## 4 Results
### Real Data  
The two types of data: video generated by two cameras, and RADAR generated by an automotive sensor with two receive antennas, were obtained from an experiment concerning the moving of a car. In Figure 7, some frames extracted from the video data are presented. The scene recorded by the cameras was registered by a 24 GHz RADAR sensor with two receive antennas as well. The specific parameters of this RADAR sensor are the following:  
* Tx modulation scheme--rapid chirps;
* Operation bandwidth--200 [MHz];
* Field of view (10 dBsm)--0 deg \(\pm\) 75 deg @ 20 [m];
* Detection range (FoV): \(\bigcirc\) 5 dBsm @ 0 deg azimuth--68 [m] \(\bigcirc\) 10 dBsm @ 0 deg azimuth--105 [m]
* Range resolution--0.75 [m];  
Figure 6: Results of the fourth experiment with simulated data: (**a**) third order polynomial trajectory; (**b**) waveform of the result obtained after the simulated tracking; (**c**) the effect of the wavelet-based polynomial fitting method. * Range precision--0.3 [m];
* Speed resolution--0.24 [m/s];
* Speed precision--0.05 [m/s];
* Azimuth angle precision--0.4 [\({}^{\circ}\)];
* Cycle count--50 [ms]. We pre-processed the corresponding RADAR signals: separating the moving targets of clutter, converting the polar coordinates of the target into Cartesian coordinates, and applying a geometric-based data association of the moving targets' measurements. Next, we applied Kalman filtering to the obtained data. The blue points in the example in Figure 1 represent the result of geometrical data association of measurements delivered by one of the receive antenna and the red points represent the result of Kalman filtering of those data. Next, we achieved the fusion of results obtaining the blue points in Figure 8. The bottom zone, in this figure (marked in yellow), contains untrusting target positions whose distances towards sensors exceed the maximal detection distance. The middle zone in Figure 8, marked in orange, contains target positions recorded before the car starts, corresponding to the frames in Figure 7a,b. The upper zone in Figure 8, marked in light blue, corresponds to the frames of video recording neighbors of the frames in Figure 7e,f. These frames show the target car stopping maneuver. Therefore, the target car's movement starts at a distance of approximately 85 m, follows a linear trajectory and stops near the stationary car carrying the sensor. The spreading of the blue points illustrates the uncertainty at the output of Kalman filter. To reduce this uncertainty, we applied the implicit polynomial fitting procedure and the wavelet-based fitting procedure. We first applied the implicit polynomial fitting procedure, imposing a polynomial degree equal to one to the sequences \(\{x_{t}\}\) and \(\{y_{t}\}\), obtaining the coordinates of the points represented in green in Figure 8. So, the green line in Figure 8 represents the result of the implicit polynomial fitting procedure. Figure 7: Real video data used for the last experiment, [16]: (**a**) right camera before car starting; (**b**) left camera before car starting; (**c**) right camera during car moving; (**d**) left camera during car moving; (**e**) right camera after car stopping; (**f**) left camera after car stopping. The uncertainty at the output of the Kalman filter was eliminated for the car positions situated at a distance towards the RADAR sensor inferior to 50 m.  
Next, we applied the wavelet-based polynomial fitting method. For the sequence \(\{x_{t}\}\), we applied [PERSON]'s denoising method, computing the DWT with the aid of Daubechies 20 MW and six levels of decomposition. We extracted the polynomial part of the result. We computed the DWT using the Haar MW (which has a single VM) with eight decomposition levels obtaining the horizontal coordinates of the points marked in red in Figure 8. We modelled the sequence \(\{x_{t}\}\) with a zero-degree polynomial.