Rao-Blackwellized Gaussian Sum Particle Filtering for Multipath Assisted Positioning

<div>Structure of the RBGSPF representation: the user state <svg height="8.94341pt" id="M151" style="vertical-align:-3.29567pt" version="1.1" viewbox="-0.0498162 -5.64774 11.8288 8.94341" width="11.8288pt" 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 0V32C450 38 426 53 393 105L296 260C330 305 354 338 375 361C411 396 421 401 476 410V442H293V410C332 402 337 394 323 371C311 351 295 324 274 293L227 371C213 393 218 402 252 410V442H16V410C70 402 80 391 108 344L196 199C166 159 140 123 115 95C81 54 61 43 7 32V0H196V32C156 41 150 53 167 81C182 105 199 138 219 166L269 79C287 49 283 38 245 32V0H494Z" id="g13-118"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.266,3.132)"><path d="M527 54L498 55C459 56 451 63 451 114V445C436 442 413 438 384 435C353 432 318 430 291 429V402L328 396C361 390 370 387 370 331V101C336 70 300 54 262 54C217 54 173 78 173 166V300C173 361 173 412 176 445C160 442 132 438 105 434C77 431 52 430 29 429V402L59 395C83 390 92 385 92 331V141C92 30 150 -12 218 -12C246 -12 266 -4 295 13C324 29 346 47 370 64V-6L376 -12C396 -7 421 1 448 8C476 15 504 21 527 24V54Z" id="g58-115"></path></g></svg> is represented by a number of particles. Each particle estimates the transmitters’ states on its own. Each of the <svg height="11.8174pt" id="M152" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 22.7545 11.8174" width="22.7545pt" 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="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z" id="g113-79"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.062,3.132)"><path d="M601 496C596 555 591 627 591 675H567C551 656 544 650 516 650H120C91 650 79 651 64 675H41C38 619 34 555 29 492H63C75 537 83 566 96 582C110 604 128 612 207 612H272V126C272 46 264 38 170 33V0H464V33C368 38 359 48 359 126V612H430C502 612 520 605 535 582C547 566 556 541 567 492L601 496Z" id="g58-82"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.014,3.132)"><path d="M665 0V33C595 38 568 55 523 124C476 196 422 278 366 366C436 471 466 514 487 540C533 599 553 609 628 617V650H396V617C459 610 463 599 440 558C413 507 382 460 343 400C300 467 263 522 232 575C216 602 218 609 278 617V650H27V617C100 609 114 598 160 531C193 479 239 409 291 325C206 194 151 118 127 89C99 53 67 38 8 33V0H242V33C177 41 172 50 196 91C229 151 269 219 316 288C380 189 422 120 446 81C465 49 459 38 398 33V0H665Z" id="g58-86"></path></g></svg> transmitter states is represented by a sum of <svg height="11.9316pt" id="M153" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 28.7099 11.9316" width="28.7099pt" 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="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z" id="g113-79"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.062,3.132)"><path d="M727 650H480V617C552 612 575 600 580 563C583 531 587 491 587 398V326C587 153 534 44 398 44C281 44 210 124 210 296V519C210 607 218 612 298 617V650H33V617C114 609 123 607 123 519V274C123 153 151 81 211 34C258 -1 314 -14 374 -14C441 -14 509 7 556 56C615 116 633 202 633 322V398C633 491 635 533 639 561C643 600 667 614 727 617V650Z" id="g58-83"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.86,3.132)"><path d="M676 0V33C628 38 606 47 555 101S396 279 321 373C388 440 457 509 495 545C556 601 582 609 660 617V650H412V617L436 615C479 608 479 601 452 566C405 510 345 447 289 394C258 366 239 353 216 348V518C216 605 226 612 305 617V650H40V617C123 612 130 605 130 518V131C130 46 121 38 44 33V0H310V33C226 38 216 46 216 131V318C235 322 249 319 274 290C367 181 444 84 520 0H676Z" id="g58-73"></path></g><g transform="matrix(.0091,0,0,-0.0091,23.093,3.132)"><path d="M502 500C497 551 492 613 491 650H43V617C122 612 130 606 130 521V129C130 45 122 38 41 33V0H319V33C227 38 217 45 217 129V305H319C411 305 413 295 427 225H461V421H427C414 357 411 348 319 348H217V580C217 609 219 612 250 612H330C401 612 423 605 439 578C452 557 458 539 467 496L502 500Z" id="g58-68"></path></g></svg> Gaussian distributions <svg height="12.3054pt" id="M154" style="vertical-align:-3.29108pt" version="1.1" viewbox="-0.0498162 -9.01432 17.5207 12.3054" width="17.5207pt" 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="M569 131C584 203 591 291 596 391C603 524 609 615 622 658L609 669C545 642 461 523 357 312C267 129 194 14 119 14C104 14 91 21 88 36H91C96 33 101 32 107 32C134 32 149 54 149 77C149 104 128 128 97 128C65 128 38 101 38 62C38 19 71 -15 118 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Journal of Electrical and Computer Engineering

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Figure 4

Figure 4: Rao-Blackwellized Gaussian Sum Particle Filtering for Multipath Assisted Positioning 