## 1 Introduction  
The problem of tracking targets using the measurements of an automotive RADAR sensor supposes the integration of measurements into a longer-term picture [1]. Multiple target tracking is realized by the cooperation of two algorithms: a measurement-to-track data association algorithm and a tracks filtering algorithm. Tracks filtering, usually realized by Kalman filters, is the process of estimating the trajectory (i.e., position, velocity, and possibly acceleration) of a track from measurements (e.g., range, bearing, and elevation) that have been assigned to that track. A trajectory estimate always has an associated uncertainty, as can be observed in Figure 1. This uncertainty makes the target's localization more difficult. Hence, the reduction in this uncertainty is very important for the trajectory's accuracy and the target localization improvement. Kalman filters are widely used to estimate the state of a linear dynamical system from noisy measurements [1; 2; 3; 4]. Despite its wide use and success, the Kalman filter is not completely automated yet, and practitioners employing the Kalman filter still must realize the manual tuning of its parameters. As a result, there is a certain incertitude at the output of the Kalman filter. A way to reduce this value consists of the adaptive selection of parameters during the filtering process. We will call such a filter an adaptive Kalman filter in the following.  
Many researchers have proposed methods for automatically tuning the Kalman filter's parameters. They proposed different signal processing methods to accomplish this task. For example, they tried to jointly learn the parameters and state/output sequence. To do this, they proposed different strategies, for example, the expectation maximization algorithm, or different optimization approaches such as the simplex algorithm, the coordinate descent algorithm, genetic algorithms, nonlinear programming using finite differencing to estimate the gradient, Bayesian optimization, reinforcement learning, and automatically tuning hyper-parameters in the least squares [2].  
In this paper, we propose a blind approach based on polynomial fitting to reduce the tracker's uncertainty. This approach starts from the conjecture that almost all trajectories encountered in automotive RADAR and global positioning system (GPS) localization problems are polynomials in rectangular coordinates because the roads are polynomials, as can be observed in the example in Figure 2.  
We highlight, by simulations, the improvement of the estimated trajectory's accuracy due to the polynomial fitting in the case of single or multiple targets, and, further to this, we propose three new polynomial fitting methods for the trajectories estimated by Kalman filters. The first two data fitting methods, which are proposed in this paper, fuse the two  
Figure 1: An example of a trajectory estimated by a tracker based on a Kalman filter.  
Figure 2: Roads in the neighborhood near our faculty building [5; 6].  
trajectories, which correspond to the two coordinate axes, \(x\) and \(y\), obtained at the output of the Kalman filter into a polynomial \(y(x)\) by separate polynomial fitting on each axis. The third proposed data fitting method uses wavelets and has two steps for each coordinate axis: denoising and polynomial part extraction. It compares favorably to the first two data fitting methods proposed. The effect of the proposed post-processing methods is visible, the accuracy of targets' trajectories estimations being hardly increased.