# Robust Bluetooth AoA Estimation for Indoor Localization Using Particle Filter Fusion
## 4 Simulation Experiments and Analyses  
For the navigation and positioning problem based on moving targets, a simulation experiment was conducted to verify the effectiveness of the proposed algorithm. In this chapter, we tested the effectiveness of an improved Bluetooth AoA navigation algorithm. This algorithm combines particle filtering and the MUSIC algorithm, and we evaluated it through experimental simulation. The main aim of the simulation was to assess how the algorithm performs under different signal-to-noise ratios, numbers of snapshots, and numbers of particles when the target object moves at either a uniform or variable speed. The simulation experiment showed that, with a certain number of particles and snapshots, the improved algorithm can accurately and consistently navigate and track targets with uniform and variable speeds in space. 1. Simulation experiment on the impact of the target object's uniform motion on the particle filter-based DOA navigation and tracking algorithm for moving targets. Experimental conditions: L-shaped acoustic array, four array elements on each X-axis and Y-axis, and 0.2 m between array elements (the distance between array elements is greater than half the wavelength of the signal). The initial azimuth and elevation angles were set at (45\({}^{\circ}\), 45\({}^{\circ}\)), and the wave signal was assumed to be a parallel wave. The number of snapshots was 256, the number of particles was 800, and observation noise was introduced with a signal-to-noise ratio of 10 dB. The entire process was iterated over 50 steps. Figure 5a shows the deviation between the real trajectory of the target object in the spatial direction and the trajectory predicted by the algorithm. Figure 5b,c shows the relationship between the predicted angle and the true angle of each iteration from two angles: the azimuth angle and the overhead angle. The results of the figure show that, except for the target's starting position, the direction angle of the target object predicted by the algorithm deviated significantly, and the deviation between the predicted angle and the true angle at the remaining time is small. Therefore, it is concluded through simulation that under uniform speed conditions, the moving target DOA navigation and tracking algorithm based on particle filtering has good navigation and tracking performance for moving targets. 2. The effect of the target object under variable speed motion on the improved DOA navigation algorithm for Bluetooth signals based on particle filtering algorithm. Experimental conditions: Assuming that the target object is stationary at the initial moment based on the conditions of Experiment 1, the initial velocity of each particle is modified to be 0.3\({}^{\circ}\)/s, and the acceleration is randomly transformed in the range of [\(-\)0.5, 0.5]. To better observe the tracking effect of the algorithm, the initial position of the particles is initialized as the real position. The simulation results are shown in Figure 6.  
Figure 6a shows the deviation of the target object orientation trajectory and the algorithm-predicted trajectory in terms of the spatial orientation angle in the variable-speed condition. Figure 6b shows the prediction results of the algorithm's azimuth and elevation angles on the target's true angle under the variable speed condition. As can be seen from the change in the spatial angular position of the target in Figure 6a, the target object experienced accelerated motion, a decelerated motion process, and a reverse motion state during the whole moving process. In the simulation process, the trend of the direction change in the predicted curve and the trend of the target curve change is consistent, and the azimuth and elevation angles fluctuate around the actual value with small errors. It is concluded that in the case of variable speed motion of the target object, the algorithm can still predict the direction of the target correctly and track the target accurately. Figure 5: Tracking results under uniform velocity conditions.