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Chapter 3 / Sensors / Accelerometers
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3.5.3.1 IMU Case Misalignment Error
Manufacturing tolerances mean that the case containing the accelerometers
is rotated with respect to the Missile Body frame, an alignment error that
preserves sensor triad orthogonality. For small angles, assuming that the
expected error is the same about each axis,
D
B
D
D B
( 0 , σ ) ⇒ f : = [ I + ∆E
] f
∆ E ∈ N
⋅
IMU
MA
3.5-3
r,
u
3
B
r,
u
Equation 3.5-1
The IMU case misalignment error is initialised from a zero-mean Gaussian
distribution with a deviation of (IMUσMA). This error is common to both
gyroscope and accelerometer triads and is computed in both sensor modules
so that they can be activated in isolation.
3.5.3.2 Sensor Triad Non-Orthogonality Error
The orientation of each sensor axis with respect to the case results in a nonorthogonality
error between sensors that is initialised from a zero-mean
Gaussian distribution with a deviation of (ACσNO). If the expected error is
the same for each axis,
i
i
i D
{ R , P , Y } ⇒ f : = [ I + ∆E
] ⋅ ( M f )
∀ i ∈
⋅
r,
u
3
D
B
r,
u
Equation 3.5-2
When selected values from symmetrical statistical distributions the sign of
the rotations in the transform are irrelevant. Although the input axes are
nominally aligned with Missile Body axes, the Hinge (output) and
Pendulum axes can be selected to minimise acceleration sensitive drifts.
The dominant g-sensitive biases are stimulated by accelerations along the
Input and Pendulum axes.
The configurations shown in Figure 3-34 and Figure 3-35 contain 6 of the
possible 12 sensor orientations (6 more are obtained by rotating each input
axis through 180°). The negative signs in these figures indicate that the
positive axis is in the opposite direction to that shown.
For each sensor, let the (X,Y,Z) Missile Body axes be aligned with the
Input-Hinge-Pendulum (I,H,P) sensor axes such that a clockwise pendulum
motion about the Hinge axis implies positive output and input accelerations.
The configurations in Figure 3-34 and Figure 3-35 minimise torque due to
missile lateral and longitudinal acceleration respectively. For the orientation
shown in Figure 3-34 the mapping of the case inputs to the (I,H,P) axes for
mechanical RPY accelerometers is the same as that for the gyroscopes in
§3.4.3.2. For solid state devices that are insensitive to acceleration induced
errors the mappings are simply the identity matrix.