Techniques
Focused notes on navigation-analysis techniques that stand on their own, outside the GNC foundations and any single system study: how to cancel a sensor error instead of estimating it, how to turn a residual into a decision, how to predict a filter's performance without Monte Carlo, when two unknowns are jointly observable, and how you convince yourself a delivered IMU actually meets spec.
Symbols used on this page are defined in the Nomenclature → notation conventions.
Cancel it, or detect it
Two techniques that sidestep estimation entirely: make the error average itself away, or catch it the moment it appears.
Gyro bias cancellation by rotation
Carouselling, indexing and dithering: why physically rotating an IMU modulates a constant bias into a zero-mean signal, what it does to the observability of heading, and the error terms it introduces in exchange.
FDI decision functions
From residual to declaration: normalised innovations, the $\chi^2$ and GLR tests, parity space, thresholds from false-alarm probability, CUSUM for slow drifts, and why detectability is a geometry question.
Predict it, or prove it cannot be separated
Analysis before simulation: what the error budget will be, how the error dynamics behave, and which unknowns are fundamentally indistinguishable from each other.
Linear covariance analysis
Getting a performance answer in one run instead of ten thousand: the dual-covariance formulation, how it separates true error from the filter's believed error, and exactly when it stops being valid.
Joint observability: attitude & misalignment
Why a single star tracker can never separate its own boresight misalignment from vehicle attitude, and the geometric conditions — multiple units, or motion — that break the degeneracy.
Schuler oscillation in strapdown INS
Why inertial horizontal error oscillates with an 84.4-minute period set by nothing but $g$ and $R_e$, why the vertical channel diverges instead, and the full menu of suppression methods — including why internal damping only trades the oscillation for a drift.
Verify it on the bench
Before any of the analysis above means anything, the delivered hardware has to behave the way the budget assumed.
IMU acceptance testing
What a bench can actually measure: Allan variance and the five noise regimes, multi-position tumble tests for bias/scale/misalignment, rate-table scale factor, and why repeatability matters more than the headline drift number.
The parts being tested →
Per-grade IMU specs and part tables in the Hardware section, so the bench numbers have something to be compared against.
Scope & sourcing
These pages are written from the open literature — IEEE/AIAA standards and papers, NASA technical publications, and the standard textbooks (Titterton & Weston, Groves, Farrell, Bar-Shalom, Gustafsson) — and are deliberately generic. They explain the techniques and their mathematics, not any particular organisation's implementation, hardware, or results, and contain no vehicle-specific or vendor-specific data.
Related: Filtering · EKF · IMU & inertial navigation · Star trackers · NASA filter best practices · Rocket Navigation.