I have been working on this subject for a while and I couldn't get a proper answer.
I am trying to estimate the phase of the input signal :
$x(t)=Ae^{j(at^2+bt+c)}+n(t)+i(t)$
Where $n(t)$ is a AWGN, $i(t)$ is an interfiring signal and $a,b,c$ are constant values. As you can see, the central frequency of the useful signal changes over time ($f_c(t)=2at+b$).
First, I have to filter out the interfering signal so I implemented a low-pass FIR filter H and I compute the output of the filter as follow $y[n]=\sum{h[k].x[n-k]}$. However because of the moving frequency my signal will not stay in the filter passband very long.
One solution I had was to estimate the central frequency of the signal every 1 second and shift the input signal by this estimate (which means the I add to the FIFO of my FIR the samples $x[k]e^{-2\pi f_ck/F_e}$) but when I estimate the new central frequency I will have samples with different central frequencies in my FIFO and the filter doesn't like that (I can see phase jump at the time of frequency change). So can anybody tell me how I am supposed to tackle this issue ?
Thank you !
EDIT : Thank you very much for your answers, I realized while reading your answers that I simplified my problem too much. The actual evolution of the phase of my interest signal is much more complicated than a second order polynomial. My signal is more like $x(t)=Ae^{jd(t)}+n(t)+i(t)$ with $d(t)$ a very complex function taking into account the distance and the speed of the object emitting the signal (which is a pure carrier). Also, the $i(t)$ is a function representing other object emitting other pure carrier at different speed and position (so my signal is more like $x(t)=\sum{A_ke^{jd_k(t)}}+n(t)$). I want to get the phase of each signal separately so first of all I did a small accumulation of signal to compute the spectrum of the signal and get the approximate frequency of each signal. Then I apply several FIR filters, one for each signal hoping I would get each $A_ke^{jd_k(t)}$ separately. The problem I have is that the frequency of each signal moves a lot and I have to "adapt" my FIR filter (and I don't know how to do that...) I talked about a second order phase polynomial because it is a good model of the function $d(t)$ on a short term observation.
Thank you once again for the time and effort you put in your answers.