Abstract
Validation gating is central to Kalman-based tracking, but it changes the statistical population that downstream diagnostics observe. This paper shows that normalized innovation squared (NIS) statistics computed after ellipsoidal gating converge to gate-conditioned, not nominal unconditional, reference values. Under classical linear-Gaussian assumptions, the work derives exact first- and second-order moments for gate-conditioned innovations and proves that validation gating induces deterministic, dimension-dependent contraction of innovation covariance. The analysis is extended to nearest-neighbor association, showing that selecting the minimum-norm in-gate innovation introduces additional order-statistic contraction even when the filter model is perfectly matched. Monte Carlo experiments and an end-to-end tracking study demonstrate that nominal NIS-based tuning can learn biased measurement-noise scales, while gate-aware correction remains close to the true scale.