Multi-Axis Position Sensing System

Multi-axis self-location method and apparatus wherein de Bruijn sequences on 2 or more axes are convolved into an array of symbols such as halftone dots to form a reference scale. The position of an imaging device such as a camera relative to the reference scale is ascertained from the captured camera image by bit-wise reconstitution of axis position codes with simple, predominantly linear operations over small neighbourhoods. Judicious choice of differential coding, LFSR generator polynomials, mathematical operators, and deconvolution kernels enables code digits of an axis to be regenerated while simultaneously cancelling out the contributions of other axes. Also optionally provided are uniform DC-balanced variants yielding greatly improved position interpolation, isometric implementations decodable from high-aspect-ratio sample windows, robust concatenated error correction, and extensions into n-space.