Statistical analysis of measurement results in multiwavelength pyrometry

The reduction procedure to the linear form of a nonlinear regression model describing the results of measurement of the radiation intensity by polychromatic pyrometer has been presented. The procedure is based on the replacement of the Planck function by the modified Vine function and is applicable to special dependence of emissivity $\varepsilon$ on the wavelength. In particular, it can be used when $\varepsilon$ is constant or weakly linear in the spectral interval of measurements. The obtained linear problem of estimating parameters is solved by the method of least squares, taking into account the unequal precision of measurements and the possible correlation of random errors at different wavelengths. Using a random number generator, the output random signal of multiwavelength pyrometer is simulated and the influence of the number of wavelengths (channels) of the photodiode line on the accuracy of estimated parameters is investigated.