## Mathematics of Data FusionData fusion or information fusion are names which have been primarily assigned to military-oriented problems. In military applications, typical data fusion problems are: multisensor, multitarget detection, object identification, tracking, threat assessment, mission assessment and mission planning, among many others. However, it is clear that the basic underlying concepts underlying such fusion procedures can often be used in nonmilitary applications as well. The purpose of this book is twofold: First, to point out present gaps in the way data fusion problems are conceptually treated. Second, to address this issue by exhibiting mathematical tools which treat combination of evidence in the presence of uncertainty in a more systematic and comprehensive way. These techniques are based essentially on two novel ideas relating to probability theory: the newly developed fields of random set theory and conditional and relational event algebra. This volume is intended to be both an update on research progress on data fusion and an introduction to potentially powerful new techniques: fuzzy logic, random set theory, and conditional and relational event algebra. Audience: This volume can be used as a reference book for researchers and practitioners in data fusion or expert systems theory, or for graduate students as text for a research seminar or graduate level course. |

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### Contents

II | 1 |

III | 3 |

IV | 7 |

V | 10 |

VI | 15 |

VII | 17 |

VIII | 18 |

X | 20 |

LXXXI | 264 |

LXXXII | 266 |

LXXXIII | 269 |

LXXXIV | 274 |

LXXXV | 275 |

LXXXVI | 279 |

LXXXVIII | 280 |

LXXXIX | 289 |

XI | 22 |

XII | 23 |

XIII | 26 |

XIV | 27 |

XVI | 37 |

XVII | 43 |

XVIII | 45 |

XIX | 48 |

XX | 50 |

XXI | 54 |

XXIII | 58 |

XXIV | 61 |

XXV | 62 |

XXVII | 63 |

XXVIII | 65 |

XXIX | 68 |

XXX | 71 |

XXXI | 73 |

XXXII | 79 |

XXXIII | 91 |

XXXIV | 93 |

XXXV | 100 |

XXXVI | 112 |

XXXVII | 116 |

XXXIX | 125 |

XL | 127 |

XLI | 131 |

XLII | 135 |

XLIII | 137 |

XLIV | 138 |

XLV | 139 |

XLVI | 141 |

XLVII | 144 |

XLVIII | 150 |

XLIX | 152 |

LI | 157 |

LII | 162 |

LIII | 168 |

LIV | 170 |

LV | 171 |

LVI | 175 |

LVII | 183 |

LVIII | 184 |

LIX | 188 |

LX | 189 |

LXI | 190 |

LXII | 194 |

LXIII | 205 |

LXIV | 209 |

LXV | 217 |

LXVI | 219 |

LXVII | 221 |

LXIX | 225 |

LXX | 228 |

LXXI | 235 |

LXXII | 236 |

LXXIII | 237 |

LXXIV | 238 |

LXXV | 239 |

LXXVI | 243 |

LXXVII | 244 |

LXXVIII | 256 |

LXXIX | 261 |

LXXX | 263 |

XCI | 293 |

XCII | 295 |

XCIII | 297 |

XCIV | 302 |

XCV | 304 |

XCVI | 307 |

XCVII | 312 |

XCVIII | 313 |

XCIX | 319 |

337 | |

CI | 339 |

CII | 341 |

CIII | 345 |

CIV | 346 |

CV | 348 |

CVI | 349 |

CVII | 353 |

CVIII | 357 |

CIX | 359 |

CX | 362 |

CXI | 364 |

367 | |

CXIII | 369 |

CXIV | 373 |

CXV | 376 |

CXVI | 377 |

CXVII | 378 |

CXVIII | 381 |

CXIX | 383 |

CXX | 395 |

CXXII | 397 |

CXXIII | 399 |

CXXIV | 401 |

403 | |

CXXVI | 405 |

CXXVII | 415 |

CXXVIII | 417 |

423 | |

CXXX | 425 |

CXXXI | 426 |

CXXXIII | 428 |

CXXXIV | 434 |

CXXXV | 436 |

CXXXVI | 440 |

CXXXVII | 448 |

CXXXVIII | 453 |

CXXXIX | 455 |

CXL | 457 |

CXLI | 458 |

CXLII | 460 |

CXLIII | 465 |

CXLIV | 466 |

CXLV | 474 |

479 | |

CXLVII | 481 |

CXLVIII | 482 |

CXLIX | 485 |

CL | 489 |

CLI | 492 |

CLII | 499 |

501 | |

503 | |

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### Common terms and phrases

absolutely continuous absolutely continuous finite algebraic metric approach assume assumptions basic Bayesian belief measure boolean algebra Chapter closed subset compute concept conditional event algebra conditional probability consider constraint continuous finite random corresponding data fusion data fusion algorithm defined Definition denotes density function detection DGNW disjoint disjunction distribution equation estimation example filter finite random subset finite set finite subsets finite-set fuzzy logic fuzzy set given global density Goodman ground truth Hence hypotheses identically independent inequality Lemma mathematical measurement model measurement space membership function multisensor multitarget Nguyen nontrivial notation Note number of targets operations possible posterior prior probability evaluation probability measure probability space problem Proof properties Proposition Radon-Nikodym derivative random closed sets random variable random vector recursive relational event algebra respect Section sensor set function set integral set-functions single-sensor single-target statistics Suppose Systems Theorem tracking triangle inequality uncertainty

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