# Stationary Target Identification in a Traffic Monitoring Radar System
## 4 Proposed Stationary Target Identification Method  
To classify the stationary targets in the detection results, we can simply select targets with a relative velocity of zero and remove them. However, even for a stationary target, the relative velocity cannot always be zero because the location of the target may fluctuate slightly along the radar signal reflection path. Therefore, we propose a method for discriminating stationary targets that can be applied more generally and stably. In this work, we use the detected targets in the angle-velocity domain to determine the stationary targets. Figure 8 shows the target detection results in the angle-velocity domain, which correspond to the detection results shown in Figure 7.  
Figure 6: Method of estimating the position of the target using the radar detection result. Figure 7: Target detection result in the Cartesian coordinate system. As shown in Figure 8a, one dominant curve can be found in the vicinity of zero velocity from the detection result. In the figure, the unit for the angle axis is degree (i.e., deg.) and the unit for the velocity axis is m/s. We can predict that stationary targets in the angle-velocity domain will exist on a specific straight line because the relative velocity is close to zero. However, as shown in Figure 8b, the velocity values of the detected points near zero velocity are not completely zero, and there is some variation around the curve. Although general linear regression methods, such as the linear least squares (LLS) [25], are applied to the given data, an appropriate trend line cannot be found because they estimate the line using all outliers. In other words, even points corresponding to the targets with velocities greater than zero are used to find the trend line in the LLS method, which degrades the estimation performance. Thus, we use the method of RANSAC [13], which is one of the methods for fitting inliers in the presence of outliers. In the case of the RANSAC algorithm, the optimal trend line is found by iteratively estimating the line while randomly sampling the minimum points required to determine the model parameter among all the original points. Therefore, outliers are excluded from the trend line estimation, and the accuracy of the method is very high. The RANSAC algorithm is performed in the following steps:  
1. Several sample points are randomly selected, and model parameters are determined from the selected sample points. 2. The number of sample points close to the determined model is counted. 3. If the fraction of the number of inliers over the total sample points in the set exceeds a predefined threshold, re-estimate the model parameters using all the identified inliers. 4. Otherwise, Steps 1 to 3 are repeated again. Figure 8: Target detection results in the angle-velocity domain: (**a**) velocity ranges from \(-40\) m/s to \(40\) m/s (**b**) velocity ranges from \(-1\) m/s to \(1\) m/s (same data as Figure 8a, but reduced velocity range). In the RANSAC method, we have to set the type of function for fitting and determine how to calculate the distance between the model and the sample points. Ideally, stationary targets should be on a straight line with zero velocity, so we set the linear function for fitting. We also calculated the distance as:  
\[d_{i}=\sum_{i=1}^{M}(v_{i}-f(v_{i}))^{2}, \tag{15}\]  
where \(M\) is the total number of detected targets and \(f(\cdot)\) is the function for fitting. In addition, we set the minimum sample size and maximum distance for inliers as two and one, respectively. In our work, we used the MSAC algorithm [14], which is a enhanced version of RANSAC. The MSAC algorithm performs better than the RANSAC algorithm because the cost of the fitting function is not set uniformly for sample points, but set based on the deviation from the required functional relation [26; 27]. Including the target detection results in Figure 8, we applied the proposed MSAC-based method to several successive detection results. Figure 9 shows the estimation results for the trend line.