Use of Nonlinear Least Squares in Meteorological Applications

Abstract

This paper derives formulas for the application of nonlinear least squares. The need for doing statistical error analyses before undertaking any system development is pointed and formulas are derived to compute the covariance matrix of the estimated parameters. The technique is illustrated with application to three systems developed by the GAMP Group at NCAR, namely the GHOST sun angle tracking system, the use of Omega navigation system in the Carrier Balloon System, and the Safesonde, a Doppler wind measuring radiosonde system. The techniques developed are general enough for a universal application of nonlinear least squares.