An Adaptive Filter for Subdivision of Circular Grating Signal of Angle Measurement

Angle is an important physical quantity in International Systems of Units (SI). The precise measurement of an angle is of great significance for scientific research and production. The circular grating is a widely used angle measurement sensor because of its large range and high resolution. Subdivision is the key part of grating measurement to ensure high resolution. In order to guarantee the subdivision function, we propose an adaptive filter to suppress the noises in the moiré signals of the circular grating. The principle of subdivision is introduced and the arc-tangent subdivision method mapping the phase of the moiré signals into the displacement is adopted. The influence of noises on subdivision results is analyzed by building the error model of the moiré signals. A detailed description of the adapted filter, which is composed of a linear prediction filter and the least mean square (LMS) adaptive algorithm, is provided herein. The structure of the adapted filter is optimized with a symmetrical structure and the hardware resources are reduced by about 1/3. Finally, evaluation tests are performed with a calibration platform for positioning the accuracy of a turntable and a laboratory-made field-programmable gate array (FPGA) circuit. The results confirmed that the adaptive filter proposed in this article can filter out random noises more effectively than the conventional finite impulse response (FIR) filter with the same order, revealing a phase error fluctuates within [−0.012, +0.003 rad]. The positioning accuracy of the turntable with a laboratory-made circuit using an adaptive filter is better than 0.8.