**4. Experimental results**

In this part, we attempt to prove the ability of the proposed algorithm "MONTE CARLO-JPDA" to model simulate a precise model based on target tracking parameters. This algorithm contributes to improving the state estimation of two crossing target in 2D using two separated sensors in a MIMO radar system. We will compare the results obtained from the MATLAB software.

#### **4.1 Presimulation part**

Firstly, we show the sensor-target geometry for tracking two crossing targets as follows (**Figure 1**):

Sensor 1:*Rx*1ð Þ 0; 0 ; Sensor 2: *Rx*<sup>2</sup> (1.8e5; 0.8e5). Initial state of the targets: Target 1: (100e3 150; 150e3 (�10)) Target 2: (100e3 150; 148e3 10)

#### **4.2 Simulation scenarios**

In order to implement our algorithm, there are different variables and metrics for more accurate results interpretation were selected as follow:

• Time (T) = 200 s

*Improved Multi Target Tracking in MIMO Radar System Using New Hybrid Monte… DOI: http://dx.doi.org/10.5772/intechopen.95948*

**Figure 1.** *Initial target-sensor geometry.*


#### *4.2.1 Two crossing targets tracking using EKF-JPDAF algorithm*

We start the tracking scenario of two crossing targets in 2-D using the conventional algorithm as known by EKF-JPDAF, the estimated trajectories and the RMSE values are given as follows (**Figures 2** and **3**):

Where: Blue dot: true target states

Green dot: estimates

Cyan star: resolved measurements

Black star: unresolved measurements

The trajectory losses of each target is given as follows:

Trajectory losses of target1: 0.187 (18.7%)

Trajectory losses of target2: 0.172 (17.2%)

According to the figures above, it is noticed that the tracking of the two targets once using EKF-JPDAF algorithm is more complex, more losses of trajectories are showed especially when the cross path phenomenon is appear, such as: Percentage of Trajectory losses for target1 is 18.7% and Percentage of Trajectory losses for target 2 is 17.2%.

#### *4.2.2 Two crossing targets tracking using the suggested MC-JPDAF algorithm*

In order to improve the tracking scenario regarding the obtained results by EKF-JPDAF, we implement our new approach based on numerical filter called MC-JPDAF to

**Figure 2.**

*Trajectories of two crossing targets using measurements from the two sensors estimated by EKF-JPDAF algorithm.*

**Figure 3.**

*The RMSE position and RMSE velocity of each target.*

perform the tracking of two crossing targets in 2-D during the same estimation period (200 s). The estimated trajectories and the RMSE values are given as follows:

Where: Blue dot: true target states.

Green dot: estimates.

Cyan star: resolved measurements.

Black star: unresolved measurements.

The trajectory losses of each target is given as follows:

Trajectory losses of target1: 0, 06 (6%)

Trajectory losses of target2: 0, 07 (7%)

As shown in **Figure 4**, JPDA classifier associated to MONTE CARLO runs, provides a lower trajectories losses compared to EKF-JPDA results, such as; in **Figure 5**, during 20s the amplitude of the RMSE position is reduced from 80 m to 20 m approximately. Likewise, the RMSE velocity value goes from 22 m / s to 0.5 m / s evenhanded after 20 seconds of calculation.

The acquired results of both simulation scenarios are compared and classified in the **Table 1** hereunder.

#### **4.3 Discussion**

In order to strengthen the theoretical comparison in the previous section, it's clear from the results presented in **Table 1** that the EKF-JPDAF's average Ratio

*Improved Multi Target Tracking in MIMO Radar System Using New Hybrid Monte… DOI: http://dx.doi.org/10.5772/intechopen.95948*

**Figure 4.**

*Trajectories of two crossing targets using measurements from both sensors estimated by MC-JPDA algorithm.*

**Figure 5.** *The RMSE position and RMSE velocity of each target.*


#### **Table 1.**

*Comparative results.*

Mean Square Error (RMSE) is much higher than the RMSE of MC-JPDAF algorithm in both simulation scenarios. Our new MC-JPDAF method is more effective in MIMO radar system with two sensors, it gives minus tracking risk than EKF-JPDAF.

In addition to RMSE, we have added the trajectory losses percentage as a new metric for more accurate results interpretation. Thus, we notice from **Table 1** that our new hybrid algorithm have a low trajectory percentage that does not exceed a 7% of losses, which reflects the robustness of our algorithm.

The simulations are approved by comparison metrics. Therefore, in the light of this investigation, it is possible to conclude that our contribution has been verified. The new proposed hybrid MC-JPDAF algorithm estimates the state of tow crossing targets more accurately than the EKF-JPDAF algorithm. Thus it's clear to see the robustness of our approach during a long period (200 s) without performance degradation especially once the cross path phenomenon is by using a large number of Monte Carlo runs up to 100 samples.
