Introduction to Flight Testing

Recent developments in MEMS have revolutionized sensor design and fabrication, making these sensors available at low cost and in small packages. Complex sensors such as gyroscopes and magnetometers can be fabricated with an extremely small form factor, allowing for them to be installed in very compact devices (see Figure 3.9). Most notably, the rapid development of MEMS has been driven by the proliferation of smartphones, which have many of the same sensors as those found on aircraft. MEMS developments have also enabled integration of these instruments into the cockpit – the modern avionics glass cockpit systems discussed in the previous section rely upon MEMS sensors for determining aircraft state. Alternatively, small external sensor packages such as smartphones, or the custom‐built unit, illustrated in Figure 3.9, can be mounted in any convenient location within the aircraft cockpit for simple installation and reasonably accurate DAQ. These comprehensive sensor suites are roughly equivalent to the AHRS that supports glass panel avionics.

Figure 3.9 Modern flight testing board with built‐in GPS, accelerometers, gyroscopes, magnetometers, and pressure transducer.

Source: Photo courtesy of Matthew H. McCrink.

The most significant deficiency of these instrumentation packages is the lack of air data measurements such as total pressure, static pressure, and OAT. Measurement of these properties requires direct access to dedicated instrumentation on the aircraft (the pitot‐static system), which is not normally possible on GA aircraft commonly accessible to students in an aircraft flight testing course. However, there are techniques (“work‐arounds”) for inferring these missing flight data. OAT changes very slowly at a given altitude, allowing it to be manually read and recorded at sparse intervals at a particular flight condition. Freestream static pressure can be measured to fairly good approximation by measuring cockpit pressure using a MEMS barometer on the DAQ device (see Gregory and McCrink 2016 for details). Total pressure (and, thus true airspeed) cannot be measured in flight without access to a pitot probe. However, using the techniques described in Chapter 8, true airspeed may be found by measuring ground speed during flight at a single test condition along three separate headings.

Key sensors in a typical external DAQ unit are a satellite navigation receiver and antenna (e.g., the GPS), 3‐axis gyroscopes, 3‐axis accelerometers, 3‐axis magnetometers, and a pressure transducer (barometer). A brief overview of each of these sensors is discussed as follows, but a much more detailed discussion is available in Titterton and Weston (2004).

3.3.1 Global Navigation Satellite System

One example of a global navigation satellite system used for determining position in 3D space (latitude, longitude, and altitude) is the GPS (for the remainder of this book, GPS will be considered synonymous with GNSS, although there are other satellite‐based navigation systems in use such as the Russian GLONASS, the European Galileo, or the Chinese BeiDou systems.). GPS signals offer very high positioning accuracy, typically resolving location to within a few meters or less. The basis for the measurement is transmission of a modulated carrier signal with a known pseudorandom code, a time stamp based on a highly stable atomic clock on board the satellite, and the precise location of the satellite in space. The GPS receiver infers the distance to each satellite being received based on the time required for the signal to traverse the distance from the satellite to the receiver (based on the ultrastable clock on each satellite). Since the position of each satellite in space is known with high accuracy and precision, and the speed of light is well known, the receiver can infer the distance to each satellite by phase aligning the pseudorandom code. The receiver then uses multilateration techniques to infer its own location in space based on these distances – the calculated distance from a particular satellite restricts the receiver location to being somewhere on a spherical shell centered on the satellite. The intersection of at least three spherical shells results in position being defined as a single point in space. Note that the clock on the receiver itself generally does not have a high degree of accuracy, so this represents an unknown in the calculation of position. Therefore, there are four unknowns in the computation: latitude, longitude, altitude, and instantaneous time, so the GPS receiver must have at least four satellites in view simultaneously in order to determine an accurate position estimate. GPS receivers can reliably report latitude and longitude with high accuracy, but altitude indications typically have much more error. In particular, smartphone‐based GPS receivers lack an external antenna and rely upon algorithms that are optimized for terrestrial applications. Thus, altitude reported by smartphone‐based GPS sensors is generally unreliable and should not be used for measurement of altitude in aircraft flight testing (see Gregory and McCrink 2016 for details). General overviews of satellite‐based navigation schemes are provided by Misra and Enge (2010) and Kaplan and Hegarty (2017).

Several key error sources limit the accuracy of GPS position estimates. These errors include propagation delays due to dispersion of the signal by the ionosphere (termed ionospheric delay), uncertainty in the time due to drift of the atomic clocks on board the satellites, and uncertainty in the location of the satellites (ephemeris error). Advanced signal processing algorithms have been introduced to correct for these errors, but the most basic correction scheme is to introduce a real‐time error correction term from a receiver at a fixed, accurately known position. These correction schemes include differential GPS (DGPS), real‐time kinematic (RTK) GPS, and the FAA's Wide Area Augmentation System (WAAS). We will provide a brief overview of each of these as follows.

Differential GPS can provide refined position and velocity histories for flight test applications (Sabatini and Palmerini 2008). A typical DGPS architecture for flight testing is shown in Figure 3.10. The system consists of a reference receiver located at a known location that has been previously surveyed, and one or more DGPS user (mobile) receivers mounted on a test aircraft. The reference receiver antenna, differential correction processing system, and datalink equipment are collectively called the reference station. Both the user receiver and the reference receiver data can be collected and stored for later processing, or sent to the desired location in real time via the datalink. DGPS is based on the principle that receivers in the same vicinity will simultaneously experience common errors on a particular satellite ranging signal. In general, mobile receivers use measurements from the reference receiver to remove the common errors. The limiting factor for DGPS is that the mobile and fixed receivers need to be in proximity to one another such that they experience the error sources in the same way and to facilitate radio communication from the fixed reference receiver to the mobile receiver on board the aircraft. Thus, DGPS is most applicable to local‐area flight operations such as takeoff and landing flight tests.

Figure 3.10 Typical differential GPS architecture.

RTK GPS is a technique similar to DGPS, but offers higher accuracy. Similar to DGPS, RTK provides a correction to the position estimate, which can be transmitted in real time to the mobile GPS receiver or stored for subsequent analysis. The correction factor is determined by measuring the distance to the satellite using a different technique from traditional GPS. Instead of relying solely on the pseudorandom code transmitted by the satellites, RTK GPS uses statistical methods to estimate the number of cycles present in the waveform between the receiver and the satellite and then multiplies the number of cycles by the wavelength (19 cm for the L1 signal) to infer range. There is some resulting error in the estimated distance, due to ambiguity in determining the correct integer number of cycles due to phase differences. The RTK technique can provide remarkable positioning accuracy, improving the position estimate to 1 cm accuracy. However, RTK GPS also requires that the mobile receiver be in the same vicinity as a fixed reference station, which limits its applicability to downrange flight tests.

In the aviation realm, an augmentation system has been recently developed in order to improve upon the baseline accuracy of the satellite‐based position measurement system and enable precision instrument approaches without requiring nearby ground‐based reference stations. The Wide Area Augmentation System is a satellite‐based augmentation system developed by the US Federal Aviation Administration that covers the majority of North America. It is based on a system of ground‐based reference stations that calculate the local difference between the GPS‐indicated position and the station's actual position (surveyed to very high accuracy). This error data, expressed as a deviation correction, is uplinked in real time to geostationary WAAS satellites at least once every five seconds, which then broadcast the correction to aircraft throughout the national airspace. WAAS GPS corrects for positioning errors predominantly resulting from ionospheric disturbances, which add phase distortion to received GPS signals. The WAAS correction is broadcast over the same frequency bands used for the baseline GPS signal, which reduces system cost and complexity. The resulting accuracy of a WAAS GPS receiver is improved to approximately 2‐m in the horizontal and vertical directions, which is an order of magnitude improvement relative to the baseline accuracy of standard GPS.

An important point to recognize when using GPS data for flight test is that the position from a GPS receiver is reported as decimal degrees for latitude and longitude, with a sign convention for positive being North of the equator and East of the prime meridian (e.g., the latitude/longitude coordinates 40.074199 ° , – 83.07968° are in North America). If relative distance is desired (say, in units of ft, m, or nautical miles), then some type of transformation is needed to convert the difference between latitude/longitude coordinate pairs into distance. This transformation is commonly done in the fields of geodesy and navigation, where a model of the Earth's shape must be assumed. Generally speaking, Earth is in the shape of an ellipsoid that bulges near the equator (relative to a perfect sphere) due to the rotation of the planet. One of the most common Earth models is the World Geodetic System 1984 ellipsoid (WGS84), which is periodically refined and revised (National Imagery and Mapping Agency 2000; Pavlis et al. 2012). WGS84 forms the basis of GPS position reporting, with latitude and longitude forming a measure of distance within the WGS84 coordinate system. However, these coordinates must be transformed to local Cartesian coordinates before distance calculations can be made for flight testing. This transformation can be done via the Universal Transverse Mercator conformal projection. This system involves the segmentation of Earth's surface into 60 zones, each measuring 6° of longitude wide. Bands of latitude measuring 8° high are sometimes used to further subdivide the zones. The transformation for each zone from WGS84 to Cartesian coordinates can be performed by methods described by Snyder (1987), and a wide array of MATLAB toolboxes are available for this purpose (e.g., see Wasmeier 2015).

3.3.2 Accelerometers

A three‐axis accelerometer provides a direct measurement of acceleration in all three directions, with the acceleration being relative to the local inertial frame of reference. Thus, an aircraft in steady level flight will have an acceleration of 9.81 m/s2 in the vertical direction (+1g), and zero acceleration in the other directions, since the local inertial frame corresponds with a freely falling object and the aircraft is accelerating upwards relative to the inertial frame. Accelerometers essentially operate as a spring‐mass‐damper system, where the applied acceleration along a particular axis will cause a displacement of the mass by an amount that depends on the properties of the system. The displacement is then measured by converting it to a voltage, and calibrating this voltage to acceleration. In MEMS devices, the spring‐mass‐damper system is often a cantilevered beam with a proof mass, where transduction of the displacement to voltage is most often done through capacitive or piezoresisitve schemes. Capacitive transduction involves a gap between the cantilevered beam and a fixed beam, which varies the capacitance of a circuit which can then modulate a measured voltage. The piezoresistive scheme involves a piezoelectric material as the spring in the system, where the voltage drop across the piezoresistor changes with the applied strain due to acceleration.

Accelerometers can be used in flight testing to detect events with sudden changes in acceleration (such as stall), measure the orientation of the aircraft relative to the ground in steady flight, indicate the bank angle in a steady turn by measuring g's in the aircraft's frame of reference, determine the period of dynamic stability phenomena such as the long‐period phugoid mode, and other applications. In principle, the measured acceleration can be integrated in order to infer a change in velocity, although the noise in the signal often precludes this in practice. Further, the measured accelerations are integrated into the flight data computer for determining vehicle state in modern avionics systems.

3.3.3 Gyroscopes

Building upon our earlier discussion of gyroscopic principles for traditional flight instruments, we will now consider how they are used for modern avionics systems and instrumentation. Rate gyros used in modern glass panel avionics and DAQ systems are based on MEMS‐fabricated gyros. These gyros sense the rate of angular motion, rather than directly measuring the angle itself. A three‐axis gyro will have three independent rate gyros mounted along mutually perpendicular planes. One example of a MEMS rate gyro is based on the principle of sensing Coriolis acceleration. In this configuration, a proof mass is mounted on springs and oscillated in a direction perpendicular to the measured axis of rotation. As the proof mass oscillates, its radial distance from the aircraft's center of rotation also changes, leading to time‐varying tangential velocity that subjects the mass to varying amounts of Coriolis acceleration while the body rotates. This leads to a time‐varying reaction force in a direction perpendicular to the axis of rotation and the direction of oscillation of the proof mass. This reaction force is applied across springs in the lateral direction, which translate the reaction force into a linear motion that is sensed by capacitive elements (interdigitated fingers).

Since rate gyros measure the angular speed – pitch rate, roll rate, or yaw rate – rather than directly measuring the respective angles, the rotation rates must be integrated with respect to time in order to determine the pitch, roll, or yaw angles. Through the integration process, any noise present in the signals accumulates and leads to growing error in time.

3.3.4 Magnetometers

A three‐axis magnetometer can be used to sense the aircraft's magnetic heading, much in the same way that a compass provides magnetic heading by always pointing toward magnetic north. On a MEMS‐based device, each of the three magnetometers is mounted mutually perpendicular with a reasonably high degree of precision. Each magnetometer senses the local magnetic field via the Hall effect, whereby a voltage difference is induced across an electrical conductor in a direction transverse to both an applied magnetic field and an electric current flowing through the device. For sensing the aircraft's heading, each axis of the magnetometer responds to Earth's magnetic field lines, which are aligned between the magnetic North and South poles. Since the North and South poles are not aligned with the physical poles, there is a difference between magnetic north and true north (referred to as magnetic declination, or variation). The amount of magnetic variation depends on geographic location and time, with a time scale of years (National Centers for Environmental Information 2019).

When using a magnetometer in an aircraft, the sensing of the Earth's magnetic field can be strongly influenced by nearby magnetic fields and ferromagnetic materials, through an effect known as magnetic deviation. Thus, an aircraft's compass must be calibrated to account for these error sources – this is typically done by positioning the aircraft along various points of the compass (typically referenced to a so‐called “compass rose” painted on the ramp with 30° heading intervals) and noting the difference between the compass reading and the actual magnetic bearing. The two error sources are referred to as hard and soft iron distortions. Hard iron distortions are due to the presence of nearby magnetic fields, which could be from magnets or electronic circuits, and result in a constant bias offset on the measured magnetic field. Soft iron distortions are due to the presence of nearby ferromagnetic materials (such as the engine block), and result in skewing of the measurement or an offset whose magnitude is heading‐dependent. These error sources can be nontrivial when using a three‐axis magnetometer on board an aircraft. Thus, a magnetometer that is part of an external DAQ system should be calibrated before flight to remove these effects (the magnetometers built into the aircraft's built‐in avionics have already been calibrated).

Fortunately, a compass rose is not required for calibration of a MEMS magnetometer, and the required calibration process is fairly straightforward. Before takeoff, with all electronics operating, the DAQ unit in place, and the magnetometer acquiring data, the aircraft should be swung through two complete 360° circles (a total heading change of 720°). When plotted in time, data from the x‐ and y ‐ axes of the magnetometer from this maneuver will form an ellipse. If the magnetometer was not subject to any error sources, the acquired data should form a constant radius circle centered on the origin. However, the error sources result in an elliptical pattern, where the offset of the ellipse from the origin (0, 0) depends on the error from hard iron distortions, and the eccentricity of the ellipse depends on the magnitude of error from soft iron distortions. A mapping can be determined to take the acquired data and transform it to a circle. This can be done by the following equation,

(3.3)

where xnc, ync, and znc are the noncalibrated data straight from the magnetometer; the B vector contains the bias errors due to hard iron distortions, the M matrix corrects for the soft iron distortions; and xc, yc, and zc are the calibrated data. Values of M and B are determined from a least‐squares fit to the data and subsequently applied to all magnetometer data acquired during the flight test.

3.3.5 Barometer

A MEMS pressure transducer can be used as a barometer for an indication of pressure altitude. MEMS barometers are typically piezoresistive devices, where the deformation of a thin silicon diaphragm is measured through piezoresitive principles. The silicon diaphragm is doped at certain locations, thus locally altering the electrical conductivity and imparting resistor‐like properties. As the diaphragm deflects in response to an imposed pressure, the resistances of the doped regions change. If these piezoresistors are connected to a Wheatsone bridge, the change in resistance is converted to a change in voltage that can be easily measured. The calibration of these sensors is typically temperature dependent, so MEMS barometers often include an integrated temperature sensor for compensation.

The pressure reading of a MEMS barometer can be converted to altitude via hydrostatics. Necessary input values are the local barometric pressure reading and/or field elevation, along with OAT. All of the necessary theory for this conversion is detailed in Chapter 2 on the definition of the standard atmosphere. The pressure reading (and indicated altitude) of MEMS barometers used in some external DAQ devices can have a nonnegligible bias error (offset) in the reading. This is a minor concern, however, since it is a straightforward matter to determine the offset when the aircraft is on the ground, where a pressure measurement is made and field elevation and/or local barometric pressure are known. For flight testing, the other predominant source of error is a difference between cabin pressure (where the DAQ unit is typically mounted for student flight testing) and freestream static pressure. Gregory and McCrink (2016) evaluated the magnitude of this error for flight in a Diamond DA40 and found that cabin pressure was approximately 140 Pa higher than freestream static pressure at cruise conditions. For this particular aircraft, ram air effects that slightly pressurize the aircraft cabin in flight are the likely cause of the discrepancy. Despite these error sources, altitude indication from cabin pressure tends to be more accurate than GPS‐reported altitude.

3.3.6 Fusion of Sensor Data Streams

As noted in the previous subsections, each individual sensor has some limitations to its utility due to various sources of noise or other errors such as temperature drift. This makes direct inference of vehicle state from one set of sensors problematic (e.g., integrating the signals from the rate gyros alone to determine vehicle orientation would introduce substantial errors). Optimal performance, however, is obtained when different data streams can be fused together in a manner such that the collected set provides a much more accurate and reliable estimate of vehicle state. One very common method for fusing together data streams is Kalman filtering. The Kalman filter is an algorithm that takes multiple time records of sensor data and produces estimates of vehicle state with improved accuracy compared to the estimate if only a single data stream were available. In essence, it gives a solution or prediction of vehicle state with an accuracy that is much improved over the estimate provided by any subset of sensors. The basis of the Kalman filter is described as follows.

First, we need a precise definition of the vehicle's state. It is the set of data that completely describes the vehicle's position and orientation, along with the rates of change of position and orientation. Thus, the position estimate and its derivatives would be the spatial location of the vehicle, its velocity, and its acceleration in some frame of reference. The orientation estimate is the vehicle's pitch, yaw, and roll angles, along with rates and accelerations of those same angles. These estimates of position and orientation have some uncertainty associated with them, which the Kalman filter assumes to be random and Gaussian distributed.

At each time step, a prediction of the vehicle's state at the next time step is formulated based on knowledge of the current state, an estimate of the uncertainty of the knowledge of that state, and a model based on the vehicle dynamics. When that next time step arrives, the prediction of the vehicle state is compared with measured data of the vehicle's state (along with the associated uncertainty in both the prediction and the measurements of the state). A refined estimate of the vehicle's state is generated by a weighted sum of the predicted state and measured state. Since the Kalman filter relies on both measurements of the vehicle state and model predictions of the vehicle state, the accuracy of the resulting state estimate is dramatically improved.