A comprehensive method for magnetic sensor calibration: A precise system for 3-D tracking of the tongue movements

Abstract

Magnetic localization has been used in a variety of applications, including the medical field. Small magnetic tracers are often modeled as dipoles and localization has been achieved by solving well-defined dipole equations. However, in practice, the precise calculation of the tracer location not only depends on solving the highly nonlinear dipole equations through numerical algorithms but also on the precision of the magnetic sensor, accuracy of the tracer magnetization, and the earth magnetic field (EMF) measurements. We have developed and implemented a comprehensive calibration method that addresses all of the aforementioned factors. We evaluated this method in a bench-top setting by moving the tracer along controlled trajectories. We also conducted several experiments to track the tongue movement in a human subject.

Multimodal Speech Capture System for Speech Rehabilitation and Learning

“…Although a brief description of this method can be found in [24]–[26], this section provides a more thorough explanation, specific to the MSCS application.…”

“…The magnetic tracer, which can be considered a magnetic dipole point-source as long as its size is negligible compared to its distance from the sensors, is a cylinder with diameter d , thickness l , residual magnetic strength B r dipole moment $\overrightarrow{\mathit{M}}$, and location $\overrightarrow{\mathit{a}}=\left(a_x,a_y,a_z\right)$. The magnetic dipole equation relates these parameters [24], $${\stackrel{false\to }{\mathrm{bold-italicB}}}_{\mathit{Model}}(\overrightarrow{\mathit{R}},\overrightarrow{\mathit{M}})=\frac{{\mathrm{normal\mu }}_0}{4\pi }\frac{[3(\overrightarrow{\mathit{M}}\cdot \overrightarrow{\mathit{R}})\overrightarrow{\mathit{R}}]-\left[{false\Vert \overrightarrow{\mathit{R}}false\Vert }^2\overrightarrow{\mathit{M}}\right]}{{\Vert \stackrel{false\to }{\mathrm{bold-italicR}}\Vert }^5},$$where $\overrightarrow{\mathit{R}}=\overrightarrow{\mathit{s}}-\overrightarrow{\mathit{a}}$ is the distance vector between the sensor and magnetic tracer. The dipole moment can be expressed in terms of its strength and direction, $$\overrightarrow{\mathit{M}}=\frac{B_r{d}^{2}l\pi }{4{\mu }_0}\overrightarrow{\mathit{m}},$$ $$\overrightarrow{\mathit{m}}=\left[\sin \theta \cos \phi \sin \theta \sin \phi \cos \theta \right],$$where θ and φ are the zenith and azimuth angles of the dipole moment, respectively.…”

“…1 is known a priori and does not change. Based on our previous work [24] and literature [27], one approach to solve the inverse problem is to use a numerical optimization method based on an error function. The objective is to estimate the magnetic tracer’s position and orientation ( a x , a y , a z , θ , φ ) that minimize the error, E , between the calculated and measured magnetic fields at the position of every sensor.…”

“…The objective is to estimate the magnetic tracer’s position and orientation ( a x , a y , a z , θ , φ ) that minimize the error, E , between the calculated and measured magnetic fields at the position of every sensor. There is a multitude of mathematical optimization methods available, such as Particle Swarming Optimization (PSO), DIRECT, Powell, and Nelder-Mead [24]–[26]. We have used the latter as a suitable candidate with sufficient accuracy and reasonable computational load for our application, $$E(\overrightarrow{\mathit{a}},\mathrm{normal\theta },\mathrm{normal\phi })=true{\sum }_{i=1}^N{\Vert {\stackrel{false\to }{\mathrm{bold-italicB}}}_i^{\mathit{meas}}-{\stackrel{false\to }{\mathrm{bold-italicB}}}_i^{\mathit{estim}}(\overrightarrow{\mathit{a}},\mathrm{normal\theta },\mathrm{normal\phi })\Vert }^2,$$ $${\stackrel{false\to }{\mathrm{bold-italicB}}}_i^{\mathit{meas}}={\mathbf{\Gamma }}_{\mathit{i}}\cdot {\mathit{G}}_{\mathit{i}}\cdot \left[\left(B_i^x{B}_i^y{B}_i^z\right)+{\mathit{O}}_{\mathit{i}}-{\mathit{EMF}}_{\mathit{i}}\right],$$ $${\stackrel{false\to }{\mathrm{bold-italicB}}}_i^{\mathit{estim}}(\overrightarrow{\mathit{a}},\mathrm{normal\theta },\mathrm{normal\phi })={\stackrel{false\to }{\mathrm{bold-italicB}}}_{\mathit{Model}}(\overrightarrow{\mathit{s}}-\overrightarrow{\mathit{a}},\mathrm{normal\theta },\mathrm{normal\phi }),$$where N is the number of magnetometers (24 in the current version), ${\stackrel{false\to }{\mathrm{bold-italicB}}}_i^{\mathit{meas}}$ and ${\stackrel{false\to }{\mathrm{bold-italicB}}}_i^{\mathit{estim}}$ are the measured and estimated magnetic field values at the i th magnetometer, respectively.…”

“…G i and O i are the gain (3×3 diagonal matrix) and offset (1×3) of the i th magnetometer, respectively, and are required to ensure that every sensor provides the same measured outputs when exposed to the same magnetic field. Due to process variations during manufacturing and other soft-iron magnetic effects, it is imperative for all magnetic sensors to be carefully calibrated before being used for localization [24]. G i also includes a coefficient that converts the sensor 16-bit digital output to gauss unit.…”