Kalman  Filter

 

Rudolf E. Kalman ÀÌ ¹ß¸íÇÑ Ä®¸¸ÇÊÅÍ´Â ÃÖ¼ÒÀڽ¹ý (Least Square Method) ¸¦ »ç¿ëÇؼ­ ½Ç½Ã°£À¸·Î ÀâÀ½ (noisy) ¿îµ¿ ¹æÁ¤½Ä (equations of motion) À» °¡Áø ½Ã°£¿¡ µû¸¥ ¹æÇâ (time-dependent state vector) ¸¦ ÃßÀûÇÏ´Â È¿À²ÀûÀÎ Àç±Í °è»ê¹ý (recursive computational solution) ÀÌ´Ù. Ä®¸¸ÇÊÅÍ´Â ÇϳªÀÇ ½Ã½ºÅÛÀÌ ½Ã°£¿¡ µû¸¥ º¯È­¸¦ ÀûÀýÇÏ°Ô ¿¹ÃøÇÒ ¼ö ÀÖµµ·Ï ÀâÀ½ (noise) À¸·ÎºÎÅÍ ½ÅÈ£ (signal) ¸¦ ã¾Æ³»±âÀ§ÇØ »ç¿ëµÈ´Ù.

½ÇÁ¦·Î´Â Peter Swerling ÀÌ ÀÏÂî±â À¯»çÇÑ ¾Ë°í¸®ÁòÀ» °³¹ßÇß´Ù. Stanley Schmidt ´Â ÃÖÃÊ·Î Ä®¸¸ÇÊÅ͸¦ ½ÇÁ¦·Î ÀÀ¿ëÇÏ¿© »ç¿ëÇß´Ù°í ¾Ë·ÁÁ®ÀÖ´Ù. Kalman ÀÌ NASA Ames Research Center ¸¦ ¹æ¹®ÇßÀ» ¶§ ¿ìÁÖ¼± ¾ÆÆú·ÎÀÇ ±Ëµµ¸¦ ÃßÁ¤ÇÏ´Â ¹®Á¦¿¡ ±×ÀÇ ¾ÆÀ̵ð¾î°¡ »ç¿ëµÉ ¼ö ÀÖ´Ù´Â °ÍÀ» ¾Ë°ÔµÇ¾ú°í, ¿ìÁÖ¼± ¾ÆÆú·ÎÀÇ ¿îÇàÄÄÇ»ÅÍ (navigation computer) ¿¡ Æ÷ÇÔµÇ°Ô µÇ¾ú´Ù.

´Ù¾çÇÑ Á¾·ùÀÇ Ä®¸¸ÇÊÅÍ°¡ Áö±Ý±îÁö °³¹ßµÇ¾ú´Âµ¥, ¼ÒÀ§ simple Kalman filter À̶ó ºÒ¸®¿ì´Â Ä®¸¸ÀÇ ¿ø·¡ÀÇ Çü½Ä¿¡¼­ºÎÅÍ, Schmidt ÀÇ extended filter, information filter, Bierman °ú Thornton µîµî¿¡ ÀÇÇØ °³¹ßµÈ ´Ù¾çÇÑ squrar-root filter µéÀÌ ÀÖ´Ù. Ä®¸¸ÇÊÅÍ´Â Á¦¾î½Ã½ºÅÛ°øÇп¡¼­ ±¤¹üÀ§ÇÏ°Ô »ç¿ëµÈ´Ù. Wiener filter ¿Í ºñ±³µÈ´Ù. ...... (Wikipedia : Kalman filter)

´ëºÎºÐÀÇ »ç¶÷µéÀº Ä®¸¸ ÇÊÅÍ¿¡ ´ëÇØ µé¾î º¸Áö ¸øÇß´Ù. ±×°ÍÀº ºñÇà±â¿Í ¿ìÁÖ Å½»ç ·ÎÄÏ, ±×¸®°í ¼øÇ× ¹Ì»çÀÏÀ» À¯µµÇÏ°í, À§¼º°ú °æÁ¦ÀÇ Ãß¼¼¿Í Ç÷¾× È帧ÀÇ º¯È­ µîÀ» ÃßÀûÇÑ´Ù. ±×°ÍÀº 'ÃÖÀûÀÇ' ¿¹Ãø±âÀÌ´Ù. ±×°ÍÀº ºñÇà±â°¡ ±¸¸§¿¡ °¡¸®¾î ÀÖÀ» ¶§ ºñÇà±âÀÇ ¹æÇâ¿¡ ´ëÇØ '°¡Àå Àß' ¿¹ÃøÇÒ ¼ö ÀÖµµ·Ï ÇÑ´Ù. ¿©·¯ºÐÀº ¾î¶»°Ô ¹Ì»çÀÏÀÌ ¸ñÇ¥¹°À» ã°í, ¾î¶»°Ô ¿ìÁÖ ºñÇà»çµéÀÌ Áö±¸·Î µ¹¾Æ¿À´ÂÁö ±Ã±ÝÇØÇØ º» ÀûÀÌ ¾ø´Â°¡? Ä®¸¸ ÇÊÅÍ´Â ¾î¶»°Ô ÀÌ·¯ÇÑ ÀÏÀÌ °¡´ÉÇÑÁö º¸¿© ÁØ´Ù. ´ÙÀ©ÀÇ ÀûÀÚ »ýÁ¸ ÀÌ·ÐÀÌ ÁøÈ­ »ý¹°ÇÐÀ» ´ëÇ¥ÇÏ´Â °Í°ú ¸¶Âù°¡Áö·Î, Ä®¸¸ ÇÊÅÍ´Â ´ëºÎºÐÀÇ °øÇÐÀ» ´ëÇ¥ÇÑ´Ù. ¼öõ ¸íÀÇ ¿£Áö´Ï¾îµéÀº Ä®¸¸ ÇÊÅÍ¿¡ ¾à°£ µ¡ºÙÀ̰ųª º¯ÇüµÈ ³í¹®µéÀ» ¹ßÇ¥ÇÏ¿´´Ù. ..............

term :

¿¹Ãø (Prediciton)   Rudolf E. Kalman   Á¦¾î (Control)

Site :

The Kalman Filter

Kalman Filtering

Kalman filters

Paper :

Ä®¸¸ÇÊÅ͸¦ ÀÌ¿ëÇÑ ¿ì¸®³ª¶óÀÇ ÀáÀçÀû GNP ÃßÁ¤°ú °æ±âº¯µ¿ÀÇ ÃßÀÌ¿¡ °üÇÑ ¿¬±¸ (Potential GNP and Business Cycles of Korea : A Kalman Filtering Approach) : À̺´¿Ï, Çѱ¹°æÁ¦ÇÐȸ, 1994

È®Àå Ä®¸¸ÇÊÅ͸¦ ÀÌ¿ëÇÑ LEO À§¼ºÀÇ ±Ëµµ °áÁ¤ ¹æ¹ý (THE ORBIT DETERMINATION OF LEO SATELLITES USING EXTENDED KALMAN FILTER) : ÃÖ±ÔÈ«, ¼Õ°ÇÈ£, ±è±¤·Ä, Çѱ¹¿ìÁÖ°úÇÐȸ, 1995

Ä®¸¸ÇÊÅ͸¦ ÀÌ¿ëÇÑ ·¹ÀÌ´Ù ÃßÀû°èÀÇ ºñ±³¿¬±¸ : À§»ó±Ô, ÀÓûºÎ, Çѱ¹Ç×°ø¿ìÁÖÇÐȸ, 1989

ÀûÀÀ Ä®¸¸ÇÊÅ͸¦ ÀÌ¿ëÇÑ MTI ·¹ÀÌÅÍÀÇ À̵¿Ç¥Àû ÃßÀû ±â¹ý (Moving Target Tracking Technique of MTI Radar Using Adaptive Kalman Filter) : ¹ÚÀÎȯ, Á¶°â·¡, Á¶¼³, Çѱ¹Ç×°ø¿ìÁÖÇÐȸ

Ä®¸¸ÇÊÅ͸¦ ÀÌ¿ëÇÑ ÃÖ°í/ÃÖÀú ±â¿Â¿¹º¸ (The Forecasting the Maximum / Minimum Temperature Using the Kalman Filter) : À̵¿ÀÏ, ÀÌ¿ìÁø, Çѱ¹±â»óÇÐȸ, 1999

Ä®¸¸ÇÊÅ͸¦ ÀÌ¿ëÇÑ ¹«±ÃÈ­À§¼º ±Ëµµ °áÁ¤ ¼º´ÉºÐ¼® ¿¬±¸ (Performance Analysis of Kalman Filter Based KOREASAT Orbit Determination) : ¹ÚºÀ±Ô, ¾Èżº, Çѱ¹Ç×°ø¿ìÁÖÇÐȸ, 2000

¹Ýº¹Àû È®Àå Ä®¸¸ÇÊÅ͸¦ ÀÌ¿ëÇÑ ¾ó±¼ÀÇ 3Â÷¿ø ¿òÁ÷ÀÓ·® ÃßÁ¤ (3-D Facial Motion Estimation Using Iterative Extended Kalman Filter) : ¹Ú°­·É, ±èÀçÈñ, Çѱ¹Á¤º¸Ã³¸®ÇÐȸ

ÃÖ¼Ò ÃÖ´ë ÃßÁ¤·®°ú º£ÀÌÁî ÃßÁ¤·®À¸·Î¼­ÀÇ Kalman ÇÊÅÍ¿¡ °üÇÏ¿© (On the Kalman Filter as the Bayes Estimator and the minimax Estimator) : ±èÁö°ï, »ó¸í´ë ÀÚ¿¬°úÇבּ¸¼Ò, 1998