Lesson test: Estimating attitude by fusing the sensors

1.[2p]
In the complementary filter $θ \leftarrow α (θ + ω Δ t) + (1 - α) θ_{acc}$ , the term multiplied by $α$ is

the integrated gyroscope, which is fast but would drift on its own

Correct

the accelerometer's tilt, which corrects drift

The answer is: the integrated gyroscope, which is fast but would drift on its own

the magnetometer heading

The answer is: the integrated gyroscope, which is fast but would drift on its own

the motor mixer output

The answer is: the integrated gyroscope, which is fast but would drift on its own

2.[2p]
The small $(1 - α)$ accelerometer term in the filter is there to

nudge the estimate slowly toward true level and cancel the gyro's drift

Correct

speed up the response to a quick flick

The answer is: nudge the estimate slowly toward true level and cancel the gyro's drift

measure the yaw heading

The answer is: nudge the estimate slowly toward true level and cancel the gyro's drift

increase the loop rate

The answer is: nudge the estimate slowly toward true level and cancel the gyro's drift

3.[3p]
A complementary filter runs at $Δ t = 0.001$ s with $α = 0.98$ . Using $τ = α Δ t / (1 - α)$ , what is its time constant, in seconds, to three decimal places?

CorrectNot quite: 0.049

4.[2p]
The accelerometer cannot correct yaw drift because

gravity points the same way whatever heading the craft faces, so it carries no heading information

Correct

yaw is too fast for it to measure

The answer is: gravity points the same way whatever heading the craft faces, so it carries no heading information

it only works upside down

The answer is: gravity points the same way whatever heading the craft faces, so it carries no heading information

yaw does not drift

The answer is: gravity points the same way whatever heading the craft faces, so it carries no heading information

5.[2p]
A magnetometer is added to a craft that must hold a heading because

it reads the Earth's magnetic field to give an absolute heading, correcting the yaw drift

Correct

it measures tilt more accurately than the accelerometer

The answer is: it reads the Earth's magnetic field to give an absolute heading, correcting the yaw drift

it replaces the gyroscope

The answer is: it reads the Earth's magnetic field to give an absolute heading, correcting the yaw drift

it increases thrust

The answer is: it reads the Earth's magnetic field to give an absolute heading, correcting the yaw drift

6.[2p]
Acrobatic flight controllers store attitude as a quaternion rather than three angles because

three angles suffer gimbal lock at some orientations, while a quaternion never becomes singular

Correct

quaternions are easier for a pilot to read

The answer is: three angles suffer gimbal lock at some orientations, while a quaternion never becomes singular

quaternions use less memory

The answer is: three angles suffer gimbal lock at some orientations, while a quaternion never becomes singular

three angles cannot represent yaw

The answer is: three angles suffer gimbal lock at some orientations, while a quaternion never becomes singular

7.[2p]
A noisy or delayed attitude estimate can always be fixed by tuning the control loop harder downstream.

True

The answer is: False

False

Correct

1.[2p] In the complementary filter θ←α(θ+ωΔt)+(1-α)θacc, the term multiplied by α is

2.[2p] The small (1-α) accelerometer term in the filter is there to

3.[3p] A complementary filter runs at Δt=0.001 s with α=0.98. Using τ=αΔt/(1-α), what is its time constant, in seconds, to three decimal places?

4.[2p] The accelerometer cannot correct yaw drift because

5.[2p] A magnetometer is added to a craft that must hold a heading because

6.[2p] Acrobatic flight controllers store attitude as a quaternion rather than three angles because

7.[2p] A noisy or delayed attitude estimate can always be fixed by tuning the control loop harder downstream.

1.[2p]
In the complementary filter $θ \leftarrow α (θ + ω Δ t) + (1 - α) θ_{acc}$ , the term multiplied by $α$ is

2.[2p]
The small $(1 - α)$ accelerometer term in the filter is there to

3.[3p]
A complementary filter runs at $Δ t = 0.001$ s with $α = 0.98$ . Using $τ = α Δ t / (1 - α)$ , what is its time constant, in seconds, to three decimal places?

4.[2p]
The accelerometer cannot correct yaw drift because

5.[2p]
A magnetometer is added to a craft that must hold a heading because

6.[2p]
Acrobatic flight controllers store attitude as a quaternion rather than three angles because

7.[2p]
A noisy or delayed attitude estimate can always be fixed by tuning the control loop harder downstream.