PLT OF SMA GA ACFT RECEIVED A LOW ALT WARNING FROM THE TWR DURING A LOC DME INST APCH AS A DIRECT RESULT OF THE ACFT NOT BEING EQUIPPED WITH DME EQUIP AS REQUIRED BY THE APCH PROC.

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HOUSTON APCH VECTORED ME TO INTERCEPT THE LOC FOR LOC DME RWY 17R INST APCH TO KDWH. ATC HANDED ME OFF TO KDWH TWR AND TWR HAD CLRED ME TO LAND. I HAD FILED /R AS I HAVE A LORAN CERTIFIED FOR IFR ENRTE; HOWEVER; I DO NOT HAVE DME; WHICH IS REQUIRED TO IDENT THE FAF AND MAP. INSTEAD OF SIMPLY ASKING IF TWR COULD IDENT THOSE POINTS FOR ME I MADE AN ERROR OF INTERP AND; EVEN WORSE; FAILED TO EVEN CORRECTLY FLY BASED ON MY INTERP. IN PREPARATION FOR ARR I HAD LOOKED AT ALL THE SUITABLE APCHS; AND I INTERPRETED NDB RWY 17R AS BEING COLLOCATED WITH THE LOC. ON EXAMINATION LATER I SEE THAT THEY DIFFER BY 3 DEGS; AS WELL AS THE NDB APCH BEING MUCH CLOSER TO THE ARPT. INSTEAD OF ASKING FOR HELP AND ACTING ACCORDING TO THE ANSWER I GOT; I CHOSE TO 'CREATE' MY OWN APCH. I FIGURED I COULD USE THE NDB'S FAF AND MAP. THAT PROBABLY COULD HAVE WORKED OUT; BUT THEN I FAILED TO FLY CORRECTLY BASED ON MY (POOR) JUDGEMENTS. I WAS CONCERNED ABOUT LOOKING LIKE I WAS FLYING THE APCH WRONG; SO I HAD LET DOWN TOO EARLY; AND THEN I ALLOWED THE ALT TO DROP BELOW WHAT I WANTED. TWR CALLED AND ASKED ABOUT MY ALT. AT THAT POINT I THOUGHT ERRONEOUSLY THAT THEY THOUGHT I WAS TOO HIGH. INSTEAD OF VERIFYING THEIR INTENT I ACKNOWLEDGED THE CALL UP; VERIFIED MY INDICATED ALT AND ACTED AS IF NOTHING WAS WRONG. I KNEW I WAS WRONG; AND I BECAME FLUSTERED BY THE CALL UP. I LET MY ALT DROP EVEN LOWER; AND I DRIFTED L OF COURSE. TWR ISSUED AN URGENT ALT ALERT. I COULD SEE THE GND BELOW AND AHEAD AT THAT POINT; AND I ACKNOWLEDGED AND CONTINUED TO LNDG. I ESTIMATE MY FIRST AND BIGGEST FAILURE WAS IN NOT WANTING TO ADMIT MY SIT -- NO DME -- AND ASK FOR HELP. SECOND; I FOOLISHLY THOUGHT I COULD MAKE UP MY OWN APCH 'ON THE FLY.' THIRD; I ALLOWED MY FEELINGS OF GUILT AND OUTSIDE DISTRS TO WEAKEN MY FLYING ATTN. FOURTH; I DIDN'T ASSERT CTL OVER THE PLANE AS I SHOULD HAVE TO MAINTAIN MY INTENTIONS.