Getting Started With Strapdown Inertial Navigation
The book is essentially the standard reference on the subject. It covers the full set of equations you need to propagate a strapdown INS from raw gyroscope and accelerometer outputs through to position, velocity, and attitude. The treatment is rigorous and mathematical, which means you get exact derivations rather than hand-wavy approximations. That is useful when your system needs to stay within a few meters over a hundred kilometers, and it is overkill when you are just trying to keep a UAV aloft for ten minutes. I spent several weeks working through the chapter on discrete integration of the attitude update. The equations assume you know exactly how your sensors sample and how the platform moves between samples. In practice, that is rarely true. My actual problem came from an IMU that was outputting at 200 Hz but the processor was reading at irregular intervals because of interrupt jitter. The result was a position drift of roughly two meters per minute in the X direction, even with the sensors level and stationary. The workaround was simple enough: I interpolated the raw rate measurements to a fixed time grid before running the attitude propagator. That alignment algorithm in the book assumes uniform sampling, and once I broke that assumption, the results degraded fast.
Strapdown Inertial Navigation Technology 2nd Edition By David Titterton
What most people miss on the first pass through this text is how much the book relies on a clean separation between the mechanical alignment phase and the in-flight algorithm. The alignment theory is thorough. The error budget analysis is good. But the practical integration with external sensors like GPS is handled in a fairly general way. You end up writing most of that yourself. One thing that is easy to overlook is the treatment of coning motion. The book gives you the second-order coning compensation, which is the standard. If you are flying a maneuvering platform, skipping coning compensation will cost you in attitude error, and attitude error propagates directly into velocity and position. A sharp pitch maneuver during alignment can produce coning angles that exceed the linear approximation used in basic strapdown models. I saw this on a test where the mount had some elastic preload. The platform vibrated at about 120 Hz during a rapid heading change, and the uncompensated coning error added roughly 0.05 degrees to the attitude drift over a three minute span. It was small but measurable. Applying the second-order correction brought it down to the noise floor. Another thing worth noting is the numerical stability of the different attitude representations. The book covers direction cosine matrices, quaternions, and Euler angles. Direction cosine matrices drift out of orthogonality over time and require re-orthonormalization. Quaternions avoid that problem but introduce a sign ambiguity that you need to handle explicitly. I found that switching to quaternion propagation for the main loop and only converting to DCM when output was needed cut long-term drift noticeably on my hardware. The Euler angle approach should be avoided entirely for strapdown work unless your application is extremely constrained, because gimbal lock is not a theoretical concern here. It is a failure mode you will hit during normal operation.
Gyroscope bias instability is probably the single largest source of long-term error in any strapdown system you build. The book covers the random walk and bias stability models in decent detail. The practical lesson is that you need a realistic calibration before you trust the propagation equations. A bias estimated from a ten-minute static test is not the same as a bias that accounts for thermal drift over the full operating range. I ran a thermal cycle test on a MEMS unit and the bias shifted by about 0.8 degrees per hour across the temperature range. Without compensating for that, your position error grows quadratically. The book gives you the framework to model this but it does not do the measurement work for you. The integration chapters with GPS and other aiding sensors follow a standard Kalman filter structure. The formulation is correct. It is also generic. If your application involves tight coupling or deeply coupled GNSS/INS, you will need to extend the framework substantially. The book is not wrong. It just stops at the point where most real systems need to diverge into custom formulations. The main limitation of this text is that it was written for a classical aerospace and maritime audience. Strapdown systems today often run on embedded processors with strict memory and timing constraints. The book does not address implementation optimization. You will encounter this when you try to run a full attitude propagation at 400 Hz on a floating-point processor that is already managing sensor readout and communication overhead. The algorithms work. They just consume more cycles than you might expect if you are coming from a simulation background.
Get the Full Details
If your goal is to understand the complete theoretical foundation of strapdown inertial navigation, this book is still the most comprehensive resource available. If you need a quick practical guide to building a bare-bones INS for a short-range application, you might find it heavier than necessary. In that case, pairing the book with a hands-on implementation using open-source code like the one from the OpenIns project or the NASA GTN suite will get you operational faster than working through the derivations alone.
