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Scope

  • genre: textbook-chapter
  • language: en-GB
  • draft: content/drafts/course/ch3-state-estimation.md
  • created: 2026-09-15
  • corpus: 214 citekeys, digest a31f0c4b77de
  • draft digest: not recorded (run dossier stamp once the draft is ready)

Reader

Second-year undergraduates who have had one linear-algebra course and no signals or probability course beyond a first module. They have seen a mean and a variance; they have not seen a covariance matrix, and will not in this chapter.

Covers

Why a raw measurement is not enough; the one-dimensional estimator built from two variances; two steps worked by hand with every number shown; a faded example the student finishes; and an honest section on which assumptions break in practice.

Learning objectives, in the chapter's own words -- by the end a student can:

  1. state what a state estimator does and why a raw reading is not enough;
  2. derive the one-dimensional update from the two variances;
  3. hand-compute two steps on given numbers;
  4. say when the assumptions fail and what happens then.

Does not cover

The matrix form. That is chapter 4, and reaching for it here would cost the derivation its arithmetic-only property, which is the whole reason this chapter comes first.

Nonlinear filters entirely. Named in "where to go next" so a curious student knows the word, with no treatment.

Implementation. There is no code in this chapter -- students who want to build one are pointed at the lab, which is a tutorial and a separate document.

Glossary

  • State -- the quantity we want to know and cannot measure directly. Used consistently; never "the system" or "the value".
  • Measurement -- a single noisy observation.
  • Estimate -- our current best guess of the state, always paired with its variance. A number without its variance is never called an estimate in this chapter.
  • Gain -- the weight given to a new measurement against the current estimate, between 0 and 1.
  • Innovation -- measurement minus predicted measurement. Introduced only in the "where to go next" section; not used in the derivation.