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Table 2 Optimal performance obtained by OPMPD approach

From: Simple solution to the optimal deployment of cooperative nodes in two-dimensional TOA-based and AOA-based localization system

  Environment 1 Environment 2 Environment 3
(a) TOA-based
m β O,m,T \( G D O{P}_{\mathrm{C},\mathrm{TOA}}^m \) Z T β O,m,T \( G D O{P}_{\mathrm{C},\mathrm{TOA}}^m \) Z T β O,m,T \( G D O{P}_{\mathrm{C},\mathrm{TOA}}^m \) Z T
1 0 0.6283 0.7683 1 2.8794 2.9044 1.0308 6 1.6133 2.0051 0.7739 3
2 0.309 2.1991 0.7071 2.3794 2.9044 0.8010 0.9675 2.0051 0.7085
3 0 0.6283 0.6708 1.8794 2.9044 0.7004 0.3217 2.0051 0.6677
4 0.309 2.1991 0.6325 1.3794 2.9044 0.6425 −0.3241 0.4343 0.6332
5 0 0.6283 0.6055 0.8794 2.9044 0.6045 0.3217 2.0051 0.6037
6 0.309 2.1991 0.5774 0.3794 2.9044 0.5775 −0.3241 0.4343 0.5778
(b) AOA-based
m β O,m,A \( G D O{P}_{\mathrm{C},\mathrm{AOA}}^m \) Z A β O,m,A \( G D O{P}_{\mathrm{C},\mathrm{AOA}}^m \) Z A β O,m,A \( G D O{P}_{\mathrm{C},\mathrm{AOA}}^m \) Z A
1 0.0015 2.1057 26.3141 2 0.0002894 2.0944 45.8142 1 0.0024 1.7526 27.4448  
2 0.0002527 2.1057 22.5644 −0.0009206 0.5236 26.8686 0.0002859 1.7526 22.7065
3 −0.000948 0.5349 19.2462 0.0002894 2.0944 22.8770 −0.0041 0.1868 14.8350
4 0.0002527 2.1057 17.5197 −0.0009206 0.5236 19.4544 0.0052 1.7526 13.9309
5 −0.000948 0.5349 15.9077 0.0002894 2.0944 17.6657 0.0037 1.7526 12.8015
6 0.0002527 2.1057 14.8611 −0.0009206 0.5236 16.0237 0.0008377 1.7526 11.6386