Abstract Absolute positioning magnetic rulers are rulers which calculate the distance of the reading head based just on one reading of a magnetic signal. A new absolute positioning magnetic ruler method which is based on rulers with trapezoidal magnetic poles is considered in this paper. On a fixed position of a ruler, the reading head reads a signal on two stripes with several Hall sensors and is supposed to recover the reading position. The main aim of the paper is to create an algorithm for recovering the position for a fixed reading altitude. In order to model a ruler some angle restrictions on trapezoids are considered. We build a ruler with a simple heuristic tactic, extending it with a randomly chosen trapezoid if its angles satisfy the required angle conditions. The magnetic field of a ruler is numerically calculated with the software Radia and is used for testing of the algorithm. For an approximation of the signal function, we introduce a new piecewise approximation method which is based on the low rank approximation of a matrix. Compared to the piecewise polynomial approximation, this method significantly reduces the required memory while having the same accuracy, which is a crucial goal if the whole algorithm needs to be implemented on an FPGA. Creating this type of ruler raises the natural question of the maximum possible length. The algorithm naturally defines the stability of any ruler as a positive real number, which is crucial for its functioning. We show the correlation between the length of a constructed ruler and its stability.

## Citation

Sedmog jula 106, 11251 Belgrade, Serbia.