Almost sure convergence rates for system identification using binary,quantized, and regular sensors

This paper presents almost sure convergence rates for system identification under binary, quantized, and regular sensors. To accommodate practical model complexity constraints, the system under consideration is represented by a modeled part together with an unknown-but-bounded unmodeled dynamics. Under uncorrelated noise sequences, identification errors with different sensor types are studied and tight error bounds are obtained without information or constraints on noise moment conditions. The results are then extended to correlated noise sequences whose remote past and distant future are asymptotically independent. In both cases, almost sure error bounds of the laws of iterated logarithms type are derived.