recursive Bayesian estimation

Recursive Bayesian estimation is the master recipe for keeping a robot's belief up to date as time ticks forward. "Bayesian" means it follows one simple rule of reasoning: start with what you already believe, then revise it in proportion to how well new evidence fits. "Recursive" means it does this over and over in a loop, and — this is the clever part — each round only needs the answer from the round before, not the entire history of everything that ever happened. The robot never has to re-chew its whole past; it just carries forward one running summary, its current belief, and keeps refreshing it.

Each cycle has two beats. First the robot predicts: it takes its old belief and pushes it forward using what it knows about its own motion — "I commanded the wheels to roll forward, so my belief should shift ahead too." Because motion is never exact, this step always smears the belief out a little, making the robot less certain. Then the robot corrects: a fresh sensor reading comes in, and the robot pulls its belief toward whatever the measurement suggests, sharpening it back up. Predict loosens, measure tightens; the belief breathes out and in with every step.

Almost every famous estimator in robotics — the Kalman filter, the particle filter, and their many relatives — is just one concrete way of carrying out this same abstract loop. They differ only in how they store the belief and how they crunch the math, not in the underlying logic. Grasp the predict-then-correct rhythm of recursive Bayesian estimation, and you have the skeleton key to the entire family.