# An Interactive Transient Model Correction Active Sonar Target Tracking Method
## 3 Simulation Verification and Offshore Testing
### Simulation Verification
#### 3.1.2 Simulation Results and Analysis  
Figure 4 compares the processing results of the simulation data using the conventional KF tracking method and the TMC tracking method. In Figure 4a, when the target transitions from uniform to accelerated motion, the tracking trajectory starts to deviate from the true target trajectory, and the tracking error gradually increases. In Figure 4b, when using the TMC tracking method, the target tracking trajectory deviates less from the true trajectory. Figure 4c further compares the tracking results of the conventional KF method with those of the TMC method. It is evident that the tracking performance of the TMC method is superior to that of the conventional KF method. In Figure 4d, the residual covariance of the two tracking methods is compared after normalization. During the first 15 scan cycles (when the target is in uniform motion), the residual covariance of the KF tracking is relatively small. As the target transitions into accelerated motion after three cycles (after the 18 th scan cycle), the residual covariance of the KF tracking gradually increases. The residual covariance of the TMC tracking method is comparable to that of the KF tracking during the uniform motion stage and the initial period of accelerated motion. In the latter half of the trajectory, as the residual covariance of the KF tracking gradually increases, the residual  
Figure 3: True trajectory and sonar measured values of the underwater simulated target. (**a**) The trajectory in cartesian coordinates, (**b**) The trajectory in polar coordinates.  
covariance of the TMC tracking method remains at a relatively low level comparable to that during the uniform motion stage.  
Figure 4: _Cont_.  
The target's distances on the X- and Y-axis obtained from both KF tracking and TMC tracking are converted to the target's radial distance and azimuth for comparison with the true value and measurement value, as shown in Figure 5. To illustrate the deviation of the measurement or tracking estimation points from the true target position, the position distance error is defined as the straight-line distance between the true target position and either the measurement point position or the filtered output position of the target tracking. The RMSE of the position distance and azimuth for KF tracking are 237.5 m and 5.17\({}^{\circ}\), respectively, while those for TMC tracking are 57.33 m and 0.49\({}^{\circ}\), respectively. The TMC tracking method improves the accuracy of both the target's radial distance and azimuth tracking.  
Figure 4: Comparisons of tracking results between the conventional KF method and the TMC method. (**a**) Conventional KF tracking results, (**b**) TMC tracking results, (**c**) Comparison of target trajectories, (**d**) Comparison of normalized residual covariance.  
Figure 5: _Cont_.  
Mean-square error (MSE) analysis of the simulation test results was carried out, as can be seen in Table 2. Due to model mismatch, the KF tracking MSE significantly increased. However, after the TMC method is processed, the tracking error can be reduced.