My input signal is given by $$ x[n] = A\sin(2\pi f n/F_s + \varphi)$$ The signal is uniformly sampled at a sampling rate of $F_s $[Hz]. However some of the samples are missing. Assume that there are not many missing samples and that their location is known (i.e. I know the timestamp for each sample), I am interested in estimating $A$ and $f$.
My initial approach is to interpolate the vector and use standard methods (e.g. FFT). Another thought is to perform some kind non-linear regression (which I am unfamiliar with).
Any help would be appreciated.