Questions submitted by members of various forums, understandably, frequently involve one or more of the following topics:
* some or all facets of inertial navigation
* means of updating and reinitializing the drifting inertial solution
* satellite navigation (GPS/GNSS) for providilng the updates
* other means of updating (radar, laser, optics, VOR, DME, hyperbolic, … )
* best ways to use what’s available for various applications.
The pool of literature that might be offered can be vast, partly due to a vast array of operations – each with application-dependent requirements. Finding just the relevant information from a mountain of available references can be a daunting task, especially for young designers. I’ll try to make their search easier, by offering a list they can ask themselves early in the design process:
* do you need a lat/lon/altitude Earth reference or just a designated point?
* is the path determined from provisions onboard (nav) or remote (track)?
* what’s your required accuracy for “absolute” (geolocation) position?
* what’s your required accuracy for relative position (e.g., from a runway)?
* do you need precise incremental position history (SAR motion compensation)?
* do you need precise angular orientation (e.g., laser pointing)?
* do you need precise angular rates (for image or antenna stabilization)?
* for direction do you use a North reference or just along-track/cross-track?
* will you have dependable access to updating information (GPS, radar, …)?
* if not, how irregular will dynamics be over active parts of your mission?
* if so, how irregular will the dynamics be during inter-update periods?
* also if so, what data rate? Longest expected “blind period” between updates?
* also if so, will measurements need averaging to meet your required accuracy?
* also if so, how accurate are your measurements AND their time stamps?
* also if so, can you use postprocessing or do you need everything real-time?
* are you willing to accept partial updates (some but not all directions)?
* do you need just position or derivatives too (velocity, acceleration)?
* if so, how long can your dynamics be trusted to conform to model fidelity?
* are you doing INS update (e.g., replacing acceleration with tilt states)?
* if so, will you need to deduce drift rates – and how long will those hold?
* do your sensors measure distances, angles, doppler, differences of those?
* for how long does your sensor information content provide observability?
* how’s your sensor integrity (bad readings at least detectable if present)?
* for safety-critical operations — what are your backup provisions?
* are you accommodating multiple modes with time-shared sensing resources?
* do you need to perform image registration with different imaging sensors?
etc.etc. — the list goes on. I won’t even try to claim thoroughness; you get the idea. Designers with new tasks dumped in their lap can understandably feel overwhelmed. Searching for references can become a trip through a maze of half-relevant sources.
A first step, then, is to separate the relevant (what you need) from the irrelevant (what you don’t need), instantly dismiss any thought of the latter, and do the opposite with the former (nail it).
Brief examples — the first two items from the above list —
* If you just need to know your location relative to a designated point, irrespective of its latitude and lingitude — this
* If you’re tracking instead of navigating — check these out —
and one from the last item from that list —
Again, you get the idea — volumes have been written on all facets. Many won’t apply to your immediate task; disregard those.
The good news is — paths to logical solutions are known and documented. To avoid abandoning you to an enormous maze of references I’ll point out some fundamental and advanced (state-of-the-art) tracts that address all issues just cited and more. Several blogs and short “1-pagers” will help individual designers to choose, based on their specific tasks, passages from available references.
Before GPS we struggled hard for accurate measurements in enough places. That actually produced a benefit — we had to be resourceful. My biggest challenge was to understand subjects (Kalman filtering, strapdown inertial navigation) then considered exotic. Again a benefit; pulling information from 1950s books and papers forced me to understand, focus, and reduce concepts to whatever level became necessary. The experience prompted me to write the first of my two books on navigation
That first book has been used in myriad courses, including one currently taught by Prof. Hablani who wrote the most recent testimonial shown on that URL .
For example, slow (“W” radian/sec) oscillations with “W” corresponding to the Schuler period (between 83 and 84 minutes). In that case position error from accelerometer bias, propagating as (1 – cos Wt), rises much sooner than gyro drift, propagating as (t – sin Wt/W). Page 80 of that book sketches an example of behavior over a cycle. Development offered beyond there expands as far as many analysts wish to go (other natural frequencies of error propagation, rectification of vibration-sensitive errors, etc.).
Not long after that first book appeared, GPS became operational — and I was a newcomer to that. By the time I understood it there were many experts. Once again I had to catch up, and the process was gradual. With an exceptionally strong client interested in my inertial background, a synergism was formed. That led to a flight test producing state-of-the-art accuracy in dynamics; see the table
describing several innovations also resulting from the work just described.
That second book, after a review chapter, begins where the first (pre-GPS) one left off. It also (1)is used in tutorials and (2)has received testimonials from other instructors, as the URL shows. Sources cited here, plus an online 1.5-hr tutorial
, free to Inst-of-Navigation members, plus a “try-before-you-buy” 100-page excerpt available from this site, should be helpful to many.