## 4 Results, Discussions and Achievements
### Estimation Accuracy  
Estimation accuracy of FPA and PSO is looked into by varying the number of sources and their positions. This analysis is set out by best, worst and mean values of the angles estimated by proposed methods to validate their performance along with statistical analysis. In the case of seven targets, we clearly monitored that angles estimated by FPA are accurate than PSO at 0 dB, \(-5\) dB and \(-10\) dB SNRs as depicted in Tables 1-3. Furthermore, Tables 1-3 includes the standard deviation (STD) analysis for the FPA and PSO models, which clearly define that the proposed model has optimized outcomes.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Actual Angles** & \(\theta_{1}=20\) & \(\theta_{2}=40\) & \(\theta_{3}=60\) & \(\theta_{4}=80\) & \(\theta_{5}=100\) & \(\theta_{6}=120\) & \(\theta_{7}=140\) & \(\theta_{8}=160\) & \(\theta_{9}=170\) \\ \hline \multirow{4}{*}{**FPA**} & **Best** & 18.168 & 38.385 & 59.174 & 79.491 & 101.673 & 119.234 & 140.863 & 158.025 & 170.230 \\  & **Mean** & 0.000 & 32.733 & 58.255 & 77.206 & 101.260 & 117.178 & 127.036 & 148.510 & 169.016 \\  & **Worst** & 11.230 & 38.897 & 61.967 & 79.402 & 100.536 & 119.506 & 143.753 & 2.138 & 0.000 \\  & **STD** & 11.5865 & 15.2439 & 15.913 & 15.1088 & 15.3368 & 13.0878 & 13.8784 & 12.2759 & 11.0899 \\ \hline \multirow{4}{*}{**PSO**} & **Best** & 0.371 & 36.758 & 59.827 & 79.031 & 97.880 & 120.000 & 120.000 & 106.209 & 0.000 \\  & **Mean** & 29.041 & 41.913 & 59.563 & 80.782 & 102.079 & 119.840 & 73.947 & 0.000 & 0.000 \\  & **Worst** & 37.783 & 37.524 & 59.243 & 78.662 & 99.615 & 58.886 & 0.000 & 0.000 & 0.000 \\  & **STD** & 19.9239 & 39.508 & 40.2039 & 36.9535 & 42.1866 & 48.3715 & 55.2631 & 58.0799 & 51.2382 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Estimation accuracy and STD for nine targets at SNR = \(-10\) dB.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Actual Angles** & \(\theta_{1}=20\) & \(\theta_{2}=40\) & \(\theta_{3}=60\) & \(\theta_{4}=80\) & \(\theta_{5}=100\) & \(\theta_{6}=120\) & \(\theta_{7}=140\) & \(\theta_{8}=160\) & \(\theta_{9}=170\) \\ \hline \multirow{4}{*}{**FPA**} & **Best** & 20.399 & 34.092 & 50.469 & 66.942 & 80.878 & 95.569 & 109.970 & 118.790 & 134.319 & 150.301 & 160.555 \\  & **Mean** & 17.832 & 20.145 & 40.542 & 55.367 & 73.083 & 99.377 & 104.883 & 115.665 & 124.661 & 145.335 & 149.661 \\  & **Worst** & 2.486 & 28.774 & 44.332 & 58.798 & 74.446 & 89.797 & 103.624 & 118.702 & 136.652 & 148.535 & 0.257 \\  & **STD** & 12.8879 & 13.0721 & 9.6502 & 10.2882 & 10.2654 & 10.3802 & 10.0996 & 8.9518 & 9.696 & 9.9422 & 12.3896 \\ \hline \multirow{4}{*}{**PSO**} & **Best** & 33.810 & 45.343 & 60.019 & 73.433 & 82.736 & 92.641 & 112.055 & 120.000 & 101.111 & 0.000 & 0.000 \\  & **Mean** & 1.489 & 32.933 & 54.975 & 65.939 & 75.908 & 97.667 & 110.797 & 119.215 & 85.444 & 42.657 & 0.000 \\  & **Worst** & 0.653 & 38.887 & 39.501 & 63.090 & 83.131 & 74.659 & 96.677 & 114.281 & 55.525 & 0.489 & 0.276 \\  & **STD** & 19.8683 & 34.3679 & 23.1016 & 23.4132 & 27.2577 & 30.5871 & 34.19 & 33.4794 & 37.3056 & 39.7499 & 45.8805 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Estimation accuracy and STD for eleven targets at SNR = \(0\) dB.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Actual Angles** & \(\theta_{1}=20\) & \(\theta_{2}=40\) & \(\theta_{3}=60\) & \(\theta_{4}=80\) & \(\theta_{5}=100\) & \(\theta_{6}=120\) & \(\theta_{7}=140\) & \(\theta_{8}=160\) & \(\theta_{9}=170\) \\ \hline \multirow{4}{*}{**FPA**} & **Best** & 20.063 & 40.167 & 59.702 & 79.861 & 100.205 & 120.889 & 140.965 & 162.774 & 171.189 \\  & **Mean** & 23.035 & 34.792 & 57.209 & 80.132 & 100.174 &