CBE20258 Lecture 13: NASA lecture 13
22 Mar 2016
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Will often distort the data (when you transform the non-linear model) Magnitude does not matter, just the pattern does (for the weighting!) There is usually some sort of systematic error. If necessary, transform the model so that it is linear in the new unknowns. Each row is a different evaluating time or position. = a column vector of data x = a column vector of the modeling parameters. Estimate : (cid:1876)(cid:1318)=(cid:1827)\b(cid:4652)(cid:1318) (solves with qr) (cid:1827)(cid:3021)(cid:1827)(cid:1876)(cid:1318)=(cid:1827)(cid:3021)(cid:1854)(cid:4652)(cid:1318) (plu) (cid:1876)(cid:1318)=[((cid:1827)(cid:3021)(cid:1827))(cid:2879)(cid:2869)(cid:1827)(cid:3021)](cid:1854)(cid:4652)(cid:1318) (cid:1870)(cid:1318)=(cid:1827)(cid:1876)(cid:1318) (cid:1854)(cid:4652)(cid:1318) If (cid:2026)(cid:3029)(cid:2870)is not uniform, figure out how (cid:2026)(cid:3029)(cid:2870)varies. Calculate matrix of covariance of the original parameters figure out how (cid:2026)(cid:3029)(cid:2870)varies. Remember, linear regression always has assumptions, so it will never be perfect. If you have a large number of data points, you are condemned to underestimating the error (because of the assumption of independence) Same as linear regression, but problem is that it is a nonlinear optimization problem. You really have to know the answer before you start.
