Lesson 4 Least-squares Estimation: Singular-value Decomposition

Summary

The purpose of this lesson is to show how least-squares estimates can be computed using the singular-value decomposition (SVD) of matrix H(k). This computation is valid for both the overdetermined and underdetermined situations and for the situations when H(k) may or may not be of full rank. The SVD of H(k) also provides a practical way to test the rank of H(k).

The SVD of H(k) is also related to the pseudoinverse of H(k). When H(k) is of maximum rank, we show that the pseudoinverse of H(k) reduces to the formula that we derived for Image in Lesson 3.

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