Semidefinite Relaxation Algorithm for Multisource Localization Using TDOA Measurements with Range Constraints

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/wcmc/volume-2018/9430180/figures/9430180.fig.001a.svgz" name="9430180.fig.001a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>RMSE of target 1</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/wcmc/volume-2018/9430180/figures/9430180.fig.001b.svgz" name="9430180.fig.001b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>RMSE of target 2</td></tr></table>

<div>Comparison of RMSE and measurement noise <svg height="11.7978pt" id="M178" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 12.4186 11.7978" width="12.4186pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z" id="g113-240"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.347,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g></svg> for two targets with different <span class="nowrap"><svg height="9.49473pt" id="M179" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.84582 9.49473" width="6.84582pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z" id="g113-226"></path></g></svg>.</span></div>

Wireless Communications and Mobile Computing

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Figure 1

Figure 1: Semidefinite Relaxation Algorithm for Multisource Localization Using TDOA Measurements with Range Constraints 