## 7 Application to UWB Doppler Radar Simulation
### Tracking of Medium Maneuvering Target
#### 7.1.3 Evaluation Results  
Figure 4 shows the simulation results for \(a_{\text{D}}^{2}=0.04\) ((a) \(R_{\text{xv}}=9.0\), (b) \(R_{\text{xv}}=1.0\)). Clearly, the filters using velocity measurements achieve greater accuracy than the best \(\alpha\)-\(\beta\) filter in both cases. For \(R_{\text{xv}}=9.0\), the mean steady state prediction RMS errors (\(E[\epsilon_{k}]\) in \(2<kT<4\)) of the RA, PVM Kalman and proposed filters are 2.48, 2.30 and 2.33 cm, respectively. These results indicate that the proposed filter achieves better accuracy than the RA filter even for realistic situations. Although the PVM Kalman filter is slightly better than the proposed filter, because it considers the correlated noise in  
Figure 3: UWB Doppler radar simulation scenario: (a) radar positions and true orbit; (b) true acceleration; UWB: ultra-wideband.  
the \(x\)- and \(y\)-axes, their errors are almost the same. This shows that the steady state performance of the PVM filter is close to that of the \(\alpha\)-\(\beta\)-\(\eta\)-\(\theta\) filter, and the \(\alpha\)-\(\beta\)-\(\eta\)-\(\theta\) filter analysis is effective in performance predictions of the PVM Kalman filters. The relationship of these filters is similar to the traditional \(\alpha\)-\(\beta\) and position-only-measured Kalman filters. The computational load of the \(\alpha\)-\(\beta\)-\(\eta\)-\(\theta\) filter is considerably smaller than that of the PVM Kalman filter; the mean calculation times for each \(k\) of the \(\alpha\)-\(\beta\)-\(\eta\)-\(\theta\) and PVM Kalman filters are 14.0 and 38.1 us using an Intel Core i7-4600U [EMAIL_ADDRESS] GHz 2.70 GHz processor and Scilab 5.5.0. This is because the \(\alpha\)-\(\beta\)-\(\eta\)-\(\theta\) filter does not require the adaptive calculations of the gains and error covariance matrices. In addition, although the difference in steady state accuracy between the proposed and best \(\alpha\)-\(\beta\) filters is small (Figure 4b), the proposed filter achieves better accuracy even for \(R_{\mathrm{xv}}\)=1. The mean steady state prediction RMS errors of the RA, PVM Kalman and proposed filters are 3.84, 3.61 and 3.68 cm, respectively, and these results lead to the same conclusions as those from Figure 4a. These results are matched to the analysis results presented in the previous section.  
We next investigate the performance of the proposed filter for different values of \(a_{\mathrm{c}}\) to assess appropriate settings. Table 3 shows the steady state RMS error (\(E[\epsilon_{k}]\) in \(2<kT<4\)) for different values of \(a_{\mathrm{c}}\) for \(R_{\mathrm{xv}}=9.0\); \(a_{\mathrm{c}}=0.4\) m/s\({}^{2}\) is assumed as a rough approximation for the mean acceleration of the target, and \(a_{\mathrm{c}}=0.1\) and 1 m/s\({}^{2}\) are considered as the order of the acceleration. The performance of the proposed filter deteriorates for \(a_{\mathrm{c}}=0.1\) and 1 m/s\({}^{2}\). This is because the difference between the true target accelerations and these very rough approximate accelerations is too large. This means that the proposed strategy requires some minimum degree of accuracy in target acceleration prediction to perform adequately. However, the \(a_{\mathrm{c}}=0.4\) and 0.6 m/s\({}^{2}\) cases have almost the same accuracy, implying that strict values of the target acceleration are in practice not required with UWB Doppler radars. As a method to obtain an approximated acceleration, communications of the tracking systems and the accelerometers embedded in targets can be considered. Many sensing targets have acceleration sensors, e.g., the robots and vehicles have inertial sensors, and humans have accelerometers embedded in smart phones. In the near future, the Internet-of-Things technology will make data communications between robots, smart phones and radar possible. Thus, we can obtain approximated acceleration based on this novel technology.