Variational Bayesian inference for the identification of FIR systems via quantized output data

For identifying the parameters in finite impulse response (FIR) systems via the quantized output, existing expectation maximization (EM) methods are involved with the intractable integrals. To overcome the above shortcoming, this paper proposes an approach referred to as explicit EM (EEM). First, we fit the quantized output data by a linear Gaussian regression distribution with some compensation parameters. As a result of the linear Gaussianity, the posterior of the excited output can be explicitly computed, so that EEM has the less computation burden than the existing EMs. Second, through optimizing these compensation parameters by resorting to variational Bayesian inference, the intrinsic distribution of the quantized output can be well fitted with guaranteed identification accuracy. Third, the linear Gaussian regression distribution is independent of the specific quantization function form, which enables EEM applicable for different quantization forms. Finally, the simulation demonstrates the feasibility and effectiveness of the proposed approach.