Modeling of magnetic fields on a cylindrical surface and associated parameter estimation for development of a size sensor

This paper develops analytical sensing principles for estimation of circumferential size of a cylindrical surface using magnetic sensors. An electromagnet and magnetic sensors are used on a wearable band for measurement of leg size. In order to enable robust size estimation during rough real-world use of the wearable band, three estimation algorithms are developed based on models of the magnetic field variation over a cylindrical surface. The magnetic field models developed include those for a dipole and for a uniformly magnetized cylinder. The estimation algorithms used include a linear regression equation, an extended Kalman filter and an unscented Kalman filter. Experimental laboratory tests show that the size sensor in general performs accurately, yielding sub-millimeter estimation errors. The unscented Kalman filter yields the best performance that is robust to bias and misalignment errors. The size sensor developed herein can be used for monitoring swelling due to fluid accumulation in the lower leg and a number of other biomedical applications.