*5.2. Performance Evaluation*

The simulation parameters associated with the proposed schemes, comprising the initial target existence probability, track confirmation threshold and track termination threshold were assumed to obtain the greatest capability. These experiment parameters are shown in Table 3.

The results were obtained from 600 Monte Carlo simulations for both transmit modes. During each simulation run, three trackers (the extended Kalman filtering technique, LMIPDA, LMIPDA-DDA) were applied to the same measurement data employing three schemes: (1) Updating tracks via target range measurements based on extended Kalman filtering as presented in [12], (2) updating tracks via target range measurements based on the regular trackers LMIPDA, and (3) updating tracks via both target range measurements and the supplementary target velocity measurements based on the advanced trackers LMIPDA-DDA.


**Table 3.** Tracker parameter settings.

The comparisons of NCTT across three methods are illustrated in Figure 5a,b. The average computation time is presented in Table 4.

**Figure 5.** The performance of the number of confirmed true tracks (NCTT): (**a**) CW mode; (**b**) pulse mode.

**Table 4.** The average computation times in CW and pulse transmission methods.


As shown in Figure 5 and Table 4, the LMIPDA-DDA algorithm had an enhanced confirmation response to multi-target observations. Meanwhile, the accuracy of NCTT provided by the LMIPDA-DDA algorithm was obviously superior to the LMIPDA algorithm. The LMIPDA method played an important part on single scan tracking but was not robust enough for abrupt changes in target tracking, while the LMIPDA-DDA method played an important part on multiple scan tracking. The extended Kalman filtering method as stated in [12] was slightly better than the proposed DDA scheme. The nonlinear filtering technique was optimal in this case.

As shown in Table 4, a faster calculating speed can be obtained. With Doppler data association, the average operation times of the LMIPDA-DDA algorithm were lower. Furthermore, the top operation times of the LMIPDA-DDA algorithm were also lower than other methods due to data association. Faster termination of false tracks can be observed. As can be expected, the nonlinear filtering technique spent the most time to implement iterated operation. However, if the distribution of target velocity

component is hard to distinguish from the distribution of false target velocity component, the tracking capability of data association method would reduce to that of the traditional method. It is worth noting that if the proposed system switched between CW and phase modulated pulse transmission modes, the measurement errors of target range and Doppler would vary as presented in Table 2. The errors would undoubtedly impact the multi-target tracking performance under consideration. To simplify the discussion, the problem has been ignored in this paper.

The comparison of NCFT across methods is shown in Figure 6. As can be seen from Figure 6, a remarkable reduction in NCFT was seen for both CW and pulse modes. The presence of confirmed false tracks can severely limit confidence level and usage of trackers; better discrimination of false tracks allows for reduction of track confirmation threshold, which leads to better response to target measurements. When the transmitter was switched to pulse mode, target Doppler measurements got larger errors as present in Table 2. As can be expected, a remarkable reduction in NCFT was still obtained from Figure 6b. That is because the distribution of target Doppler measurements could be discriminated from that of false Doppler measurements.

**Figure 6.** The performance of the number of confirmed false tracks (NCFT): (**a**) CW mode; (**b**) pulse mode.

The comparison of the ability of capturing the target across methods is presented in Figures 7 and 8. Performance difference for targets 1–3 is given in this section. The rest of targets show a similar trend. The proposed DDA method had a better confirmation response to target measurements in most cases.

**Figure 7.** *Cont.*

**Figure 7.** The capabilities of capturing targets 1–3 in CW mode; (**a**) target 1; (**b**) target 2; (**c**) target 3.

**Figure 8.** The capabilities of capturing targets 1–3 in pulse mode; (**a**) target 1; (**b**) target 2; (**c**) target 3.

As can be seen from Figure 7c, during the first 10 scans, only the proposed DDA method had captured the underlying target 3. We can explain the phenomenon by understanding that the LMIPDA-DDA algorithm works on single scan measurements, while the extended Kalman filtering technique stated in [12] works on multiple scan measurements. Hence, the former will be more adaptable to abrupt changes in target measurements.

Furthermore, as shown in Figure 8, the proposed DDA method and the extended Kalman filtering technique suffered from a longer true track confirmation delay compared with the CW mode case, as presented in Figure 7, because target information flow rate from the target measurements was lower. It is easy to see that, if the distribution of target Doppler measurements is indistinguishable from the distribution of false Doppler measurements, the performance of the trackers with DDA method would reduce to that of the trackers without DDA method.

The comparisons of target resolution capability across methods are given in Figure 9a,b.

**Figure 9.** The comparisons of mean square error (MSE) performance across methods: (**a**) MSE in X-axial; (**b**) MSE in Y-axial.

As can be seen from Figure 9a,b, the target resolution capability offered by the LMIPDA-DDA algorithm was better than the LMIPDA algorithm at each scan. However, as can be expected, the performance provided by the nonlinear filtering technique was slightly better than the proposed DDA scheme. The simulation result demonstrated that, compared with the traditional tracking algorithm without DDA, the resolution capability of the sensor system provided by the LMIPDA-DDA algorithm was obviously improved. The key difference between the Doppler measurement association scheme and traditional methods without DDA was that in the Doppler measurement association scheme, the target velocity observed values were used for measurement association. The sonar sensor system improved by Doppler data association scheme had little influence on its operations in terms of system robustness and filter complexity but offered a significant decrease in the amount of false observations. The computational complexity was also greatly reduced. Therefore, if we make a trade-off between complication and performance gain, the proposed DDA scheme was superior to nonlinear filtering technique in this case.
