Narrative:

My student and I were receiving radar vectors for a practice ILS 23R approach at btl. As we were intercepting the localizer; we were advised of an SR20 at 12 o'clock and 6 miles at 2500 ft; however we weren't told anything else. We reported that we were looking for traffic. We were initially told to maintain 3000 ft. A short time later; my student and I both heard a clearance for us to descend and maintain 2500 ft. My student read-back the clearance. We started our descent down to 2500 ft. About 30 seconds later; ATC ordered a climb to 3000 ft and advised us of traffic at 12 o'clock and 1 mile. We reported traffic in sight and passed about 300 ft feet overhead. After becoming clear of the conflict ATC queried if we were in a descent. I confirmed we were and advised that we had been cleared to do so. ATC then advised that clearance was for another company aircraft that had a similar call-sign. We continued the rest of the flight without further incident. I believe that our read-back was blocked by the other aircraft also reading the clearance back; which prevented ATC from being able to correct our error. I also believe that more initial information about the cirrus would have allowed me to query ATC if the descent clearance was truly meant for us. I later found out the SR20 was outbound for the procedure turn on the RNAV 23R approach; which has the exact same approach course as the ILS. Knowing this information ahead of time would have potentially allowed me to avoid the mistake of descending due to an improper hearing of an ATC instruction.

Related reports:

Google
 

Original NASA ASRS Text

Title: PA-44 Instructor Pilot reported a NMAC with another light aircraft in the vicinity of BTL airport.

Narrative: My student and I were receiving radar vectors for a practice ILS 23R approach at BTL. As we were intercepting the localizer; we were advised of an SR20 at 12 o'clock and 6 miles at 2500 ft; however we weren't told anything else. We reported that we were looking for traffic. We were initially told to maintain 3000 ft. A short time later; my student and I both heard a clearance for us to descend and maintain 2500 ft. My student read-back the clearance. We started our descent down to 2500 ft. About 30 seconds later; ATC ordered a climb to 3000 ft and advised us of traffic at 12 o'clock and 1 mile. We reported traffic in sight and passed about 300 ft feet overhead. After becoming clear of the conflict ATC queried if we were in a descent. I confirmed we were and advised that we had been cleared to do so. ATC then advised that clearance was for another company aircraft that had a similar call-sign. We continued the rest of the flight without further incident. I believe that our read-back was blocked by the other aircraft also reading the clearance back; which prevented ATC from being able to correct our error. I also believe that more initial information about the Cirrus would have allowed me to query ATC if the descent clearance was truly meant for us. I later found out the SR20 was outbound for the procedure turn on the RNAV 23R approach; which has the exact same approach course as the ILS. Knowing this information ahead of time would have potentially allowed me to avoid the mistake of descending due to an improper hearing of an ATC instruction.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.