Information sufficiency limits in metaheuristicbased IIR system identification under multi-level observation reduction

This study examines information-induced limits of parameter identifiability in IIR system identification under multi-level observation representations. A fixed populationbased optimization framework is employed to isolate information effects from algorithmic variability, while the observation model is progressively reduced in information content. Using a persistently exciting white Gaussian input, three observation scenarios are analysed: full time-domain measurements, magnitude-only spectral observations, and band-limited magnitude representations. Although numerical convergence is achieved under all scenarios, parameter estimation accuracy deteriorates systematically as observation information decreases, as reflected in the distribution of relative parameter errors. Fisher information-based indicators are evaluated as complementary sensitivity measures and reveal consistent reductions in local information volume, while also illustrating their limitations under nonlinear and many-to-one observation mappings. The results indicate that identifiability loss originates from structural information insufficiency in the observation model and cannot be compensated by optimization alone.