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

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.

[1]  Gerald J. Bierman,et al.  Measurement updating using the U-D factorization , 1975, 1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes.

[2]  N. A. Carlson.  Fast triangular formulation of the square root filter. , 1973 .

[3]  New method for propagating the square root covariance matrix in triangular form. [using Kalman-Bucy filter] , 1975 .

[4]  James S. McCabe,et al.  Square-Root Consider Filters with Hyperbolic Householder Reflections , 2018, Journal of Guidance, Control, and Dynamics.

[5]  Kyle J. DeMars,et al.  Joseph Formulation of Unscented and Quadrature Filters with Application to Consider States , 2013 .

[6]  James S. McCabe,et al.  Considering Uncertain Parameters in Non-Gaussian Estimation for Single-Target and Multitarget Tracking , 2017 .

[7]  John Junkins,et al.  Optimal Estimation of Dynamic Systems, Second Edition , 2011 .

[8]  Byron D. Tapley,et al.  An algorithm for propagating the square-root covariance matrix in triangular form , 1976 .

[9]  Renato Zanetti,et al.  Recursive Implementations of the Schmidt-Kalman ‘Consider’ Filter , 2013 .

[10]  James S. McCabe,et al.  Design and Analysis of Descent-to-Landing Navigation Incorporating Terrain Effects , 2020 .

[11]  A. Andrews,et al.  A square root formulation of the Kalman covariance equations. , 1968 .

[12]  Bob E. Schutz,et al.  Consider Covariance Analysis , 2004 .

[13]  J. Junkins,et al.  On the Consider Kalman Filter , 2010 .

[14]  Renato Zanetti.  Design and Flight Performance of the Orion Pre-Launch Navigation System , 2017 .

[15]  J. Bellantoni,et al.  A square root formulation of the Kalman- Schmidt filter. , 1967 .

[16]  John L. Crassidis,et al.  Filtering for Attitude Estimation and Calibration , 2014 .