JAMES L FARRELL, PHD
GYRO MOUNTING MISALIGNMENT: DEAL BREAKER
Schuler cycles distorted — Here’s why
A
1999 publication I coauthored took dead aim at a characteristic that received far too little attention — and still continues to be widely overlooked: mechanical mounting
misalignment
of inertial instruments. To make the point as clearly as possible I focused exclusively on gyro misalignment — e.g., the sensitive axes of roll, pitch, and yaw gyros aren’t quite perpendicular to one another. It was easily shown that the effect in free-inertial coast (i.e., with no updates from GPS or other navaids) was serious, even if no other errors existed.
Misalignment: mechanical mounting imprecision
Whenever this topic is discussed, certain points must be put to rest. The first concerns terminology; much of the petinent literature uses the word misalignments to describe small-angle directional uncertainty components (e.g., error in perception of downward and North, which drive errors in velocity). To avoid misinterpretation I refer to nav-axis direction uncertainty as misorientation . In the presence of rotations, mounting misalignment contributes to misorientation . Those effects, taking place promptly upon rotation of the strapdown inertial instrument assembly, stand in marked contrast to leisurely (nominal 84-minute) classical Schuler dynamics.
A third point involves error propagation and a different kind of calibration (in-flight). With the old (gimbal) mechanization, in-flight calibration could counteract much overall gyro drift effect. Glib assessments in the 1990s promoted widespread belief that the same would likewise be true for strapdown. Changing that perspective motivated the investigation and publication mentioned at the top of this blog.
The final point concerns the statistical distribution of errors. Especially with safety involved (e.g., trusting free-inertial coast error propagation), it is clearly not enough to specify RMS errors. For example, 2 arc-sec is better than 20 but what are the statistics? Furthermore there is nothing to preclude unexpected extension of duration for free-inertial coast after a missed approach followed by a large change in direction. A coauthored investigation (Farrell and vanGraas, ION-GNSS-2010 Proceedings) applies Extreme Value Theory (EVT) to outliers, showing unacceptably high incidences of large multiples (e.g., ten-sigma and beyond). To substantiate that, there’s room here for an abbreviated explanation — even in linear systems, gaussian inputs produce gaussian outputs only under very restrictive conditions.
