Is this a robust method for analysing correctness of a filtered signal? Is there a more robust method? I have a recorded signal which contains several frequency components with stochastic phase and amplitude changes and want to extract the true signal with the other frequency components and noise removed. I have performed several filtering techniques to attempt to achieve this. However I need a robust measure of how correct my filtered signal is and I do not have a method of measuring the signal on it's own, without the noise and other frequency components, in order to validate it that way. One method I have applied is minusing the filtered signal from the raw signal in time space and then taking the fft/psd (power spectral density) of the remaining signal and I see that the peak is gone, is this a robust measure of checking the signal I am tracking is correct? Is there any other methods for analysing this without having a way of measuring the true signal?

Some examples of the raw and differences signals for a couple of different filtering methods are shown below: (blue is the PSD of the original raw signal, and green is the PSD of [raw - filtered])
Given you can have a "reference waveform" representing the characteristics of your expected signals, to test the "correctness" of the signal extracted from noise use the Normalized Correlation Coefficient. I reference other posts below where I give the details of computing and using the Normalized Correlation Coefficient:

Noise detection

How can I find SNR, PEAQ, and ODG values by comparing two audios?

This will be an interesting approach to compare your different algorithms as the result of removing portions of your signal of interest or keeping noise contributions will both reduce the correlation coefficient as expected; so this will be an excellent approach to accurately indicate which algorithm you use is optimum for your waveform.