Estimation of angular velocity and acceleration from shaft encoder measurements

The output of a shaft encoder is basically a quantized measurement of the shaft angle. One method of angular velocity and acceleration measurement is by finite difference of angle measurements (net pulse counts) at regular time samples. It is shown that these estimates become significantly degraded as sampling rates increase. Kalman filtering of the angle measurements, based on some model of signal generation, is proposed. Asymptotic analysis of constant sampling rate as the intersample time tends to zero shows that the error variances tend to zero, but at decreasing rates for the angle, velocity, and acceleration errors. The analysis also suggests the use of multiple-integrator systems to model the angle signal