רÀûÃû³Æ£º·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»·½·¨¼°ÏµÍ³µÄÖÆ×÷·½·¨
¼¼ÊõÁìÓò£º
±¾·¢Ã÷Éæ¼°ÎÞÏß¶¨Î»·½·¨£¬ÓÈÆäÉæ¼°·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»·½·¨¼°ÏµÍ³¡£
±³¾°¼¼Êõ£º
³¬¿í´øÐźÅÓÉÓÚÆä¼«¸ßµÄʱÓò·Ö±æÂÊ£¬ÀíÂÛÉÏ¿ÉÒÔ´ïµ½ÀåÃ×¼¶µÄ²â¾à¶¨Î»¾«¶È£¬Í¬Ê±ÓÉÓÚÆäÆµÓòÐÅÏ¢·ÖÁ¿·á¸»£¬¾ß±¸½ÏºÃµÄÕϰÎﴩ͸ÄÜÁ¦£¬Òò´ËÔÚÊÒÄÚ¶¨Î»ÁìÓò¾ßÓй㷺µÄÓ¦Óᣳ£¼ûµÄ¶¨Î»·½·¨°üÀ¨µ½´ïʱ¼ä¹À¼Æ(¦³0¦¡)¡¢µ½´ï½Ç¹À¼Æ(¦¡0¦¡)¡¢µ½´ïʱ¼ä²î¹À¼Æ (TD0A)¡¢ÐźÅÇ¿¶È(RSS)µÈ;¾¶£¬¶ø»ùÓÚµ½´ïʱ¼äÀàµÄ¹À¼Æ·½·¨Äܹ»³ä·ÖÍÚ¾ò³¬¿í´øÐźÅÔÚʱÓò·Ö±æÂÊÉϵÄÓŵ㣬´Ó¶øµÃµ½¹ã·ºÓ¦Óá£Ïà±È½ÏTOAºÍTDOA·½·¨£¬¶þÕ߸÷ÓÐÓÅÊÆ¡£ÆäÖÐTDOAϵͳÄܹ»ÈÝÄɸü¶àµÄÓû§£¬µ«ÊÇÐèҪê½Úµãµ¥ÔªÖ®¼äÍê³É¾«È·µÄʱ¼äͬ²½¡£ÓÉÓÚÊÒÄÚ¶¨Î»µÄ¾«¶ÈÒªÇó½Ï¸ß£¬µ±Í¬²½Îó²î³¬¹ý1ns£¬²â¾àÎó²î¾Í´ïµ½30cm£¬»á¶ÔϵͳÐÔÄܲúÉúÑÏÖØÓ°Ïì¡£¶øÄ¿Ç°³£Óõĵ͸´ÔÓ¶ÈÈ«¾Öͬ²½Ëã·¨ºÜÄÑ´ïµ½Èç´Ë¸ß¾«¶ÈµÄÒªÇ󣬴ӶøÒ²ÏÞÖÆÁË TDOA·½·¨µÄÓ¦Óá£Ë«Ïò²â¾à(Two way ranging)ÊÇÒ»ÖÖ³£¼ûµÄÒì²½²â¾à·½·¨¡£¸Ã·½·¨ÀûÓÃÐźŵÄÍù·µÊ±¼ä(Round trip time)½øÐоàÀë²âÁ¿¡£ÕâÖÖ·½·¨²»ÐèÒªÊÕ·¢½ÚµãµÄʱÖÓͬ²½£¬Òò´Ë¸´ÔӶȽϵ͡£²»¹ýÓÉÓÚ¶¨Î»ÏµÍ³ÖÐÖÁÉÙÐèÒª3¸öÒÔÉϵÄê½Úµãµ¥Ôª½øÐж¨Î»¸¨Öú£¬¶øÃª½Úµãµ¥ÔªÖ®¼äÐèÒªÉè¼ÆºÏÀíµÄʱ·ÖÐÒéÒÔÍê³ÉÏȺó´«Ê䣬Ôö¼ÓÁËϵͳµÄ¸´ÔÓ¶È¡£
·¢Ã÷ÄÚÈÝ
ΪÁ˽â¾öÏÖÓм¼ÊõË«Ïò²â¾àÖÐϵͳ¸´ÔӶȸߵÄÎÊÌ⣬±¾·¢Ã÷ÌṩÁËÒ»ÖÖ·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»·½·¨¡£±¾·¢Ã÷ÌṩÁËÒ»ÖÖ·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»·½·¨£¬°üÀ¨Ä¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥Ôª¾àÀë²âÁ¿²½Ö裬¸ÃÄ¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥Ôª¾àÀë²âÁ¿²½Öè°üÀ¨Èçϲ½ÖèA.Ä¿±ê½Úµãµ¥ÔªÓò»Í¬µÄÖÜÆÚ·¢ËͶà¸öÂö³å£»B.ÖÁÉÙÈý¸öê½Úµãµ¥Ôª¹²Í¬ËÑË÷Ä¿±ê½Úµãµ¥Ôª·¢Ë͵ÄÂö³å,ÖÁÉÙÈý¸öê½Úµãµ¥ÔªµÄËÑË÷ÖÜÆÚ²»Í¬£»C.ÿ¸öê½Úµãµ¥Ôª²¶»ñÂö³åN´Î¡¢ÅжϦǴÎÔÚͬһʱ¿Ì²¶»ñµ½Ä¿±ê½Úµãµ¥Ôª·¢Ë͹ýÀ´µÄÂö³åµÄ¸ÅÂÊÊÇ·ñ´óÓÚP¡¯£¬ÈçÊÇ¡¢Ö¤Ã÷¸Ãê½Úµãµ¥Ôª³É¹¦²¶×½µ½Âö³å¡¢ÄÇôִÐÐD²½Ö裬·ñÔò¸Ãê½Úµãµ¥Ôª½áÊø¼ì²â£»ËùÊöN¡¢¦ÇºÍP ¡¯¾ùΪ¸ù¾Ý·ÂÕæËã·¨É趨µÄÖµ£»D.³É¹¦²¶×½µ½Âö³åµÄê½Úµãµ¥Ôª½«¼ì²âµ½µÄÂö³å»Ø´«ÖÁÄ¿±ê½Úµãµ¥Ôª£»¦¥.Ä¿±ê½Úµãµ¥Ôª¼ÆËã³öÄ¿±ê½Úµãµ¥ÔªÓë²¶×½µ½Âö³åµÄê½Úµãµ¥ÔªÖ®¼äµÄ¾àÀ룬²¢ÇÒÄ¿±ê½Úµãµ¥Ôª½«¸Ã¾àÀë½øÐмǼ£»Ö´ÐÐÄ¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥Ôª¾àÀë²âÁ¿²½ÖèµÄ´ÎÊýÓëê½Úµãµ¥ÔªµÄ¸öÊýÏàͬ£¬ÔÚ²½ÖèAÖÐÄ¿±ê½Úµãµ¥ÔªÃ¿´Î·¢Ë͵ÄÂö³å½íÕ곤¶È¾ù²»Ïàͬ£»´ýÄ¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥Ôª¾àÀë²âÁ¿²½ÖèµÄ´ÎÊýÖ´ÐÐÍê±Ïºó£¬Ä¿±ê½Úµãµ¥Ôª¸ù¾ÝÄ¿±ê½Úµãµ¥ÔªÓëÿ¸öê½Úµãµ¥ÔªµÄ¾àÀëÖµ¼ÆËã³ö¸ÃÄ¿±ê½Úµãµ¥ÔªµÄλÖá£×÷Ϊ±¾·¢Ã÷µÄ½øÒ»²½¸Ä½ø£¬ÔÚËùÊö²½ÖèCÖУ¬ÅжÏê½Úµãµ¥ÔªËÑË÷Âö³åµÄÖÜÆÚÓëÄ¿±ê½Úµãµ¥Ôª·¢ËÍÂö³åµÄÖÜÆÚÊÇ·ñÏàͬµÄ·½·¨ÎªÅжÏê½Úµãµ¥ÔªÁ¬Ðø¶à´Î²¶»ñµ½Ä¿±ê½Úµãµ¥Ôª·¢Ë͹ýÀ´µÄÂö³åÊÇ·ñÔÚͬһλÖã¬ÈçÔÚͬһλÖá¢ÔòÖ¤Ã÷Ä¿±ê½Úµãµ¥Ôª·¢ËÍÂö³åµÄÖÜÆÚÓëê½Úµãµ¥Ôª²¶»ñÂö³åµÄÖÜÆÚÏàͬ£¬Ãª½Úµãµ¥ÔªÄܹ»³É¹¦²¶×½µ½Âö³å¡£×÷Ϊ±¾·¢Ã÷µÄ½øÒ»²½¸Ä½ø£¬ÔÚËùÊö²½ÖèCÖУ¬ÔÚËùÊö²½ÖèCÖУ¬ÅжÏê½Úµãµ¥ÔªËÑË÷Âö³åµÄÖÜÆÚÓëÄ¿±ê½Úµãµ¥Ôª·¢ËÍÂö³åµÄÖÜÆÚÊÇ·ñÏàͬµÄ·½·¨ÎªÃª½Úµãµ¥Ôª¶à´Î¼ì²âê½Úµãµ¥ÔªµÄ¼ÆÊýÖÜÆÚÓëÄ¿±ê½Úµãµ¥Ôª·¢Ë͵ÄÂö³åÖ¡³¤¶ÈÊÇ·ñÏàͬ£¬Èçê½Úµãµ¥ÔªÁ¬ÐøÓЦǴβ¶»ñµ½Ä¿±ê½Úµãµ¥Ôª·¢Ë͹ýÀ´µÄÂö³åÔÚͬһλÖá¢ÔòÖ¤Ã÷ê½Úµãµ¥Ôª³É¹¦²¶×½µ½Âö³å£¬ ¸Ã¦Ç´ÎΪԤÉèÖµ¡£×÷Ϊ±¾·¢Ã÷µÄ½øÒ»²½¸Ä½ø£¬ËùÊöê½Úµãµ¥ÔªµÄÊýÁ¿Îª6¸ö¡£×÷Ϊ±¾·¢Ã÷µÄ½øÒ»²½¸Ä½ø£¬ÔÚËùÊö²½ÖèEÖУ¬Ä¿±ê½Úµãµ¥ÔªÍ¨¹ýË«Ïò²â¾à·½·¨¼ÆËã³öÄ¿±ê½Úµãµ¥ÔªÓë²¶×½µ½Âö³åµÄê½Úµãµ¥ÔªÖ®¼äµÄ¾àÀë¡£±¾·¢Ã÷»¹ÌṩÁËÒ»ÖÖ·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»ÏµÍ³£¬°üÀ¨Ä¿±ê½Úµãµ¥Ôª¡¢ÖÁÉÙÈý¸öê½Úµãµ¥Ôª£¬ËùÊöÄ¿±ê½Úµãµ¥Ôª°üÀ¨ÓÃÓÚ·¢ËͺͽÓÊÕÂö³åµÄÊÕ·¢Ä£¿é£»ÓëÊÕ·¢Ä£¿éÏàÁ¬¡¢ÇÒÓÃÓÚ¼ÆËã³öÄ¿±ê½Úµãµ¥ÔªÓë²¶×½µ½Âö³åµÄê½Úµãµ¥ÔªÖ®¼äµÄ¾àÀëµÄ¾àÀë²âÁ¿Ä£¿é£»Óë¾àÀë²âÁ¿Ä£¿éÏàÁ¬¡¢ÇÒÓÃÓÚ¸ù¾ÝÄ¿±ê½Úµãµ¥ÔªÓëÿ¸öê½Úµãµ¥ÔªµÄ¾àÀëÖµ¼ÆËã³ö¸ÃÄ¿±ê½Úµãµ¥ÔªµÄλÖõĶ¨Î»Ä£¿é£»ËùÊöê½Úµãµ¥Ôª°üÀ¨ÓÃÓÚ½ÓÊպͻط¢Âö³åµÄ´«ÊäÄ£¿é£»Óë´«ÊäÄ£¿éÏàÁ¬¡¢ÇÒÓÃÓÚÅжÏê½Úµãµ¥ÔªµÄËÑË÷Âö³åµÄÖÜÆÚÓëÄ¿±ê½Úµãµ¥Ôª·¢Ë͵ÄÖÜÆÚÊÇ·ñÏàͬµÄÅжÏÄ£¿é¡£×÷Ϊ±¾·¢Ã÷µÄ½øÒ»²½¸Ä½ø£¬ËùÊöÊÕ·¢Ä£¿éΪÎÞÏßÊÕ·¢Ä£¿é£¬ËùÊö´«ÊäÄ£¿éΪÎÞÏß´«ÊäÄ£¿é¡£×÷Ϊ±¾·¢Ã÷µÄ½øÒ»²½¸Ä½ø£¬ËùÊöê½Úµãµ¥ÔªÊýÁ¿Îª6¸ö¡£±¾·¢Ã÷µÄÓÐÒæÐ§¹ûÊDZ¾·¢Ã÷ͨ¹ýÄ¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥Ôª¾àÀë²âÁ¿²½ÖèÊ×ÏȵóöÄ¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥ÔªÖ®¼äµÄ¾àÀ룬ȻºóÔÙ¶ÔÄ¿±ê½Úµãµ¥Ôª½øÐж¨Î»£¬Í¨¹ý¸Ä±ä·¢ÉäÂö³åµÄÖØ¸´ÖÜÆÚ£¬Äܹ»·Ç³£·½±ãµØÊµÏÖê½Úµãµ¥ÔªÓëÄ¿±ê½Úµãµ¥ÔªµÄʶ±ð£¬¼õÉÙÁ˶¨Î»¸´ÔÓ¶È£¬Ìá¸ßЧÂÊ¡£
ͼIÊDZ¾·¢Ã÷µÄÄ¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥Ôª¾àÀë²âÁ¿²½ÖèÁ÷³Ìͼ¡£Í¼2ÊDZ¾·¢Ã÷µÄ·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»ÏµÍ³ÔÀí¿òͼ¡£Í¼3ÊDZ¾·¢Ã÷µÄÇóCount [¦Ç]µÄËã·¨Á÷³Ìͼ¡£Í¼4ÊDZ¾·¢Ã÷µÄÊý¾Ý·ÖÎöͼI¡£Í¼5ÊDZ¾·¢Ã÷µÄÊý¾Ý·ÖÎöͼ2¡£Í¼6ÊDZ¾·¢Ã÷µÄÊý¾Ý·ÖÎöͼ3¡£
ͼ7ÊDZ¾·¢Ã÷µÄÊý¾Ý·ÖÎöͼ4¡£Í¼8ÊDZ¾·¢Ã÷µÄÊý¾Ý·ÖÎöͼ5¡£Í¼9ÊDZ¾·¢Ã÷µÄÊý¾Ý·ÖÎöͼ6¡£
¾ßÌåʵʩ·½Ê½
ÈçͼIËùʾ£¬±¾·¢Ã÷¹«¿ªÁËÒ»ÖÖ·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»·½·¨£¬°üÀ¨Ä¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥Ôª¾àÀë²âÁ¿²½Ö裬¸ÃÄ¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥Ôª¾àÀë²âÁ¿²½Öè°üÀ¨²½ÖèSIÖÁ²½ÖèS5£¬ÔÚ²½ÖèSIÖУ¬Ä¿±ê½Úµãµ¥ÔªÓò»Í¬µÄÖÜÆÚ·¢ËͶà¸öÂö³å£¬¸Ã¶à¸öÂö³åΪ´óÓÚ2¸öÂö³å¡£ÔÚ²½ÖèS2ÖУ¬ÖÁÉÙÈý¸öê½Úµãµ¥Ôª¹²Í¬ËÑË÷Ä¿±ê½Úµãµ¥Ôª·¢Ë͵ÄÂö³å£¬ÖÁÉÙÈý¸öê½Úµãµ¥ÔªµÄËÑË÷ÖÜÆÚ²»Í¬¡£ÔÚ²½ÖèS3ÖУ¬Ã¿¸öê½Úµãµ¥Ôª²¶»ñÂö³åN´Î¡¢ÅжϦǴÎÔÚͬһʱ¿Ì²¶»ñµ½Ä¿±ê½Úµãµ¥Ôª·¢Ë͹ýÀ´µÄÂö³åµÄ¸ÅÂÊÊÇ·ñ´óÓÚP¡¯£¬ÈçÊÇ¡¢Ö¤Ã÷¸Ãê½Úµãµ¥Ôª³É¹¦²¶×½µ½Âö³å¡¢ÄÇôִÐÐS4²½Ö裬·ñÔò¸Ãê½Úµãµ¥Ôª½áÊø¼ì²â¡£ÔÚ²½ÖèS4ÖУ¬³É¹¦²¶×½µ½Âö³åµÄê½Úµãµ¥Ôª½«¼ì²âµ½µÄÂö³å»Ø´«ÖÁÄ¿±ê½Úµãµ¥Ôª¡£ÔÚ²½ÖèS5ÖУ¬Ä¿±ê½Úµãµ¥Ôª¼ÆËã³öÄ¿±ê½Úµãµ¥ÔªÓë²¶×½µ½Âö³åµÄê½Úµãµ¥ÔªÖ®¼äµÄ¾àÀ룬²¢ÇÒÄ¿±ê½Úµãµ¥Ôª½«¸Ã¾àÀë½øÐмǼ¡£Ö´ÐÐÄ¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥Ôª¾àÀë²âÁ¿²½ÖèµÄ´ÎÊýÓëê½Úµãµ¥ÔªµÄ¸öÊýÏàͬ£¬ÔÚ²½ÖèSIÖÐÄ¿±ê½Úµãµ¥ÔªÃ¿´Î·¢Ë͵ÄÂö³åÖ¡³¤¶È¾ù²»Ïàͬ£»´ýÄ¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥Ôª¾àÀë²âÁ¿²½ÖèµÄ´ÎÊýÖ´ÐÐÍê±Ïºó£¬Ä¿±ê½Úµãµ¥Ôª¸ù¾ÝÄ¿±ê½Úµãµ¥ÔªÓëÿ¸öê½Úµãµ¥ÔªµÄ¾àÀëÖµ¼ÆËã³ö¸ÃÄ¿±ê½Úµãµ¥ÔªµÄλÖá£ÀýÈç,ê½Úµãµ¥ÔªµÄ¸öÊýΪ3¸ö,ÄÇôĿ±ê½Úµãµ¥ÔªÓëê½Úµãµ¥Ôª¾àÀë²âÁ¿²½Öè±ãÖ´ÐÐ3´Î¡£×÷Ϊ¸Ã·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»·½·¨µÄÒ»¸öʵʩÀý£¬ÔÚËùÊö²½ÖèS3ÖУ¬ÅжÏê½Úµãµ¥ÔªËÑË÷Âö³åµÄÖÜÆÚÓëÄ¿±ê½Úµãµ¥Ôª·¢ËÍÂö³åµÄÖÜÆÚÊÇ·ñÏàͬµÄ·½·¨ÎªÅжÏê½Úµãµ¥ÔªÁ¬Ðø¶à´Î²¶»ñµ½Ä¿±ê½Úµãµ¥Ôª·¢Ë͹ýÀ´µÄÂö³åÊÇ·ñÔÚͬһλÖã¬ÈçÔÚͬһλÖá¢ÔòÖ¤Ã÷Ä¿±ê½Úµãµ¥Ôª·¢ËÍÂö³åµÄÖÜÆÚÓëê½Úµãµ¥Ôª²¶»ñÂö³åµÄÖÜÆÚÏàͬ£¬Ãª½Úµãµ¥ÔªÄܹ»³É¹¦²¶×½µ½Âö³å¡£×÷Ϊ¸Ã·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»·½·¨µÄÁíÒ»¸öʵʩÀý£¬ÔÚËùÊö²½ÖèS3ÖУ¬ÅжÏê½Úµãµ¥ÔªËÑË÷Âö³åµÄÖÜÆÚÓëÄ¿±ê½Úµãµ¥Ôª·¢ËÍÂö³åµÄÖÜÆÚÊÇ·ñÏàͬµÄ·½·¨ÎªÃª½Úµãµ¥Ôª¶à´Î¼ì²âê½Úµãµ¥ÔªµÄ¼ÆÊýÖÜÆÚÓëÄ¿±ê½Úµãµ¥Ôª·¢Ë͵ÄÂö³åÖ¡³¤¶ÈÊÇ·ñÏàͬ£¬Èçê½Úµãµ¥ÔªÁ¬ÐøÓЦǴβ¶»ñµ½Ä¿±ê½Úµãµ¥Ôª·¢Ë͹ýÀ´µÄÂö³åÔÚͬһλÖá¢ÔòÖ¤Ã÷ê½Úµãµ¥Ôª³É¹¦²¶×½µ½Âö³å£¬¸Ã¦Ç´ÎΪԤÉèÖµ£¬¸ÃÔ¤ÉèֵΪ´óÓÚ2¡£ÔÚËùÊö²½ÖèS5ÖУ¬Ä¿±ê½Úµãµ¥ÔªÍ¨¹ýË«Ïò²â¾à·½·¨¼ÆËã³öÄ¿±ê½Úµãµ¥ÔªÓë²¶×½µ½Âö³åµÄê½Úµãµ¥ÔªÖ®¼äµÄ¾àÀë¡£Èçͼ2Ëùʾ£¬±¾·¢Ã÷»¹¹«¿ªÁËÒ»ÖÖ·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»ÏµÍ³£¬°üÀ¨Ä¿±ê½Úµãµ¥ÔªI¡¢ÖÁÉÙÈý¸öê½Úµãµ¥Ôª2,ËùÊöÄ¿±ê½Úµãµ¥ÔªI°üÀ¨ÓÃÓÚ·¢ËͺͽÓÊÕÂö³åµÄÊÕ·¢Ä£¿é11 ;ÓëÊÕ·¢Ä£¿é11ÏàÁ¬¡¢ÇÒÓÃÓÚ¼ÆËã³öÄ¿±ê½Úµãµ¥ÔªIÓë²¶×½µ½Âö³åµÄê½Úµãµ¥Ôª2Ö®¼äµÄ¾àÀëµÄ¾àÀë²âÁ¿Ä£¿é12 ;Óë¾àÀë²âÁ¿Ä£¿é12ÏàÁ¬¡¢ÇÒÓÃÓÚ¸ù¾ÝÄ¿±ê½Úµãµ¥ÔªIÓëÿ¸öê½Úµãµ¥Ôª2µÄ¾àÀëÖµ¼ÆËã³ö¸ÃÄ¿±ê½Úµãµ¥ÔªIµÄλÖõĶ¨Î»Ä£¿é13¡£ËùÊöê½Úµãµ¥Ôª2°üÀ¨ÓÃÓÚ½ÓÊպͻط¢Âö³åµÄ´«ÊäÄ£¿é21 ;Óë´«ÊäÄ£¿é21ÏàÁ¬¡¢ÇÒÓÃÓÚÅжÏê½Úµãµ¥Ôª2µÄËÑË÷Âö³åµÄÖÜÆÚÓëÄ¿±ê½Úµãµ¥ÔªI·¢Ë͵ÄÖÜÆÚÊÇ·ñÏàͬµÄÅжÏÄ£¿é22¡£ËùÊöÊÕ·¢Ä£¿é11ΪÎÞÏßÊÕ·¢Ä£¿é£¬ËùÊö´«ÊäÄ£¿é21ΪÎÞÏß´«ÊäÄ£¿é¡£ËùÊöê½Úµãµ¥Ôª2ÊýÁ¿Îª6¸ö£¬µ±È»¸Ãê½Úµãµ¥Ôª2µÄÊýÁ¿Ò²¿ÉÒÔÊÇ8¸ö»ò10¸ö£¬Ö»Òª´óÓÚ3¸öÒÔÉϼ´¿É¡£Ãª½Úµãµ¥ÔªµÄ¼ÆÊýÖÜÆÚÒ²¿ÉÒÔ³ÆÎªÃª½Úµãµ¥ÔªµÄËÑË÷ÖÜÆÚ»ò¼ì²âÖÜÆÚ¡£ÀýÈ磬¾ßÓÐ3¸öê½Úµãµ¥Ôª£¬·Ö±ðµÚһê½Úµãµ¥Ôª¡¢µÚ¶þê½Úµãµ¥ÔªºÍµÚÈýê½Úµãµ¥Ôª¡£¾ÙÀýµÚһê½Úµãµ¥Ôª¡¢µÚ¶þê½Úµãµ¥Ôª¡¢µÚÈýê½Úµãµ¥Ôª¡¢µÄ¼ÆÊýÖÜÆÚ·Ö±ðΪNfl¡¢Nf2¡¢Nf3¡£µ±Ä¿±ê½Úµãµ¥ÔªµÄÖ¡³¤¶ÈΪNflʱ£¬ÊµÏÖµÄÊÇÄ¿±ê½Úµãµ¥ÔªÓëµÚһê½Úµãµ¥ ÔªÖ®¼äµÄË«Ïò²â¾à¡£µ±Ä¿±ê½Úµãµ¥ÔªµÄÖ¡³¤¶ÈΪNf2ʱ£¬ÊµÏÖµÄÊÇÄ¿±ê½Úµãµ¥ÔªÓëµÚ¶þê½Úµãµ¥ÔªÖ®¼äµÄË«Ïò²â¾à¡£µ±Ä¿±ê½Úµãµ¥ÔªµÄÖ¡³¤¶ÈΪNf3ʱ£¬ÊµÏÖµÄÊÇÄ¿±ê½Úµãµ¥ÔªÓëµÚÈýê½Úµãµ¥ÔªÖ®¼äµÄË«Ïò²â¾à¡£Ä¿±ê½Úµãµ¥Ôª·¢ËÍÂö³åµÄʱ¿ÌT(i)=i*Nf£¬i=012 3¡¤¡¤¡¤ (I)µÚһê½Úµãµ¥Ôª½ÓÊܵ½Âö³åµÄʱ¿Ì=T1¢Å¡° ¦Ó 1+T(i))%Nfl ¦Ó = d^c; (2)µÚ¶þê½Úµãµ¥Ôª½ÓÊܵ½Âö³åµÄʱ¿ÌTji) = ( ¦Ó 2+T(i))%Nf2 ¦Ó 2 = d2/c ; (3)µÚһê½Úµãµ¥ÔªËÑË÷ÖÜÆÚΪ¦¦°£¬ÔÚµÚһê½Úµãµ¥ÔªµÄÿ¸öËÑË÷ÖÜÆÚ(Nfl)ÀïÖ»½ÓÊܵ½Ò»¸öÂö³å¡£¶ÔÒ»¸öÂö³å½øÐÐDP¼ì²â£¬¶øÇÒÿ´Î²¶»ñµÄʱºòÊÇÏàͬµÄ£¬¼´1\(10 = ¦Ó10µÚ¶þê½Úµãµ¥ÔªµÄËÑË÷ÖÜÆÚΪNf2£¬Count [¦Ç]ΪµÚ¶þê½Úµãµ¥ÔªÔڵڦǸöËÑË÷ÖÜÆÚÄÚ½ÓÊܵ½µÄÂö³å¸öÊý¡£µ±Nf2¡´NflʱҲֻ½ÓÊܵ½Ò»¸öO¸ö»òÕßI¸öÄ¿±ê½Úµãµ¥Ôª·¢Ë͹ýÀ´µÄÂö³å£¬¶ÔO¸ö»òÕßI¸öÂö³å½øÐмì²â£¬¼´Count [n] e {O, 1}¡£µ±Nf2>NflʱÓÐÒÔϽáÂÛ(I)T2(k)µÄÖÜÆÚΪ N£¬¼´ TJi) =T2(i+N)(4)
#×Á2 Nflfgcd(NfXNfl) h
$ Nff Ûø\1%º°Ûø1ÖÞ'\)- a '×¢gcd(a£¬b)ΪÇóa£¬bµÄ×î´ó¹«Ô¼Êý¡£(2)µÚ¶þê½Úµãµ¥ÔªÔڵڦǸöËÑË÷ÖÜÆÚÄÚ½ÓÊܵ½Ò»¸öÒÔÉϵÄÂö³å¡£´ËʱÓÐI ( Count[n] ( [Nf2/Nfl],¼´µÚ¦Ç¸öËÑË÷ÖÜÆÚ¶ÔCount [¦Ç]¸öÂö³å½øÐмì²â¡£×¢[Nf2/Nfl]:´ú±íÏòÉÏÈ¡Õû¡£Èçͼ3Ëùʾ£¬ÎªÇóCount[n]µÄËã·¨Á÷³Ìͼ£¬²ÎÊý½âÎö(×¢¸ÃÁ÷³Ìͼ¼ÆËãCount [¦Ç]µÄËã·¨£¬ÊäÈëÊÇNºÍT(i)£¬Êä³öÊÇCount [¦Ç]£¬ËùÒÔÖ»¶ÔÕâÈý¸ö²ÎÊý½âÊÍ)¡£N¶ÔÓ¦
(4)ʽÖÐ T1GO=T2G^N), T¢Å¶ÔÓ¦(I)ʽ T¢Å=k*Nf£¬i = O I 2 3-, Count [¦Ç]±íʾΪµÚ¶þê½Úµãµ¥ÔªµÚ¦Ç¸öËÑË÷ÖÜÆÚ£¬½ÓÊܵ½Ä¿±ê½Úµãµ¥Ôª·¢Ë͹ýÀ´µÄÂö³å¸öÊý¡£ÔÚËùÊö²½ÖèS3ÖУ¬ÅжÏê½Úµãµ¥ÔªµÄ¼ÆÊýÖÜÆÚÓëÄ¿±ê½Úµãµ¥Ôª·¢Ë͵ÄÂö³åÖ¡³¤¶ÈÊÇ·ñÏàͬµÄ·½·¨ÎªÅжÏê½Úµãµ¥ÔªÁ¬Ðø¶à´Î²¶»ñµ½Ä¿±ê½Úµãµ¥Ôª·¢Ë͹ýÀ´µÄÂö³åÊÇ·ñÔÚͬһλÖã¬ÈçÔÚͬһλÖá¢ÔòÖ¤Ã÷ê½Úµãµ¥Ôª³É¹¦²¶×½µ½Âö³å£»ÀýÈ磬ÅжÏê½Úµãµ¥ÔªÁ¬ÐøÁ½´Î²¶»ñµ½Ä¿±ê½Úµãµ¥Ôª·¢Ë͹ýÀ´µÄÂö³åÊÇ·ñÔÚͬһλÖ㬼ÙÉèµÚ¶þê½Úµãµ¥ÔªµÚk¸öÖÜÆÚ¼ì²âµ½µÄDPλÖÃÊÇÄ¿±ê½Úµãµ¥ÔªµÄµÚm¸öÂö³å£¬²¶»ñʱ¿ÌΪ¦Ä (m)£¬µÚ¶þê½Úµãµ¥ÔªµÚk+¦©¸öÖÜÆÚ¼ì²âµ½µÄDPÊÇÄ¿±ê½Úµãµ¥ÔªµÄµÚn(n>m)¸öÂö³å£¬²¶»ñʱ¿ÌΪ¦Ä (¦Ç):±ØÓÐ1( (n-m)áê¿Ú Nf2/Nfl ¡õ(ÒòΪ¦Ä (m) ¦Ä (¦Ç)Êǵڶþê½Úµãµ¥ÔªµÄÁ¬ÐøÁ½¸öÖÜÆÚ²¶»ñµÄ)¡£µÚ¶þê½Úµãµ¥ÔªµÄµÚk¸öÖÜÆÚ²¶»ñµ½Ä¿±ê½Úµãµ¥Ôª·¢¹ýÀ´µÄµÚm¸öÂö³å£¬²¶»ñʱ¼ä¼ÇΪ¦Ä (m) = ( ¦Ó +m*Nn)%Nf2,µÚ¶þê½Úµãµ¥ÔªµÄµÚk+¦©¸öÖÜÆÚ²¶»ñµ½Ä¿±ê½Úµãµ¥Ôª·¢¹ýÀ´µÄµÚ¦Ç¸öÂö³å²¶»ñʱ¼ä¼ÇΪ¦Ä (¦Ç) = ( ¦Ó +n*Nf I) %Nf2¡£ÏÖÔÚÖ¤Ã÷Á¬ÐøÁ½´Î²¶»ñµ½µÄDPʱ¿ÌÊDz»Í¬µÄ£¬²»ÄÜÕýÈ·¼ì²âµ½DP ·´Ö¤·¨£¬¼ÙÉèÁ½´Î²¶»ñDPµÄʱ¿ÌÊÇÏàͬµÄ£¬¼´¦Ä (m) = ¦Ä (¦Ç)£¬ÄÇô£¬( ¦Ó +n*Nf I) /Nf2 = y... ¦Ä (¦Ç) x n ΪÕûÊý£»( ¦Ó+m*Nfl)/Nf2=x¡¦Ä (m) y m ΪÕûÊý£»Nf2*x+ ¦Ä (m) =m*Nf 1+ ¦Ä (m)£»Nf2*y+¦Ä (n) =n*Nf 1+ ¦Ä (¦Ç);ËùÒÔ
ȨÀûÒªÇó
1.Ò»ÖÖ·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»·½·¨£¬ÆäÌØÕ÷ÔÚÓÚ£¬°üÀ¨Ä¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥Ôª¾àÀë²âÁ¿²½Ö裬¸ÃÄ¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥Ôª¾àÀë²âÁ¿²½Öè°üÀ¨Èçϲ½ÖèA.Ä¿±ê½Úµãµ¥ÔªÓò»Í¬µÄÖÜÆÚ·¢ËͶà¸öÂö³å£»B.ÖÁÉÙÈý¸öê½Úµãµ¥Ôª¹²Í¬ËÑË÷Ä¿±ê½Úµãµ¥Ôª·¢Ë͵ÄÂö³å£¬ÖÁÉÙÈý¸öê½Úµãµ¥ÔªµÄËÑË÷ÖÜÆÚ²»Í¬£»C.ÿ¸öê½Úµãµ¥Ôª²¶»ñÂö³åN´Î¡¢ÅжϦǴÎÔÚͬһʱ¿Ì²¶»ñµ½Ä¿±ê½Úµãµ¥Ôª·¢Ë͹ýÀ´µÄÂö³åµÄ¸ÅÂÊÊÇ·ñ´óÓÚP ¡¯£¬ÈçÊÇ¡¢Ö¤Ã÷¸Ãê½Úµãµ¥Ôª³É¹¦²¶×½µ½Âö³å¡¢ÄÇôִÐÐD²½Ö裬·ñÔò¸Ãê½Úµãµ¥Ôª½áÊø¼ì²â£»ËùÊöN¡¢¦ÇºÍP ¡¯¾ùΪ¸ù¾Ý·ÂÕæËã·¨É趨µÄÖµ£»D.³É¹¦²¶×½µ½Âö³åµÄê½Úµãµ¥Ôª½«¼ì²âµ½µÄÂö³å»Ø´«ÖÁÄ¿±ê½Úµãµ¥Ôª£»¦¥.Ä¿±ê½Úµãµ¥Ôª¼ÆËã³öÄ¿±ê½Úµãµ¥ÔªÓë²¶×½µ½Âö³åµÄê½Úµãµ¥ÔªÖ®¼äµÄ¾àÀ룬²¢ÇÒÄ¿±ê½Úµãµ¥Ôª½«¸Ã¾àÀë½øÐмǼ£»Ö´ÐÐÄ¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥Ôª¾àÀë²âÁ¿²½ÖèµÄ´ÎÊýÓëê½Úµãµ¥ÔªµÄ¸öÊýÏàͬ£¬ÔÚ²½ÖèAÖÐÄ¿±ê½Úµãµ¥ÔªÃ¿´Î·¢Ë͵ÄÂö³åÖ¡³¤¶È¾ù²»Ïàͬ£»´ýÄ¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥Ôª¾àÀë²âÁ¿²½ÖèµÄ´ÎÊýÖ´ÐÐÍê±Ïºó£¬Ä¿±ê½Úµãµ¥Ôª¸ù¾ÝÄ¿±ê½Úµãµ¥ÔªÓëÿ¸öê½Úµãµ¥ÔªµÄ¾àÀëÖµ¼ÆËã³ö¸ÃÄ¿±ê½Úµãµ¥ÔªµÄλÖá£
2.¸ù¾ÝȨÀûÒªÇóIËùÊöµÄ·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»·½·¨£¬ÆäÌØÕ÷ÔÚÓÚÔÚËùÊö²½ÖèCÖУ¬ÅжÏê½Úµãµ¥ÔªËÑË÷Âö³åµÄÖÜÆÚÓëÄ¿±ê½Úµãµ¥Ôª·¢ËÍÂö³åµÄÖÜÆÚÊÇ·ñÏàͬµÄ·½·¨ÎªÅжÏê½Úµãµ¥ÔªÁ¬Ðø¶à´Î²¶»ñµ½Ä¿±ê½Úµãµ¥Ôª·¢Ë͹ýÀ´µÄÂö³åÊÇ·ñÔÚͬһλÖã¬ÈçÔÚͬһλÖá¢ÔòÖ¤Ã÷Ä¿±ê½Úµãµ¥Ôª·¢ËÍÂö³åµÄÖÜÆÚÓëê½Úµãµ¥Ôª²¶»ñÂö³åµÄÖÜÆÚÏàͬ£¬Ãª½Úµãµ¥ÔªÄܹ»³É¹¦²¶×½µ½Âö³å¡£
3.¸ù¾ÝȨÀûÒªÇóIËùÊöµÄ·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»·½·¨£¬ÆäÌØÕ÷ÔÚÓÚÔÚËùÊö²½ÖèCÖУ¬ÅжÏê½Úµãµ¥ÔªËÑË÷Âö³åµÄÖÜÆÚÓëÄ¿±ê½Úµãµ¥Ôª·¢ËÍÂö³åµÄÖÜÆÚÊÇ·ñÏàͬµÄ·½·¨ÎªÃª½Úµãµ¥Ôª¶à´Î¼ì²âê½Úµãµ¥ÔªµÄ¼ÆÊýÖÜÆÚÓëÄ¿±ê½Úµãµ¥Ôª·¢Ë͵ÄÂö³åÖ¡³¤¶ÈÊÇ·ñÏàͬ£¬Èçê½Úµãµ¥ÔªÁ¬ÐøÓЦǴβ¶»ñµ½Ä¿±ê½Úµãµ¥Ôª·¢Ë͹ýÀ´µÄÂö³åÔÚͬһλÖá¢ÔòÖ¤Ã÷ê½Úµãµ¥Ôª³É¹¦²¶×½µ½Âö³å£¬¸Ã¦Ç´ÎΪԤÉèÖµ¡£
4.¸ù¾ÝȨÀûÒªÇóIÖÁ3ÈÎÒ»ÏîËùÊöµÄ·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»·½·¨£¬ÆäÌØÕ÷ÔÚÓÚËùÊöê½Úµãµ¥ÔªµÄÊýÁ¿Îª6¸ö¡£
5.¸ù¾ÝȨÀûÒªÇó4ËùÊöµÄ·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»·½·¨£¬ÆäÌØÕ÷ÔÚÓÚÔÚËùÊö²½ÖèEÖУ¬Ä¿±ê½Úµãµ¥ÔªÍ¨¹ýË«Ïò²â¾à·½·¨¼ÆËã³öÄ¿±ê½Úµãµ¥ÔªÓë²¶×½µ½Âö³åµÄê½Úµãµ¥ÔªÖ®¼äµÄ¾àÀë¡£
6.Ò»ÖÖ·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»ÏµÍ³£¬ÆäÌØÕ÷ÔÚÓÚ£¬°üÀ¨Ä¿±ê½Úµãµ¥Ôª¡¢ÖÁÉÙÈý¸öê½Úµãµ¥Ôª£¬ËùÊöÄ¿±ê½Úµãµ¥Ôª°üÀ¨ÓÃÓÚ·¢ËͺͽÓÊÕÂö³åµÄÊÕ·¢Ä£¿é£»ÓëÊÕ·¢Ä£¿éÏàÁ¬¡¢ÇÒÓÃÓÚ¼ÆËã³öÄ¿±ê½Úµãµ¥ÔªÓë²¶×½µ½Âö³åµÄê½Úµãµ¥ÔªÖ®¼äµÄ¾àÀëµÄ¾àÀë²âÁ¿Ä£¿é£»Óë¾àÀë²âÁ¿Ä£¿éÏàÁ¬¡¢ÇÒÓÃÓÚ¸ù¾ÝÄ¿±ê½Úµãµ¥ÔªÓëÿ¸öê½Úµãµ¥ÔªµÄ¾àÀëÖµ¼ÆËã³ö¸ÃÄ¿±ê½Úµãµ¥ÔªµÄλÖõĶ¨Î»Ä£¿é£»ËùÊöê½Úµãµ¥Ôª°üÀ¨ÓÃÓÚ½ÓÊպͻط¢Âö³åµÄ´«ÊäÄ£¿é£»Óë´«ÊäÄ£¿éÏàÁ¬¡¢ÇÒÓÃÓÚÅжÏê½Úµãµ¥ÔªµÄËÑË÷Âö³åµÄÖÜÆÚÓëÄ¿±ê½Úµãµ¥Ôª·¢Ë͵ÄÖÜÆÚÊÇ·ñÏàͬµÄÅжÏÄ£¿é¡£
7.¸ù¾ÝȨÀûÒªÇó6ËùÊöµÄ·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»ÏµÍ³£¬ÆäÌØÕ÷ÔÚÓÚËùÊöÊÕ·¢Ä£¿éΪÎÞÏßÊÕ·¢Ä£¿é£¬ËùÊö´«ÊäÄ£¿éΪÎÞÏß´«ÊäÄ£¿é¡£
8.¸ù¾ÝȨÀûÒªÇó6»ò7ËùÊöµÄ·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»ÏµÍ³£¬ÆäÌØÕ÷ÔÚÓÚËùÊöê½Úµãµ¥ÔªÊýÁ¿Îª6¸ö¡£
È«ÎÄÕªÒª
±¾·¢Ã÷ÌṩÁËÒ»ÖÖ·ÇÀíÏëÌõ¼þϵij¬¿í´øÒì²½¶¨Î»·½·¨¼°ÏµÍ³¡£±¾·¢Ã÷µÄÓÐÒæÐ§¹ûÊDZ¾·¢Ã÷ͨ¹ýÄ¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥Ôª¾àÀë²âÁ¿²½ÖèÊ×ÏȵóöÄ¿±ê½Úµãµ¥ÔªÓëê½Úµãµ¥ÔªÖ®¼äµÄ¾àÀ룬ȻºóÔÙ¶ÔÄ¿±ê½Úµãµ¥Ôª½øÐж¨Î»£¬Í¨¹ý¸Ä±ä·¢ÉäÂö³åµÄÖØ¸´ÖÜÆÚ£¬Äܹ»·Ç³£·½±ãµØÊµÏÖê½Úµãµ¥ÔªÓëÄ¿±ê½Úµãµ¥ÔªµÄʶ±ð£¬¼õÉÙÁ˶¨Î»¸´ÔÓ¶È£¬Ìá¸ßЧÂÊ¡£
Îĵµ±àºÅG01S5/00GK102928814SQ20121040096
¹«¿ªÈÕ2013Äê2ÔÂ13ÈÕ ÉêÇëÈÕÆÚ2012Äê10ÔÂ19ÈÕ ÓÅÏÈȨÈÕ2012Äê10ÔÂ19ÈÕ
·¢Ã÷ÕßÕÅöªÍ¢, ÕÅÇÕÓî, ³Â·½Ïþ, Õźì, ×ÞºéÁ¼, ÌïÐýÐý, Àîΰ½Ü ÉêÇëÈË:¹þ¶û±õ¹¤Òµ´óѧÉîÛÚÑо¿ÉúÔº