Reference-Free Automated Magnetic Sensor Calibration for Angle Estimation in Smart Knee Prostheses

In this paper, we present a method for automated calibration of an implanted anisotropic magnetoresistive (AMR) sensor for measuring the internal-external rotation in a prosthetic knee without using any reference measurement. The measurement system consists of a permanent magnet and a 2-D AMR sensor configured and embedded into the prosthesis. Using the physical relation between the measurements of channels of sensor, we proposed a reference-free calibration method through the optimization. The parameters of the measurement model of the sensor obtained via the calibration were directly used in an angle estimator. Two different optimization approaches were tested, and the resultant estimates were compared with the reference angle with the expected ± standard deviation of error of -1.69° ± 0.65° and -1.17° ± 1.13°. The reference-free calibrated estimators were also compared with the reference-dependent least-square estimators. This latter comparison showed an offset error difference among the estimators while the coefficients of determination for the both reference-free and reference-dependent estimators were high, i.e., larger than 0.91. The good performances were maintained even when using a small portion of data for the optimization. The sensor-magnet misalignment effect was also investigated. The misalignment slightly worsened the mean error of the estimates, but neither dramatically affected the variance of error nor the coefficient of determination.