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Some feature-driven navigation sources, such as cameras or lidars, often require measurement-to-feature associations between the collected data and an onboard feature catalog to be performed upstream of the filter. Standard navigation practice suggests the use of Kalman updates with measurements that have first passed residual editing tests, but this is often insufficient to prevent updates based upon incorrectly associated data, leading to filter degradation and divergence. Recent work has developed the anonymous feature processing (AFP) technique that eliminates reliance upon explicit feature associations outside of the filter entirely while maintaining desirable estimation performance. This paper continues by exploring the approximation employed by AFP, and a higher order approximation is presented to further improve the estimation performance of the AFP update.