Analytic Multisource Data Fusion and its Application to a Large-Scale Optical PSD

This paper introduces an analytic algebraic framework for multisource data fusion using covariance weighted discrete orthogonal polynomials. The approach is implemented and tested in a prototype for a large-scale optical position sensitive detector (PSD). The device is designed for the precise guidance of machines with respect to a reference laser plane in large working areas. The 1-D detector has a measurement range of 1 m and, with the present implementation, a position measurement standard deviation of s <; ±0.6 mm in a 95% confidence interval at a distance of 300 m. With this length, it is orders of magnitude larger than all presently available PSDs. The instrument´s concept is based on a multicamera image processing setup, enabling a relatively compact hardware design. An aluminum bar serves as the target for the laser. The target´s surface is specially prepared to ensure optimal scattering of the laser light. At present, four cameras with wide-angle lenses and overlapping fields of view monitor the scattered light; however, the theoretical framework supports the fusion of data from an arbitrary number of sensors. Additional optical components reduce the susceptibility to ambient light sources. Each camera is calibrated using Gram basis functions and the data from the four cameras are fused to give a consistent measurement over the complete measurement range. The linear nature of the computation offers the advantage that the error propagation can be derived analytically. Weighted polynomial approximation determines the calibration coefficients and weighted polynomial interpolation is used to obtain the measurement results. Complete testing of the instrument is presented, whereby cross validation ensures the correct quantification of errors. A Kolmogorov-Smirnov test is performed to prove the Gaussian nature of the measurement data and its error.