## 4 Experiment Study
### Bounding Box-Based Pedestrian Tracking with Occlusions  
The simulation was also conducted on the PETS09-S2L1 dataset [65] within the MOT-15 challenge, a complex scenario with up to eight pedestrians engaging in unusual patterns. The IOU matching utilized the detection box from the previous frame to compute the IOU with the current frame detections. A threshold of \(IOU_{\text{Threshold}}~{}=0.3\) was set for a match to be considered valid. If the IOU matching failed to find a maximum value due to occlusion, the Kalman filter's prediction was used to estimate the target's new position and continue tracking. However, the KF-based VOT algorithm failed to maintain tracking under occlusion conditions. The AKF-ALS VOT algorithm demonstrated robustness in maintaining the identity of the pedestrian target even when the IOU matching failed due to occlusion due to its dynamic covariance estimation, which allows the filter to adapt its parameters in response to the evolving state of the system. This adaptive mechanism is crucial for handling occlusions and erratic pedestrian movements. The AKF-ALS VOT algorithm improves upon the standard KF VOT by dynamically adjusting the process and measurement noise covariances. The state vector remains consistent with the classic AKF, with the following representation:  
\[X=[x,y,h,w,\dot{x},\dot{y}]^{T} \tag{24}\]  
where \(x\) and \(y\) denote the horizontal and vertical position of the pedestrian in the video frame (in pixels), respectively, and \(\dot{x}\) and \(\dot{y}\) denote the horizontal and vertical velocity of the pedestrian (in pixels per frame). \(h\) and \(w\) denote the height and width of the bounding box around the pedestrian (in pixels), respectively. The ALS algorithm updates the process noise covariance matrix \(Q\) and the observation noise covariance matrix \(R\) iteratively. The innovation sequence is used to calculate the autocovariance, which in turn adjusts \(Q\) and \(R\) to respond to abrupt changes in the tracked object's motion. The trajectory is shown in Figure 5.  
As indicated by the figure, the tracking of pedestrians in scenarios obstructed by objects such as a light pole, can present challenges for bounding box detection methods. However, the implementation of the adaptive Kalman filter with adaptive least squares (AKF-ALS) algorithm demonstrates robustness in tracking despite failures in bounding box detection under such conditions. \begin{table}
\begin{tabular}{c c c c} \hline
**RMSE (in Pixels)** & **Projectile** & **Free-Fall Bouncing** & **Back-and-Forth Linear** \\ \hline AKF-ALS & 1.05 & 2.76 & 0.89 \\ KF & 4.67 & 8.35 & 2.31 \\ \hline \end{tabular}
\end{table} 
Table 1: Comparisons of RMSE (in pixels) between AKF-ALS-based and KF-based VOT subjected to projectile motion, free-fall bouncing motion, and back-and-forth linear motion. To demonstrate the comparative performance of the accuracy and robustness, we use the RMSE in (23), the identity switches, and the track fragmentation as the metrics. The identity switches metric measures the number of times the tracking algorithm incorrectly switches the identity of the tracked object. Fewer identity switches indicate a more robust tracking performance. The track fragmentation evaluates the continuity of the tracking throughout the sequence. Lower numbers imply fewer instances where tracks are broken and later reacquired. We compare the proposed ALS-AKF algorithm with the classic adaptive KF algorithm using [PERSON]'s method in [66], as shown in Table 2.  
As is indicated from the table above, the AKF-ALS VOT algorithm demonstrated a markedly higher precision with a root mean square error (RMSE) of only 5.5 pixels, compared to the classic AKF VOT's 10.7 pixels. Robustness in maintaining pedestrian identity was also significantly improved in the AKF-ALS VOT, which had a mere single identity switch, whereas the classic AKF VOT recorded eight. Additionally, the AKF-ALS VOT showed greater continuity in tracking with only two instances of track fragmentation,