A BE33 BONANZA PLT EXPERIENCES A TRACK POS DEV AND INVADES THE LAX TCA CLASS B.

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I WAS PF OF A BEECH F33 BONANZA. WE WERE RETURNING FROM PSP ENRTE TO VNY. WE LEFT PSP VFR THROUGH THE BANNING PASS AND PICKED UP AN IFR CLRNC. WE WERE DIRECTED TO PDZ VOR (112.2) DIRECT; THEN V186 TO VNY. OUR ALT WAS 6000 FT MSL. ABOUT 12 MI W OF PARADISE VOR WE CHANGED TO VNY VOR (113.1). OUR HSI HAD BEEN CTRED ON THE 278 DEG RADIAL OF PDZ. WHEN VNY VOR WAS SELECTED AND NEW COURSE 275 DEGS SET ON THE HSI; THE NEEDLE DEFLECTED L; INDICATING WE WERE N OF COURSE; V186. I TOOK A HDG OF 265 DEGS (10 DEG INTERCEPT) TO REACQUIRE V186. SEVERAL MINS LATER THE SOCAL APCH CTLR TOLD ME TO TURN TO HDG 300 DEGS AND INTERCEPT V186. HE ASKED MY HDG AND I REPLIED 265 DEGS. HE SAID I WAS S OF V186. I RECHKED D6 HSI AND WET COMPASS INDICATIONS AND THEY WERE OK. MY INDICATION SHOWED I HAD CORRECTED AND WAS ON V186 CTRLINE. AT ABOUT 20 MI E OF VNY THE SOCAL CTLR SAID TURN HDG 260 DEGS AND CONTACT SOCAL ON 124.6 FREQ. THE PNF REPLIED 'ACFT IDENT' AND SET 220 DEGS IN THE HDG BUG OF THE HSI. I THOUGHT THE CTLR SAID 220 DEGS AS WELL. AT THE TIME OF THE XMISSION; WE WERE DISCUSSING WHY THE HSI DID NOT AGREE WITH SOCAL'S RPTED POS OF THE ACFT. ONLY 1 VOR WAS AVAILABLE IN THE ACFT. THE #2 SYS WAS IN THE SHOP FOR MAINT. ANYWAY; THE OTHER PLT FAILED TO READ BACK THE APPROPRIATE HDG OF 260 DEGS AND WE CHANGED FREQS. OUR FIRST 2 CALLS TO SOCAL ON 124.6 WERE NOT RECEIVED; BLOCKED. ON OUR THIRD CALL CHKING IN 'WITH THEM; LEVEL AT 6000 FT' WE WERE INSTRUCTED TO TURN TO 300 DEGS 'IMMEDIATELY.' WE DID AND PROCEEDED TO FLY THE VNY LDA C APCH UNEVENTFULLY. ON CONTACTING VNY GND CTL I WAS INSTRUCTED TO CONTACT SOCAL TRACON AND GIVEN A PHONE NUMBER. I CALLED AND SPOKE TO THE OPS SUPVR. HE SAID THAT I HAD FLOWN INTO LOS ANGELES CLASS B AIRSPACE AND POSED A POTENTIAL CONFLICT FOR LAX TFC FLOW FROM THE N. I TOLD HIM OF OUR HSI INDICATIONS AND THAT I FLEW 220 DEG HDG AS INSTRUCTED BY THE SOCAL CTLR. HE ASKED THE CTLRS WHO SAID THEY NEVER ISSUED 220 DEG HDG. I RELUCTANTLY GAVE HIM MY NAME AND PHONE NUMBER. AFTER LISTENING TO THE TAPE; HE CALLED ME AT XA00 THAT EVENING AND DEBRIEFED THE EVENT. WE WERE TOLD TO TURN 260 DEGS AND CALL SOCAL. HE CONFIRMED A GARBLED RADIO XMISSION FOLLOWED BY OUR INSTRUCTION TO TURN TO 300 DEGS. HE ALSO SAID THERE WAS SOME SCALLOPING OF THE VOR SIGNAL IN THE VICINITY OF V186 WHERE WE WERE; BUT NOT ENOUGH TO CAUSE US TO DRIFT THAT FAR S. I SAID OUR HSI INDICATED WE WERE N OF V186 BUT HE SAID OUR RADAR TRACK NEVER SHOWED US N OF COURSE. I HAD NO PRIOR EXPERIENCE FLYING THE LDA C APCH FROM THAT DIRECTION; SO I ASSUMED THE 220 DEG HDG FROM SOCAL WAS A VECTOR TO KEEP ME S OF BUR'S TFC FLOW.