What is the best to confirm that the output of a matched filter for a linear FM chirp is correct?
In the absence of noise, the output of the matched filter is exactly the autocorrelation function of the input signal, delayed in time so that the peak autocorrelation is at the chosen sampling time (cf. the first part of this answer on this forum). I don't recall off the top of my head what the autocorrelation function of a linear FM chirp signal is, but the sharp peak that in your bottom trace suggests that the autocorrelation function is sharply peaked, perhaps like a sinc function with very small null-to-null distance.