Hi,
As per my understanding you are aiming to characterize a system using the system identification to obtain an impulse response function that can be used to reconstruct the input signal from the output signal. Please refer to the below suggestions as a possible workaround.
Increase the range of "nx" to test different model orders and potentially use model selection criteria to choose the best order.
% Instead of nx=1:10, try a range and use a criterion for selection
nx_range = 1:10;
sys_id_models = cell(length(nx_range), 1);
fit_percent = zeros(length(nx_range), 1);
for i = 1:length(nx_range)
sys_id_models{i} = n4sid(iddata(input_A, output_A, 1/samplefreq), nx_range(i));
fit_percent(i) = sys_id_models{i}.Report.Fit.FitPercent; % Get the fit percentage
end
% Select the model with the best fit
[~, best_idx] = max(fit_percent);
sys_id = sys_id_models{best_idx};
If overfitting is suspected, you may use "regularization" to prevent it.
% Use regularization (requires the System Identification Toolbox)
opt = n4sidOptions('Regularization', 'auto');
sys_id = n4sid(iddata(input_A, output_A, 1/samplefreq), 'best', opt);
Perform frequency domain analysis to check if the system behaves differently at various frequencies.
% Convert to frequency response data and plot Bode plot
frd_sys = idfrd(sys_id, linspace(0, samplefreq/2, 4096), 'FrequencyUnit', 'Hz');
bode(frd_sys);
If the impulse response is estimated well, use deconvolution directly to recover the input.
% Deconvolution to estimate the input signal
input_estimation = deconv(output_A, h3);
Introduce a non-parametric impulse response estimation as an alternative to the parametric method.
% Non-parametric impulse response estimation
h = impulseest(iddata(output_A, input_A, 1/samplefreq));
impulse(h, time);
Please refer to the MATLAB Documentation for further understanding:
Hope this helps!
