DURING A DESTABILIZED APCH; A MISSED APCH IS PERFORMED BY THE PIC OF AN H25B AFTER RECEIVING A GPWS ALERT AND MISSED APCH INSTRUCTIONS FROM THE APCH CTLR AT SBA; CA.

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ON FEB/MON/04; DAY 6; 11 HRS 50 MINS INTO DUTY; WE WERE SHOOTING AN ILS 7 TO SBA FOR END OF DUTY DAY WITH 2 PAX. WX WAS CALLED 1300 FT OVCST WITH 4 MI VISIBILITY. WE WERE BEING VECTORED BY APCH CTL ON DOWNWIND. WE WERE GIVEN A SERIES OF VECTORS 240 DEGS TO 270 DEGS. WHEN ABOUT ABEAM NAPPS; WE WERE GIVEN A 360 DEG HDG AND DSCNT FROM 4000 FT TO 2000 FT. USING THE AUTOPLT; WE WENT TO 30 DEGS BANK AND 1500 FPM DSCNT AND DEPLOYED THE SPD BRAKES. WE WERE EXPECTING A LONGER FINAL. AT 300 DEG HDG; WE WERE GIVEN A FURTHER R HDG OF 050 DEGS. AT 360 DEGS - 010 DEGS; WERE CLRED FOR THE APCH. WE CROSSED THE LOC WITH A HDG OF 030 DEGS IN A FULL 30 DEG BANK AND 1800 FT DSCNT. THE AUTOPLT WOULD NOT LOCK ONTO THE LOC; BUT THE GLIDE PATH WAS FULL SCALE DOWN. WITH PAX ON BOARD; WE BEGAN A SMOOTH RECOVERY TO ABORT THE APCH. AT ABOUT 090-100 DEG HDG; APCH CTL DIRECTED A 120 DEG HDG AND CLB TO 2000 FT. I TURNED THE AUTOPLT OFF AND BANKED TO 45-50 DEGS AND BEGAN A HIGHER PWR SETTING MORE ABRUPT CLB. WE CROSSED THE LOC THE SECOND TIME AS DEPICTED ON THE ATTACHED DRAWINGS; ABOUT 1 NEEDLE WIDTH BELOW THE GLIDE PATH. THEIR DIRECTIONS WERE FOLLOWED BY 1 CYCLE OF THE GPWS TERRAIN WARNING. DURING THE ABRUPT RESPONSE TO THEIR HDG AND ALT CALL (IMMEDIATELY) WE CLBED THROUGH THE 2000 FT; AS DIRECTED TO 2500 FT; THEN DSNDED BACK TO 2000 FT. AFTER LEVELING OFF; APCH CTL ASKED US IF WE HAD TROUBLE RECEIVING THE ILS. WHEN WE RESPONDED IN THE AFFIRMATIVE; THEY TOLD US THE HAWKER IN FRONT OF US HAD THE SAME PROB; YET NO MENTION WAS MADE OF THIS SIT BEFORE WE BEGAN OUR APCH. WE GOT VECTORS FOR A WIDER DOWNWIND AND LONGER BASE. THIS APCH WAS NORMAL; BUT WE DIDN'T BREAK OUT UNTIL 350 FT; INSTEAD OF THE 1300 FT THAT WAS CALLED. WX AT THE FIELD (SBA) WAS: STRONG GUSTY WINDS WITH A SHEAR ON FINAL. RAIN AND LOW CEILINGS; 350 FT AGL; AND SMALL SQUALL CELLS IN THE AREA (NO OBSERVED LIGHTNING); HVY RAIN IN THE CELLS. THE DRAWING INDICATES HORIZ AND VERT POS AND XING POINTS ON THE LOC. THE FLT DEPICTION WAS IN REF TO THE GS FOR VERT POSITIONING. THE TURN FROM 270 DEGS TO ABOUT 100 DEGS WAS MADE ON THE AUTOPLT AT STANDARD RATE. THE TURN RADIUS WAS ABOUT 2 NM DUE TO OUR SPD; ABOUT 200 KIAS. THE ACFT WAS DISPLACED AS DRAWN; CONSIDERING THE ACFT TURNING RADIUS. THE LOC WAS DEFLECTED FULL SCALE; UNTIL RE-XING IT. AT THE MOST; THE ACFT WAS NEVER A 1/2 DOT DEFLECTION BELOW THE GLIDE PATH; TRYING TO KILL THE DSCNT RATE TO REMAIN WITHIN TERPS PROTECTED AIRSPACE.