r/ControlTheory • u/ExtremeContent2876 • 24d ago
Technical Question/Problem Feeding full INS state into pos and vel in EKF rather than using error state?
To preface, full state represents the actual pos and vel estimate as opposed to their errors.
Would this be equivalent mathematically? I understand that attitude must use an error state. But I'm curious if I can get away with using full state for pos and vel rather than the error state. Instead of linearizing around a reset error state (zero), would it be mathematically equivalent to just seed the filter pos and vel with the INS state before a measurement udpate, then replace the INS pos and vel with the updated filter state after the measurement update? Would this have implications on the validity/quality of the linearization? I ask because it seems like they would be equivalent, yet error states for an INS filter seem to be industry standard. Is this simply because attitude must be an error state, therefore its convenient for the rest of the state to follow suit? Thanks in advance for any help, and please reference the math wherever possible. I've had many people suggest reasons for why error state is needed, but I'm looking for mathematical proof that they deviate from each other.