Measurement inversion with a linear model
Inverse problems in heat diffusion . Construction and solution of the least squares problem

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BE8266 V2 Article

Measurement inversion with a linear model
Inverse problems in heat diffusion . Construction and solution of the least squares problem

Authors : Denis MAILLET, Yvon JARNY, Daniel PETIT

Review date: June 4, 2025 | Lire en français

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2. Measurement inversion with a linear model

The minimization problem is solved differently depending on whether the model output is linear or non-linear with respect to the parameters:

  • in the 1 er case, there is an explicit solution to the problem;

  • in the 2nd case, iterative non-linear programming (NLP) methods must be used to approximate the solution.

2.1 Linear ordinary least squares (OLS) estimator

When the model is linear, its output is written as :

ymo(
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