Attitude and Heading Reference Systems Questions and Answers

Answer: A

Correct answer: The magnetometer was disturbed

The symptom localises the fault precisely: heading wanders while pitch and roll stay steady. Heading is the one output that depends on the magnetometer, and pitch and roll come from the gyros and accelerometers, so a disturbance confined to heading points to the magnetic sensor. A large magnetic anomaly distorts the local field, and the recovery on leaving the area confirms it.

A gyro failure would corrupt attitude as well, since the same triad feeds all three angles. Accelerometer saturation would show in pitch and roll, and a lost alignment would not recover by itself.

Answer: B

Correct answer: Position error grows with time squared

The proposal is unsound because position would have to come from integrating specific force twice, and a constant accelerometer bias then produces a position error growing as \( t^2 \). A bias of only \( 0.001\ \mathrm{m/s^2} \) gives \( 1.8 \) m after a minute, but about \( 6.5 \) km after an hour - and a long overwater flight offers no external fix to bound it.

The system computes heading perfectly well, and magnetometers work over water; the gyros do not overheat. The limitation is not a defect but a deliberate boundary: an attitude system stops at attitude and heading because its sensors cannot support navigation unaided.

Answer: C

Correct answer: Poor coning compensation

The signature is diagnostic: drift appears only under sustained high frequency vibration and is absent otherwise. That is coning - simultaneous oscillation about two axes producing a systematic attitude drift, because finite rotations do not commute and a naive integration cannot recover the true attitude change over a cycle.

The compensation term must be computed at a rate well above the vibration frequencies; if it is inadequate or the loop too slow, the error appears exactly when vibration is present. An accelerometer bias or wrong variation would produce a steady error regardless of vibration, and a failed magnetometer would affect heading only.

Answer: D

Correct answer: specific force

An accelerometer measures specific force - the non-gravitational force per unit mass on its proof mass, which is the sum of the aircraft's acceleration and the reaction to gravity. A stationary instrument with its axis vertical therefore reads about \( 9.81\ \mathrm{m/s^2} \), not zero, because the case is pushing the proof mass upward against gravity.

This is why the two contributions cannot be separated by the sensor alone, and why the vertical reference it provides is trustworthy only in unaccelerated flight. Angular rate is what a gyro measures, and magnetic field what a magnetometer measures.

Answer: A

Correct answer: strapdown

In a strapdown system the sensors are bolted rigidly to the airframe and measure in body axes, so the transformation from body axes to the navigation frame - which a gimballed system performed mechanically by keeping the platform level - is computed in software at high rate.

Removing the gimbals removes bearings, torque motors and slip rings, so the unit is smaller, cheaper and free of mechanical wear. The cost is computational: the attitude must be integrated hundreds of times a second with coning and sculling compensation, which is why the architecture only became practical once fast processors were available.

Answer: B

Correct answer: linearly

Attitude is obtained by integrating angular rate, and integrating a constant gives a term proportional to time. A constant gyro bias \( b \) therefore produces an attitude error \( bt \), growing linearly.

The contrast with the other mechanisms is what makes each identifiable. Angle random walk, from integrated white noise, grows as \( \sqrt{t} \); an accelerometer bias in a position solution, being integrated twice, grows as \( t^2 \). Because the growth laws differ, a filter can estimate the bias separately from the noise - which is exactly what a Kalman filter does when it carries the biases as states.

Answer: C

Correct answer: Gyro compassing

Gyro compassing finds true heading by sensing the horizontal component of the earth's rotation, which points to true north. At latitude \( \phi \) that component is \( 15\cos\phi \) degrees per hour, so at 40 degrees it is about \( 11.5 \) degrees per hour - a very small signal that requires navigation-grade gyros to resolve, and one that shrinks towards the poles as \( \cos\phi \) falls.

The advantage over magnetic sensing is that it gives true heading directly, with no variation to apply and no vulnerability to local magnetic anomalies. Levelling establishes pitch and roll, and coning compensation is an integration correction.

Answer: D

Correct answer: median

Median voting sorts the three outputs and takes the middle one, so a single deviant unit is excluded automatically however far it has strayed. This is the standard scheme for triple redundancy in attitude systems.

The median is preferred to the mean precisely because an outlier drags an average but cannot move a median past the two healthy values. Unanimity would fail whenever any unit disagreed, which defeats the purpose, and weighted or sequential schemes would require information about relative trust that the system does not have.

Answer: A

Correct answer: Accelerometer bias in position

The accelerometer bias row is the one that explains the boundary. Its error grows with the square of time, reaching 16 units in four hours against the gyro bias's 4 and random walk's 2 - because specific force must be integrated twice to reach position, so a constant offset appears as \( \tfrac{1}{2}bt^2 \).

That quadratic growth is unbounded without an external fix, which is why position is left to a navigation-grade system with far better sensors and an aiding source. Attitude needs only one integration and is held in check by the gravity and magnetic references, so ordinary sensors suffice for it.

Answer: B

Correct answer: Each sensor covers the weakness of the others

The last row states the principle of sensor fusion. The gyros are accurate over seconds to minutes but drift over hours; the accelerometers hold a good long-term vertical but are corrupted by manoeuvring; the magnetometer holds a good long-term heading but is corrupted by anomalies. Each is strong exactly where another is weak, so a filter that blends them produces a solution that is smooth in the short term and bounded in the long term.

The sensors are used simultaneously, not in rotation. They are not redundant copies to be averaged, and selecting a single best sensor would discard the information only the others carry.