Least-squares estimation: from Gauss to Kalman
IEEE SpectrumPublished 1 July 1970
H.W. Sorenson
Citations740
SJR quartileQ3
SJR score0.25
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
This discussion is directed to least-squares estimation theory, from its inception by Gauss1 to its modern form, as developed by Kalman.2 To aid in furnishing the desired perspective, the contributions and insights provided by Gauss are described and related to developments that have appeared more recently (that is, in the 20th century). In the author's opinion, it is enlightening to consider just how far (or how little) we have advanced since the initial developments and to recognize the truth in the saying that we ``stand on the shoulders of giants.''
Keywords
Computer ScienceMathematics
Journal of Basic EngineeringA New Approach to Linear Filtering and Prediction Problems
30,999 Citations1960R. E. Kalman
The Annals of Mathematical StatisticsA Stochastic Approximation Method
9,581 Citations1951Herbert Robbins, Sutton Monro
Journal of Basic EngineeringNew Results in Linear Filtering and Prediction Theory
6,330 Citations1961R. E. Kalman, R. S. Bucy
The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results and properties of the variance equation are of great interest in the theory of adaptive systems.
The MIT Press eBooksExtrapolation, Interpolation, and Smoothing of Stationary Time Series
4,791 Citations1949Norbert Wiener
The Annals of Mathematical StatisticsStochastic Estimation of the Maximum of a Regression Function
2,143 Citations1952J. Kiefer, J. Wolfowitz
IEEE Transactions on Automatic ControlOn the identification of variances and adaptive Kalman filtering
1,342 Citations1970R.К. Mehra
IEEE Transactions on Automatic ControlAn innovations approach to least-squares estimation--Part I: Linear filtering in additive white noise
748 Citations1968T. Kailath
Munich Personal RePEc Archive (Ludwig Maximilian University of Munich)Filtering for stochastic processes with applications to guidance
550 Citations1968R. S. Bucy, Peter D. Joseph
This chapter discusses filter theory, applications, and applications of filter theory and modeling techniques for free flight and powered flight navigation, and error analyses and sub-optimal modeling.
Adelaide Research & Scholarship (AR&S) (University of Adelaide)001: On an Absolute Criterion for Fitting Frequency Curves.
393 Citations1912Ronald Aylmer Fisher
IEEE Transactions on Automatic ControlAn innovations approach to least-squares estimation--Part II: Linear smoothing in additive white noise
373 Citations1968T. Kailath, Peter A. Frost
Proceedings of the IREA Simplified Derivation of Linear Least Square Smoothing and Prediction Theory
280 Citations1950H.W. Bode, Chad E. Shannon
Journal of Applied PhysicsAn Extension of Wiener's Theory of Prediction
237 Citations1950Lotfi A. Zadeh, John R. Ragazzini
AutomaticaAdaptive filtering
198 Citations1969A. H. Jazwinski
Applications of the Kalman filter in orbit determination problems have sometimes encountered a difficulty which has been referred to as divergence; the phenomenon is a growth in the residuals; the state and its estimate diverge.
ESTIMATION BY LEAST SQUARES AND BY MAXIMUM LIKELIHOOD
35 Citations1956Joseph Berkson
IEEE Transactions on Information TheoryRecursion formulas for growing memory digital filters
14 Citations1958Marvin Blum
A derivation of an optimum growing memory smoothing and prediction filter in the least squares sense for polynomial input functions and a theorem on the class of time invariant sequence W_u are presented, which are solutions of a difference equation of tiite order.
