Estimation of Instantaneous Amplitude
Instantaneous amplitude is usually done in conjunction with analytic signals and the Hilbert transform. See this answer on this site.


  For signal $s(t)$, given its Hilbert Transform $\hat{s}(t)$ it is defined as a composition:
  
  $$s_A(t)=s(t)+j\hat{s}(t) $$
  
  The Analytic Signal that we obtain is complex valued, therefore we can express it in exponential notation:
  
  $$s_A(t)=A(t)e^{j\psi(t)}$$
  
  where:
  
  $A(t)$ is the instantaneous amplitude (envelope)
  
  $\psi(t)$ is the instantaneous phase.