Deconvolving known impulse response from a sampled noisy signal
This very, very much sounds like the classical problem for which you can derive that the matched filter is the optimal receive filter to maximize SNR.

You say you know the shape of the signal; I interpret this like your system looks like this

TX impulse $p$ -> Pulse shaping filter $g$ -> 500 Hz low pass $h$ -> +Noise $z$ -> Sampling

That implies that the RX signal (given we sample sufficiently fast) is the discrete

$$r[n] = p*g*h + z$$
with $*$ being the convolution operator.

Since you know the order and bandwidth of $h$, I'd argue you actually know what $h$ is precisely. Thus, you can "pre-compute" the combination 

$$m=g*h$$

The receive filter that maximizes the SNR is the matched filter – sadly, the matched filter to an IIR is not realizable (when does the time-inverse of something without end start?), you can't directly work with your actual system model.

However, if you can find a FIR filter that approximate your $h$ well enough, you should be able to  bound the error, and still get a reasonably good amplitude/power estimate by calculating the time-inverse conjugate (${}^\dagger$ operator) 
$${\hat m}^\dagger =\left(g*\hat h\right)^\dagger$$
 based on the approximative filter $\hat h$. You'd then have
 $$
\begin{align}
\hat r &amp;= p*g*h*\hat m^\dagger &amp;+ z*\hat m^\dagger\\
&amp;= p*m*\hat m^\dagger  &amp;+ z*\hat m^\dagger
\end{align}$$

Since the noise process $z$ should not be correlated to the channel/filter, the second term should become small for sufficient observation.