Determination of the angular parameters in the general altitude–azimuth tracking angle formulas for a heliostat with a mirror-pivot offset based on experimental tracking data

A set of general altitude–azimuth tracking angle formulas for a heliostat with a mirror-pivot offset and other geometrical errors were developed previously. The angular parameters with respect to the geometrical errors are the tilt angle, ψ_t, and the tilt azimuth angle, ψ_a, of the azimuth axis, the bias angle, τ₁, of the altitude axis from the orthogonal to the azimuth axis, and the canting angle, μ, of the mirror surface plane relative to the altitude axis. In view of the importance the zero angle position errors of the two rotational axes (α₀ is for the zero angle position error of the altitude axis and γ₀ for the zero angle position error of the azimuth axis), the original general tracking angle formulae have been slightly modified by replacing the tracking angles in the original tracking formulas with the difference between the nominal tracking angles and the zero angle position errors. The six angular parameters (ψ_a, ψ_t, γ₀, τ₁, α₀, μ) for a specific altitude–azimuth tracking heliostat could be determined from experimental tracking data using a least squares fit and the classical Hartley-Meyer solution algorithm. The least squares model is used on data for a specially designed heliostat model with two sets of laser beam tracking test data to show the effectiveness of the least squares model and the Hartley-Meyer algorithm.