CHAPTER 7

LEAST-SQUARES ESTIMATION: CONSTRAINTS, NONLINEAR MODELS, AND ROBUST TECHNIQUES

The previous chapter addressed least-squares topics related to modeling, model errors, and accuracy assessment. This chapter discusses extensions of basic linear least-squares techniques, including constrained least-squares estimation (equality and inequality), recursive least squares, nonlinear least squares, robust estimation (including data editing), and measurement preprocessing.

7.1 CONSTRAINED ESTIMATES

It is sometimes necessary to enforce constraints on the estimated states. These constraints may be either linear equality constraints of the form , where C is a full-rank p × n matrix with p < n, or inequality constraints such as , , , or combinations of equality and inequality constraints. This section presents a brief summary of the techniques. More information may be found in Lawson and Hanson (1974), Björck (1996), and Golub and Van Loan (1996). Also see Anderson et al. (1999) for information on the LAPACK routine S/DGGLSE.

7.1.1 Least-Squares with Linear Equality Constraints (Problem LSE)

Many ...