Electronic Navigation Systems
• Open book, open notes, open homework (hard copy). • Use of a calculator is allowed • Provide all calculations with the answers. • Make, and write down, any necessary assumptions and use reasonable values for assumed parameters.
• The problems are equally weighted.
COMPLETE 5 OUT OF 7 QUESTIONS
Consider an airplane with the following Air Data measurements: Static Pressure: 50779 N/m2, Total Pressure: 53175 N/m2, Temperature: 260 K. The reference surface pressure at the nearest airport is 0.974×105 N/m2.
a) Calculate the aircraft’s QFE altitude
b) Calculate the aircraft’s true airspeed
VOR A is located at (0, 40 nmi) and VOR B is located at (50 nmi, 0) in a local-level Cartesian coordinate frame. An aircraft measures a bearing of 120 deg from VOR A and a bearing of 315 deg from VOR B. Find the coordinates of the aircraft.
A GPS user is located at 39.21°N Latitude, 82.23°W Longitude, and 205 m height (ellipsoidal). The GPS receiver tracks PRN 18 that has an elevation angle of 22° relative to the user. The L1 pseudorange measurement is 23516280 m, and the L2 pseudorange measurement is 23516295 m. Use the following constants: c=299792458 m/s, fL1 = 1575.42 MHz, fL2 =1227.60 MHz
a) Calculate the troposphere delay for the PRN 18 measurement
b) Calculate the ionosphere delay for the PRN 18 measurement
At a given moment in time, a GPS receiver determines the following:
inv(H’*H) = [0.4000 -0.3068 0.1068 0.2035; -0.3068 1.2733 -0.7288 -0.7649; 0.1068 -0.7288 1.0288 0.6599; 0.2035 -0.7649 0.6599 0.6573]
a) Determine PDOP b) Assuming the errors on all the satellite measurements are independent white Gaussian
noise with a standard deviation of 2 meters, determine the standard deviation of the 3-D positioning error.
A ‘pseudolite’ is a ground-based transmitter that radiates GPS signals. A major problem associated with their use is the so-called ‘near-far’ problem. Specifically, free-space loss causes a much larger variation in received signal power (as a function of changing receiver position) than for space-based transmitters. Assume a pseudolite is located at an airport and is radiating an EIRP of 1 mW. Further assume the receiver on an aircraft is connected to an isotropic antenna. Approximate the GPS L1 wavelength as 0.19 m.
a) Calculate the power received (in W) if the aircraft is 1 km from the pseudolite
b) Calculate the power received (in W) if the aircraft is 20 km from the pseudolite
c) Calculate the power variation by calculating the ratio of the two received powers in dB
The following measurements are obtained from a stationary Inertial Measurement Unit in the
aircraft body frame: 𝐴 = 1.7035 −0.8420 −9.6242
a) Calculate the aircraft roll angle in degrees (round to the nearest degree)
At some point in the middle of a flight, the INS has determined that the aircraft-to-platform transformation matrix is:
[ 0.9254 -0.3265 0.1924; 0.3368 0.9413 -0.0227; -0.1736 0.0858 0.9811]
b) Calculate the aircraft pitch and yaw angles in degrees (round to the nearest degree)
Consider a DME/P signal that is contaminated with specular multipath with a multipath-to-direct ratio of -10 dB. The DME/P interrogator uses a DAC circuit with a delay of 100 ns and attenuation of 6 dB. Assume the interrogator does not apply any RF filtering that changes the shape of the pulse.
a) What phase of multipath (relative to the direct signal) will cause a peak positive error?
b) Calculate the time delay of the multipath that will cause the peak positive error c) Calculate the peak positive error