# Gesture Recognition of Sign Language Alphabet Using a Magnetic Positioning System
## 2 Materials and Methods
### Magnetic Positioning System (MPS)
#### 2.1.1 MPS System Architecture  
The transmitting magnetic node is one of the main elements of the magnetic tracking system. Its task is to transmit in space a known signal to an array of receivers, so that it is possible to track its position in the working volume. The electromagnetic emission occurs by means of a coil appropriately excited with an oscillating voltage of known frequency. Each coil is coupled to a capacitor in parallel, thus forming a resonant LC circuit. Receivers are implemented as passive LC circuits. The oscillating magnetic field of each active node induces a measurable voltage on receivers, according to [PERSON]'s law. The magnetic field of a single coil is modeled as an elementary magnetic dipole [39]. The position and orientation of each magnetic node (the orientation being defined as the direction of the coil central axis) are estimated by measuring the induced voltages on each receiver, then inverting the mathematical model by means of numerical optimization. A photo of the transmitting nodes mounted directly on the fingers is shown in Figure 2. The benefit of this configuration is that it is modular and one or more nodes can be easily removed if there is no need to track all fingers. Furthermore, a photo of the tracking nodes mounted on a glove is shown in Figure 3. The advantage of this alternative configuration is that it is quick and convenient to wear. Furthermore, the glove is comfortable and suitable for usage over long periods of time without causing distress to the user. Coils on the fingers are supplied with a square wave generated by a custom device described in Section 2.1.2, while the two coils on the back of the hand (Figure 3) are supplied by a Cypress PSoC 5 LP microcontroller, as described in [36; 38]. Supplied signal frequencies are chosen to fall on the resonance band of the receivers. The chosen frequencies are 175,138, 177,075, 179,021, 180,961, 183,031, 184,971 and 187,043 Hz. The working volume of the MPS is shown in Figures 3 and 4; the reference frame is indicated. There are overall 24 receivers inserted into wooden panels. Voltages are measured by means of analog-to-digital converters (ADCs) integrated on Texas Instruments Delfino TMS320F28379D microcontroller units (MCUs). Each MCU reads 4 receivers. Another MCU is used in a master-slave configuration to control all the others, and to transmit data to a PC via serial connection. A custom software calculates the position and orientation of each node. The measurement rate of the MPS with seven nodes is 31 Sa/s, therefore enabling robust tracking even in the presence of fast motion or shaking of the hand. The Euclidean and angular error are very similar to the six-nodes version of the MPS [36], with mean values being, respectively, 3.5 mm and 2.6\({}^{\circ}\). In Reference [36], the ADCs were configured to work in 12-bit single-ended mode, while the ADC voltage range was 3 V. Transmitting nodes were supplied with a square wave whose amplitude was 2.5 V. A constant 1.5 V signal offset was added to the input of each ADC in order to make the received signal oscillate between 0 and 3 V. For the present work, the addition of the seventh node (the configuration being the same) caused saturation issues on the ADCs. In order to avoid saturation and to raise the signal-to-quantization-noise ratio (SQNR), we reconfigured the ADCs to work in 16-bit differential mode and removed the signal offset. The differential mode allows to measure signals in the range (\(-\)3, 3) V; the SQNR is thus increased by a factor of \(2^{3}\). With the new configuration, it has been possible to use seven transmitting nodes supplied with a 3.3 V square wave, avoiding saturation issues. Figure 3: Tracking nodes of the MPS mounted on a glove, shown inside the MPS operational volume. Letters have been articulated as if an interlocutor were watching from the \(xy\) plane (e.g., letter V is shown on the right). Figure 2: (**Left**) Tracking nodes of the MPS mounted directly on the fingers.