# An Improved Kernelized Correlation Filter Algorithm for Underwater Target Tracking
## 3 Improved Kernelized Correlation Filter Algorithm
### Adaptive Filter Update Strategy Based on PSR  
The traditional KCF adopts a frame-by-frame linear updating strategy in the update of the filter model, which enhances the adaptability of the filter model to environmental changes. However, this strategy also leads to many problems. First, the model is updated frame by frame, making the update too frequent, which not only leads to a large amount of calculation, but also causes a decrease in robustness due to overfitting. Second, when the target disappears and appears again, the updating method of linear interpolation will introduce erroneous information to the filter model. In order to solve this problem, an adaptive filter update strategy based on PSR is proposed.  
In the process of the filter model updating, some method should be used to make the detection tracking process aware of whether the tracking result has a large deviation, and to timely update the model according to the result. The PSR is used as the basis for judging whether the tracking result is wrong. The PSR calculation process is:  
\[PSR_{t}=\frac{p-\mu}{\sigma} \tag{20}\]  
where \(p\) is the response diagram peak value of the \(t\)th frame. The area around the peak is the sidelobe area. \(\mu\) and \(\sigma\) are the mean and standard deviation of the sidelobe regions.  
Figure 3 is the PSR obtained by KCF in the image sequences.  
It can be seen from Figure 3 that the PSRs of the 8 th, 9 th, 10 th, 11 th, and 12 th frames are generally lower, while the 45 th and 68 th frames are higher. It can be analyzed that the disappearance of the target appears in the 8 th, 9 th, 10 th, 11 th, and 12 th frames, and the target in the 45 th and 68 th frames is  
Figure 3: The peak to sidelobe ratio (PSR) of image response diagram.  
clear and normal, so it can be concluded that the larger the value of the PSR is, the better the tracking result. Based on this conclusion, an update threshold is set. In the tracking process, the tracking filter model is updated only when the PSR of the current frame is higher than the threshold. Otherwise, it is not updated. With this update strategy, there are several advantages. First, this is an indirect update method, which reduces the amount of computation caused by frequent frame-by-frame updates to a certain extent. Secondly, the proposed update strategy can automatically avoid updating the model under the current unfavorable situation when encountering the situation of tracking deviation, so as to prevent the model from drifting due to the introduction of erroneous information.  
The filter model is mainly composed of two parts: One is the regression coefficient \(\alpha\), and the other is target template \(x\) in the nonlinear space. \(x\) is a feature extracted from the target region. \(\alpha\) is obtained by the ridge regression training. The update process of the entire filter model is as follows:  
\[\left\{\begin{array}{l}\alpha_{t}=(1-\eta)\times\alpha_{t-1}+\eta\times \alpha_{t-1}\\ x_{t}=(1-\eta)\times x_{t-1}+\eta\times x_{t-1}\end{array}\right. \tag{21}\]  
where \((\alpha_{t},x_{t})\) indicates the filter model trained by the new detection results at the \(t\)th frame. \((\alpha_{t-1},x_{t-1})\) indicate the filter model at the \(t-1\)th frame and \(\eta\) is interpolated coefficients.