the error convergence matrix in Kalman Filter provides the convergence of the filter. In similar war, how the convergence of the Complementary Filter can be obtained?
Compute the white-noise gain (WNG) of the filter. Do this in either: In the (discrete) time domain, as an infinite summation of the squared impulse response, over m = 0...Inf; or in the (continuous) frequency domain, as an integral of the squared magnitude of the filter's frequency response, over -pi...+pi. They give the same result (the WNG). In the latter case, you will need to divide the result by 2*pi. Assuming the steady-state bias is zero (because you have matched your filter model to the signal) WNG*var_mes is the variance of the estimate output by your filter at steady-state, i.e. after the filter has converged, for an input signal that is corrupted by additive white noise, with a variance of var_mes. It need not be Gaussian noise.