Chapter 3 -- Estimating what you cannot measure¶
Learning objectives¶
brief: The four objectives from scope.md, verbatim, as a numbered list. No prose around them -- students skim this box before and after reading, and framing sentences get in the way both times.
Why a raw measurement is not enough¶
brief: Motivate before mechanism. One concrete scenario -- a delivery robot whose wheel encoder drifts while its ultrasonic range-finder jitters -- introduced here and carried through every example in the chapter. Do not introduce a second scenario later.
queries:
- state estimation sensor noise motivation
Two numbers, not one¶
brief: The idea that an estimate carries a variance. This is the conceptual hinge of the chapter; if a student stops here they should still have gained something real.
The update, derived¶
brief: Build the gain from the two variances. Arithmetic only -- no matrices, no integrals, no probability density functions. Show that the gain lands between 0 and 1 and say in words what each extreme means.
Worked example: two steps by hand¶
brief: Fully worked, every number shown, using the delivery robot's numbers. Then immediately a faded version: same structure, the student supplies step two. Give the answer to the faded one at the end of the chapter, not inline.
When the assumptions fail¶
brief: Non-Gaussian noise and an unmodelled bias, in that order, each in a short subsection with the symptom a student would actually observe. Honest about what breaks -- this is where the students who go on to research get interested, and a chapter that pretends the method always works loses them.
queries:
- kalman filter assumption violation bias
- sensor fault detection residual
Exercises¶
brief: Six. Two that mirror the worked example with new numbers, two that require reasoning about the gain's behaviour, one that asks what happens when a measurement is missing entirely, and one open-ended. Hints for the last two, full solutions for the first four.
Summary, and where to go next¶
brief: Half a page of summary against the four objectives, then the pointers: the matrix form in chapter 4, the lab for building one, and one or two corpus papers for a student who wants the research framing.
queries:
- state estimation introduction survey