Selection-Induced Contraction of Innovation Statistics in Gated Kalman Filters

ArXi:2512.18508v3 Announce Type: replace-cross Validation gating is a fundamental component of classical Kalman-based tracking systems. Only measurements whose normalized innovation squared (NIS) falls below a prescribed threshold are considered for state update. While this procedure is statistically motivated by the chi-square distribution, it implicitly replaces the unconditional innovation process with a conditionally observed one, restricted to the validation event.