## 5 Experimental Setup and Results Discussion  
### Experimental Environment  
In this experiment, we conducted an indoor positioning system accuracy test in a laboratory space. As shown in Figure 1, a 3D coordinate system defined as (X, Y, Z) was established within the space. This coordinate system consists of a 12 \(\times\) 8 \(\times\) 4 grid, with each unit measuring 61 \(\times\) 61 \(\times\) 55 cm. In the figure, the green oval represents the base station (Anchor), and the gray inverted triangle represents the tag to be located (Tag). The base stations were placed in three corners of the laboratory and connected to a computer. Bilateral and bidirectional operations were then performed on the tags as described in Section 2. After measuring the distance, JAVA was used to simulate the TOA positioning  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Coordinates**} & **Triangle Centroid Algorithm** & **Inner Triangle Centroid** & **Intersection Midpoint** \\  & **(TCA) Error (cm)** & **Algorithm (ITCA) Error (cm)** & **Algorithm (IMA) Error (cm)** \\ \hline \((1,2)\) & 23.00 & 20.22 & 26.19 \\ \((3,1)\) & 3.30 & 10.84 & 10.85 \\ \((3,6)\) & 24.30 & 7.88 & 8.05 \\ \((5,3)\) & 1.92 & 14.58 & 17.00 \\ \((7,3)\) & 19.95 & 12.11 & 13.59 \\ \((7,5)\) & 63.68 & 8.54 & 8.57 \\ \((10,7)\) & 188.45 & 14.48 & 14.48 \\ \((11,3)\) & 80.49 & 9.98 & 10.03 \\ \((11,5)\) & 145.55 & 6.93 & 6.93 \\ \((12,6)\) & 202.96 & 12.92 & 13.00 \\ Average error \(\mu\) (cm) & 75.36 & 11.85 & 12.87 \\ Standard deviation \(\sigma\) (cm) & 72.91 & 3.76 & 5.36 \\ Algorithm time (\(\mu\)s) & 17.49 & 33.28 & 13.65 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Localization error for various algorithms.  
method using the measured experimental values before finally measuring the positioning error through the coordinate system.  
The UWB experimental module is integrated with a microprocessor and a DW1000 UWB chip manufactured by Qorvo, Inc., Greensboro, NC, USA, as shown in the illustration in Figure 1. The DW1000 UWB chip operates within a carrier frequency range of 3.5 to 6.5 GHz, supporting seven UWB channels. It transmits low-power UWB signals with a typical output power of \(-10.3\) dBm/MHz, in compliance with FCC and ETSI emission regulations. The signal type utilizes burst position modulation (BPM) combined with binary phase shift keying (BPSK) for data encoding. The transmitted UWB pulses are extremely short, with durations of approximately 1 nanosecond, enabling precise time-of-flight (ToF) measurements and positioning accuracy of up to 10 cm. The control program in Arduino Nano is burned and the SPI bus is used to communicate with the UWB chip. Modules are divided into two types: anchor and tag according to different burning programs. The base station and the tag transmit information using ultra-wideband. In order to observe the measured distance value on the computer, the base station module uses a UART and then uses a TTL-USB. The module connects to the computer to send data to the computer.  
Arduino Nano uses ATmega328 microcontroller manufactured by Microchip Technology Inc., USA, as the core of the control development board. It has 22 digital I/O ports and 8 analog I/O ports. It uses a 16 MHz crystal oscillator. It has a bootloader and does not need to be burned through other programs. Following recording, the program can be uploaded directly through the USB, so the language can be quickly compiled and implemented, and there is an open source for users to communicate. Therefore, this experiment uses Arduino Nano as the microprocessor controller to communicate with the ultra-wideband chip. Finally, the data is transmitted to the USB-STC-ISP module through UART (RS-232). The module uses a USB to connect to the computer to transmit the data to the computer.