Recursive Bayesian estimator for linear-Gaussian state-space models boldsymbolx_t = boldsymbolFboldsymbolx_t-1 + boldsymbolw_t, boldsymboly_t = boldsymbolHboldsymbolx_t + boldsymbolv_t. Two-step recursion: predict (hatboldsymbolx_t|t-1 = boldsymbolFhatboldsymbolx_t-1|t-1, propagate covariance) then update with Kalman gain boldsymbolK_t = boldsymbolP_t|t-1boldsymbolH^T(boldsymbolHboldsymbolP_t|t-1boldsymbolH^T + boldsymbolR)^-1. Used in finance for dynamic beta estimation, factor-model state, and yield-curve latent-factor models (Nelson-Siegel state-space). Extended/Unscented variants relax linearity.