Modular framework for implementation and analysis of recursive filters with considered and neglected parameters

Abstract

This paper develops novel covariance and square-root factor formulations of a consider-neglect Kalman filter for navigation applications. The proposed filter partitions system parameters into three distinct categories: those to be estimated by the filter, those whose contribution to the system are considered without being explicitly estimated, and those with sufficiently low effect on the system such that their contribution can be neglected altogether. Discussion on appropriate selection of parameters to be considered and neglected is provided with specific attention given to descent-to-landing navigation. Monte Carlo simulations and analysis are performed to assess the performance of the developed square-root consider-neglect filter in a descent-to-landing navigation scenario.

Uncertainty Propagation for Inertial Navigation with Coning, Sculling, and Scrolling Corrections

“…The uncertain parameters used to account for sensor errors in IMU measurements are typically identified as neglected, considered, or estimated quantities within the navigation filter, pending the results of a consider analysis as originally posed by S.F. Schmidt [28], though now widely used in application and research [29][30][31][32][33]. In the case in which all of the error parameters are estimated directly by the navigation filter, and assuming that Equation ( 24) holds, the expected values of the incremental angle E{∆θ k } = ∆ θk and the incremental velocity E{∆v k } = ∆ vk are seen to be…”