Abstract: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. This paper shows that innovation statistics computed after gating converge to gate-conditioned rather than nominal quantities. Under classical linear--Gaussian assumptions, we derive exact expressions for the first- and second-order moments of the innovation conditioned on ellipsoidal gating, and show that gating induces a deterministic, dimension-dependent contraction of the innovation covariance. The analysis is extended to NN association, which is shown to act as an additional statistical selection operator. We prove that selecting the minimum-norm innovation among multiple in-gate measurements introduces an unavoidable energy contraction, implying that nominal innovation statistics cannot be preserved under nontrivial gating and association. Closed-form results in the two-dimensional case quantify the combined effects and illustrate their practical significance.
| Comments: | 9 pages, preprint |
| Subjects: | Methodology (stat.ME); Artificial Intelligence (cs.AI); Signal Processing (eess.SP); Systems and Control (eess.SY) |
| Cite as: | arXiv:2512.18508 [stat.ME] |
| (or arXiv:2512.18508v3 [stat.ME] for this version) | |
| https://doi.org/10.48550/arXiv.2512.18508 arXiv-issued DOI via DataCite |
From: Barak Or [view email]
[v1]
Sat, 20 Dec 2025 20:56:21 UTC (1,269 KB)
[v2]
Fri, 9 Jan 2026 11:49:11 UTC (1,269 KB)
[v3]
Sat, 23 May 2026 16:58:13 UTC (1,949 KB)
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