Attitude and Heading Reference Systems Questions and Answers

Answer: C

Correct answer: The gyros

In a complementary filter the gyro signal is high-pass filtered and the accelerometer or magnetometer reference low-pass filtered, and the two are summed. Motion faster than the crossover - here \( 0.1 \) Hz - is therefore taken principally from the gyros, which respond quickly and are quiet over short intervals.

The slow behaviour comes from the reference sensors, which are noisy and disturbed by manoeuvring but do not drift. The crossover is thus a statement about which sensor is trusted at which timescale, and choosing it is the design compromise a Kalman filter replaces with an adaptive weighting.

Answer: D

Correct answer: 120 degrees

Integrating a constant rate is simply multiplication:

\[ \Delta\psi = 3\ \mathrm{deg/s} \times 40\ \mathrm{s} = 120\ \mathrm{degrees} \]

Three degrees per second is the standard rate-one turn, which completes \( 360 \) degrees in two minutes, so forty seconds gives a third of a circle - a useful check on the arithmetic. The distractor \( 13.3 \) comes from dividing rather than multiplying.

Answer: A

Correct answer: 0.002 degrees per second

Removing the bias to within 10 per cent leaves 10 per cent of it behind:

\[ b_{res} = 0.10 \times 0.02 = 0.002\ \mathrm{deg/s} \]

The distractor \( 0.018 \) is the amount removed rather than the amount remaining. The residual still matters: integrated for five minutes it gives \( 0.6 \) degrees of attitude error, which is why bias estimation is a continuous process in the filter rather than a one-off correction at start-up.

Answer: B

Correct answer: Level and unaccelerated

A reading of \( 0, 0, -9.81\ \mathrm{m/s^2} \) means the entire specific force is along the body \( z \) axis at exactly one \( g \), with nothing along the longitudinal or lateral axes. The gravity vector is therefore aligned with the aircraft's vertical axis and no additional specific force is present: the aircraft is wings-level, pitch-level and unaccelerated.

A banked turn would put a component on the lateral axis, forward acceleration a component on the longitudinal axis. Note that a steady climb at constant speed would give almost the same reading, differing only by the pitch attitude - the reason the vertical reference must be used together with the gyros rather than alone.

Answer: C

Correct answer: Both Statement I and Statement II are correct

Both statements are correct, and the second explains the first. An attitude and heading reference system outputs pitch, roll and heading but not position, and the reason is the error growth: obtaining position requires integrating specific force twice, and a constant accelerometer bias then produces a position error growing as \( t^2 \).

A bias of \( 0.001\ \mathrm{m/s^2} \) gives \( 1.8 \) m in one minute and over six hundred metres in an hour. Attitude, by contrast, involves only a single integration and is bounded by the gravity and magnetic references, which is why the same sensors can support attitude but not navigation.

Answer: D

Correct answer: Both Statement I and Statement II are correct

Both statements are correct and the second is the reason for the first. An accelerometer measures specific force and cannot distinguish the reaction to gravity from the aircraft's own acceleration, since both appear identically at the proof mass - the equivalence principle in instrument form.

So the triad gives a usable vertical reference only when the aircraft is unaccelerated; under acceleration the apparent vertical tilts by \( \arctan(a/g) \), which for \( 2\ \mathrm{m/s^2} \) is over eleven degrees. The filter therefore trusts the accelerometers as a slow correction and leans on the gyros through manoeuvres.

Answer: A

Correct answer: Both Statement I and Statement II are correct

Both statements are correct and the second explains the first. Gravity is vertical, so the accelerometers can fix pitch and roll but provide no reference at all in the horizontal plane. The gyros can measure changes of heading, but integration alone drifts and needs an absolute reference to bound it.

A magnetometer supplies exactly that: the direction of the earth's magnetic field defines magnetic north, and applying the local variation gives true heading. High-grade systems can instead find true north by gyro compassing on the horizontal component of earth rate, but that requires gyros far better than those in a typical unit.

Answer: B

Correct answer: Statement I is incorrect but Statement II is correct

Statement I is incorrect: the two errors grow quite differently. Bias produces attitude error growing linearly with time, whereas angle random walk produces error growing as the square root of time.

Statement II is correct and is the reason for that difference: bias is a constant offset, which integrates to \( bt \), while random walk comes from integrating white noise, whose independent increments accumulate as \( \sqrt{t} \). The distinct growth laws are what allow a filter to separate the two, and they explain why bias dominates over long intervals while noise dominates over very short ones.

Answer: C

Correct answer: Both Statement I and Statement II are correct

Both statements are correct and the second explains the first. Removing the gimbals leaves the sensors fixed to the airframe, so they measure in body axes; the transformation from body axes to the navigation frame, which the gimbals used to perform mechanically, must then be computed in software at high rate.

That computation - integrating the attitude quaternion or direction cosine matrix hundreds of times a second, with coning and sculling compensation - was beyond affordable processors until the 1970s and 1980s, which is why strapdown systems entered service long after the sensors themselves existed.

Answer: D

Correct answer: Both Statement I and Statement II are correct

Both statements are correct, and together they explain why three units are fitted rather than two. With two units a comparator can show that the outputs disagree, but nothing in the data says which of them is at fault, so both must be treated as suspect.

With three, the faulty unit is the one that disagrees with both of the others, and median voting excludes it automatically while the system continues on the two that agree. This is the general principle of fault detection versus fault isolation: detecting an inconsistency needs two sources, isolating the culprit needs three.