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Analytic partial derivatives for least-squares fitting incoherent scatter data


  • Wesley E. Swartz


Partial derivatives are given for efficient least-squares fitting electron temperature, ion temperature, composition, or collision frequency to incoherent scatter spectra and autocorrelation functions without the need for massive off-line storage requirements for function tables. The Debye length term is included explicitly in all appropriate functions so that no corrections need be made after the fitting sequence. One complete fit iteration (including the generation of the theoretical function and its derivatives, and including the construction and inversion of the matrix equation in the nonlinear least-squares code) can be performed on an IBM 370 computer in 8 to 15 msec, depending on the number of data points required and the number of parameters being fit. Fitting most incoherent scatter data in parallel with data acquisition should now be feasible using these functions and the fast floating point hardware currently available.

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