NDLI: The Proper Computation of the Matrix Pseudoinverse and its Impact in MVRO Filtering

Content Provider	IEEE Xplore Digital Library
Author	Kerr, T.H.
Copyright Year	1965
Abstract	There have been two new algorithms of fairly recent origin offered for the calculation of the matrix pseudoinverse. Unfortunately, nonpathological counterexamples can be constructed, as offered herein, that demonstrate the questionable nature of these two algorithms; however, a resolution is offered here to help prevent possible uncritical propagation of the questionable algorithms. As a rigorous alternative, a well-established technique (endorsed by numerical analysts) is reviewed for calculating the correct matrix pseudoinverse using a computer. Additionally, this technique possesses existent independently verified/validated and assessible software code for a convenient implementation. However, historical loose ends in calculating the associated condition number are singled out here as cause for concern and as a topic for future resolution and refinement. Finally, as the primary motivation for considering these issues, an application example is offered from estimation theory in the implementation and analysis of a minimum variance reduced-order (MVRO) filter having proper performance that critically hinges on the correct computation of the matrix pseudoinverse. While examples of applying MVRO to navigation applications were provided almost a decade ago, a clear indication of the somewhat restrictive conditions of applicability were wanting and so are elucidated here since there appears to be a resurgence of interest in this analytic technique. Another contribution is in providing a tally of the drawbacks to be incurred in using MVRO as well as its previously publicized benefits.
Starting Page	711
Ending Page	724
Page Count	14
File Size	3068039
File Format	PDF
ISSN	00189251
Volume Number	AES-21
Issue Number	5
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1985-09-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Filters Estimation theory Navigation Covariance matrix Application software Analysis of variance Performance analysis Filtering theory Fasteners Control systems
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering Aerospace Engineering

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