Grand Caravan 208B (Caravan). The IRS is installed within the cabin,
while the gust probe is mounted on a 2 m boom under the left wing of the
aircraft. We describe the calibration of this system as an example of how to
fulfill the entire calibration procedure in order to calculate the 3-D wind.
Details about the wind calculation on an aircraft are described in the
following section including a very robust method for how the angular
difference between the gust probe and the IRS can be estimated and corrected.
In Sect.

To calculate the 3-D wind vector (

While the wind and the

The principle of the wind triangle is visualised for the two-dimensional case
in Fig.

In this idealised case the nose of the aircraft always points in the
direction of the airflow (i.e. along the

Similar to

The attack and sideslip angles are often measured with a gust probe, which
might have a significant tilt relative to the aircraft CS. Also, for the IRS
small deviations from the aircraft CS will be unavoidable, even though it is
usually carefully aligned with the aircraft (e.g. the seat rail in the cabin
can be the reference).

The beta-offset (

Starting with an appropriate initial guess for

The partial derivatives in the equation can be directly calculated from the
third component of the wind equation

The results are used to calculate the correct offset angles

These values are needed to calculate the correct flow angles and finally also the correct 3-D wind signal.

In the programming code the method requires several steps: to start the
procedure, the vertical wind (

It is important that the calculation is performed for the entire flight,
which has to be long enough and must include several turns to get reliable
results. A bias in the correction values is also possible when the aircraft
flies systematically in updraft or downdraft regions. Such biases will be
discovered easily by comparing the result with previous flights, which is
a necessary step in the quality control. The results of this calculation for
more than 800 research flights with a Dassault Falcon20 since 2001 are
displayed in Fig.

It is not possible to reach a similar accuracy for the flow angles through a direct measurement of the nose boom and IRS alignment on the ground. Additionally to the technical difficulties, no ground-based procedure is available to account for the aero-dynamical effects (e.g. compression, flow distortion) significantly influencing the result as well.

Results of the flow angle correction for 803 flights with the DLR
Falcon20 research aircraft after 2001. The correction for the attack angle
offset (

The research aircraft used for this study is a modified Cessna Grand Caravan
208B (see Fig.

Cessna Grand Caravan 208B with meteorological sensor package (METPOD) mounted under the left wing.

Key properties of the research aircraft.

The basic meteorological measurement equipment in the research aircraft
consists of three major elements: (i) the METPOD containing the main sensors
for pressure, temperature, humidity and wind measurement, (ii) the
AEROcontrol from IGI systems (IGI), which is a combined DGPS and IRS system
for high-accuracy measurement of the aircraft position and attitude

List of the main hardware components included in the three major parts of the meteorological sensor system on the Caravan.

The nose boom is tilted downward
about 4

The regular calibration of all the components preserves the quality of the
various sensors. The calibration of the IGI is performed by the manufacturer,
while the calibration of the pressure, temperature and humidity sensors is
performed in-house with test equipment which is traceable to national
standards. A list of the involved quantities with their relevant properties
is shown in Table

List of the main measurement parameters included in the
meteorological sensor package on the Caravan. The frequency describes the
rate of recording after the appropriate filtering and

The first calibration step of the temperature sensors is realised in
a stirred fluid bath with a precision reference sensor (Heraeus PW-EZ 100
PRT). Including the second step – the calibration of the signal path – the
measurement uncertainty of the temperature sensors is calculated to be

The humidity has a weak influence on the air density and hence also on the

The contributors for the 3-D wind calculation, temperature and humidity are
recorded with at least 100

The measurement of the

The calibration process starts with the determination of the static source
error (

List of the calibration flights performed for the static and dynamic
calibrations of the Caravan measurement system. Four tower-flyby (TFB) and
four racetrack (RTR) flights were conducted to parametrise the static
pressure error (

The gravity (

Results of the pitot-static calibration: deviation of the static
source error (

The performance of the 5HP has been thoroughly tested and characterised by
the manufacturer in the laboratory and in the wind tunnel

Under stable horizontal flight conditions the attack angle (

The expected next step would be the calibration of the sideslip angle

A similar calibration procedure can be realised for the

The

The correlation of

Results of the flow angle correction for 43 flights with the Caravan
system after 2011. The correction for the attack angle offset shows
significantly less scatter than for the sideslip angle. While the measurement
system on the Falcon20 (see Fig.

Results of the horizontal wind calculation during harmonic yaw
oscillation.

For the wind calculation of the Caravan system, the flow angle offsets

Applying the steps in Sect.

The harmonic yaw oscillation manoeuvre is performed during all four racetrack
test flights listed in Table

Results of the vertical wind calculation during harmonic pitch
oscillation. The sinusoidal signal can clearly be seen in the vertical
velocity of the aircraft, while it vanishes completely in the vertical wind
component. The criterion for an accurate calibration is that the residual
error of the vertical wind is less than 10

A similar test is performed for the vertical wind component. The pilot
induces a harmonic pitch oscillation via pulling and pushing the elevator.
This manoeuvre is easier to realise than the yaw oscillation, but as before
it is important to keep direction and altitude constant. Figure

For turbulence measurements the data acquisition system logs all relevant
parameters with 100

Power spectra of the three wind components in the aircraft
coordinate system. The results of the vertical wind component (

Above this frequency the attenuation of the
fluctuation due to dampening effects within the tubes becomes visible. No
white noise contribution can be detected, which would counteract this decay
in the power spectrum. Also, the vibrations of the nose boom influence the
power spectra, where the major impact is expected in the vertical and
cross-wind directions due to the eigenfrequency of the 2 m long boom.
A ground vibration test conducted in 2004 for certification purposes
determined the strongest vibrations of the boom at 17.3 Hz, but also at
12.8, 22.5, 23.8 and 30.6 Hz an oscillation of the boom and the instrument
container were detected. These frequencies are plotted with blue dashed lines
in Fig.

In the previous sections we derived the measurement uncertainties of the
various parameters which are needed for the wind calculation. The respective
results are summarised in Table

In this paper we demonstrate a simple, effective and robust alternative to
these methods, which yields a precise result even for very complex data
processing schemes

The method benefits from the basic properties of a white noise signal: (i) the mean value of the added signal is zero; that is, the mean value of the input parameters is left unchanged. (ii) The white noise time series is represented by a Gaussian data distribution which is in accordance with the classical error model. (iii) White noise data points are statistically independent of each other, which allows for an easy identification of the white noise contribution to a time series by means of autocovariance.

The calculation of the error propagation with this method is realised by the
following four steps.

The original data set is processed with the existing algorithms. The calculated results are analysed with respect to their “natural” white noise contributions caused by the sensors themselves or the data acquisition. It is interesting to note that for the measurement system discussed in the current paper no white noise is visible in the raw data.

An artificial white noise signal is added to all the original data time series (in our case: position and attitude, other avionic data such as ADC pressure or ADC temperature and all pressure, flow angles, temperature or humidity signals of the METPOD). The amplitude of this signal represents the size of the error for the respective data, while a specific initial value of random numbers (i.e. a software-specific “seed value” in a pseudorandom number algorithm) for each parameter ensures that no correlation occurs between the different white noise signals. However, in some cases a correlation between different parameters does actually exist. One example is the uncertainty in the static source correction of the static and dynamic pressure. In this case one can use identical seed values but different signs for these input parameters.

The modified data are processed again using the same algorithms as before.

The calculated data are then analysed for their white noise contribution by means of autocovariance. This analysis is done for a short time interval with a sufficient number of data points for statistical reasons. A comparison of these results with the original data set directly yields the error contribution to the specific input parameters.

Error analysis for the calculated data caused by measurement
uncertainties of the input data for the static temperature. The example in

Figure

The advantages of the presented error propagation calculation are obvious:

The method is extremely easy to establish since it concerns only the manipulation of input data and the analysis of processed data, no modification of the data processing algorithms is necessary.

The method works for any kind of data processing algorithm.

Changes in the data processing software do not cause any additional work.

The method does not include any simplifications and can handle even very nonlinear data dependencies.

The method allows one to study the individual contributions from single sources to the final error by switching all other error signals off.

The proposed solution can handle any kind of error (statistical as well as systematic).

The error calculation works very fast and it delivers precise results for every phase of a flight. The measurement uncertainties for flight segments with different meteorological conditions or flight parameters (like aircraft height and speed, mean wind and relative direction to the aircraft) can be estimated separately.

The method can handle correlated systematic errors by using identical seed values.

However, for statistical reasons the presented error calculation requires a certain time window to calculate a representative autocovariance function. This means that the error analysis for non-stable flight conditions like turns or level changes is not possible.

List of the calculated measurement uncertainties of the main derived parameters. Details to the method and the calculation of the presented results are given in the text.

In the example of Fig.

The measurement uncertainties of the humidity in Table

The calibration error of the flow angles has different sources, the sensor
calibration errors and the in-flight calibration errors, as described in
Sect.

For high-quality measurements of the 3-D wind with an airborne system, it is
crucial to determine the dynamic influences on the measurement equipment
during flight. We introduced a method to correct these influences step by
step and tested it for the new meteorological sensor system on a Cessna Grand
Caravan which is adapted for investigations in the atmospheric boundary
layer. The measurement system includes a meteorological sensor package for
temperature, humidity and wind, high accuracy position and attitude
determination inside the cabin, and a data acquisition system with an
integrated time server. The bases for the successful calibration of the
system were a well-designed sensor suite, valid laboratory calibrations that
are traceable to national standards for all the involved sensors, the
opportunity to perform a series of test flights during favourable weather
situations, and an appropriate software package. This software allows one to
perform an automatic and manual quality check on the flight data right after
each flight, including the calculation of the flow angle offset
(

The correction routines for the temperature and humidity are independent of
the specific aircraft, but for the different pressure signals of the gust
probe an aircraft has to be tested individually. Four different basic
manoeuvres were needed to allow for a stepwise parametrisation of the
different dynamic influences on the pressure devices: (i) the static pressure
error was calculated from the tower-flyby manoeuvre and with this the static
and dynamic pressures were corrected. (ii) The racetrack manoeuvre was
performed to check on possible height dependencies of the static pressure
error. The test points from these two flight tests were also evaluated for
the correction of the attack angle (

A high accuracy of the attitude angles and especially of the aircraft
altitude was the key to the great precision of the calibration. The static
pressure error ranges from 1 to 3

We calculated the error propagation with a new method. The measurement
uncertainty is added to the raw data as an artificial white noise signal. The
effect can easily be detected at the end of the calculation procedure with an
autocovariance analysis. Especially for complex data processing routines with
a big number of involved parameters and nonlinear formulations such as
humidity and wind calculation, this method displays its strength. We
calculated an overall measurement uncertainty for the temperature of

We have demonstrated that a vast test program is necessary to calibrate an airborne measurement system. The new system implemented on the Cessna Grand Caravan proved to be a reliable system for high-frequency measurements in the atmospheric boundary layer. The objective determination of the measurement uncertainties builds the basis for any scientific usage of the meteorological data.

For the calculation of the flow angle offsets described in
Sect.

It is the only term in Eq. (

To fulfill the requirement for Eq. (

Providing a research aircraft for meteorological purposes demands the professional support and commitment of the entire team at DLR flight experiments. Therefore, we want to thank the pilots, flight test engineers, technicians and members of operations for their assistance. We thank Ulrich Schumann for useful discussions. Edited by: T. F. Hanisco