Flexible least squares for approximately linear systems
Abstract
A probabilityfree multicriteria approach is presented to the problem of filtering and smoothing when prior beliefs concerning dynamics and measurements take an approximately linear form. Consideration is given to applications in the social and biological sciences, where obtaining agreement among researchers regarding probability relations for discrepancy terms is difficult. The essence of the proposed flexibleleastsquares (FLS) procedure is the costefficient frontier, a curve in a twodimensional cost plane which provides an explicit and systematic way to determine the efficient tradeoffs between the separate costs incurred for dynamic and measurement specification errors. The FLS estimates show how the state vector could have evolved over time in a manner minimally incompatible with the prior dynamic and measurement specifications. A FORTRAN program for implementing the FLS filtering and smoothing procedure for approximately linear systems is provided.
 Publication:

IEEE Transactions on Systems Man and Cybernetics
 Pub Date:
 October 1990
 Bibcode:
 1990ITSMC..20..978K
 Keywords:

 Fortran;
 Kalman Filters;
 Least Squares Method;
 Linear Systems;
 Lagrange Multipliers;
 Matrices (Mathematics);
 Probability Density Functions;
 Communications and Radar