Robust adaptive masked and filtered hierarchical multi-innovation stochastic gradient identification for multivariable ARX systems with missing outputs and common colored non-Gaussian disturbances

Subsystem-by-subsystem recursive identification is very inefficient for an $ r $-input $ m $-output multivariable autoregressive with exogenous input (ARX) system since it performs multiple operations due to the common input-information vector used by all output channels. Methods that take advantage of this coupled structure such as hierarchical stochastic-gradient and hierarchical multi-innovation stochastic-gradient methods cut down on computations. Unfortunately, most of the formulations are based on full output measurements and white noise of the measurement, and this restricts their use in networked and industrial acquisition systems. In this paper, a powerful multivariable ARX system with missing output samples, corrupted by a typical first-order colored disturbance and a set of impulsive non-Gaussian innovations, was dealt with using a new stochastic-gradient hierarchical multi-innovation adaptive algorithm (RAMF-HMISG). A masked coupled identification model was initially proposed including one-step reconstructed outputs and binary output-availability variables to ensure that the autoregressive regressors are still available, while the missing samples were not included in the identification loss. A commonly used auxiliary prewhitening filter was then applied to the output, the autoregressive regressors, as well as the shared input regressor, leading to preservation of the deterministic part of the ARX model, while factually separating the filtering/reconstruction mismatch. The correction term was based on Huber loss and the bounded score to make it more robust. A filtered reliability mask was also added as this takes into account current and previous output measurements for each filtered output sample. Based on the previous innovation energy, which was smoothed, non-circular adaptive laws were also proposed for the innovation length $ p(t) $ and convergence index $ \varepsilon(t) $. It was shown that a residual relation and a conservative mean-square boundedness result can be made under the conditions of bounded regressors, block excitation, stable filtering, bounded reconstruction mismatch, and stochastic-approximation step-size conditions. The analysis ensured the stability to a noise/mismatch dependent neighborhood for nonzero disturbances. Numerical simulations, ablation tests, and Monte Carlo statistics demonstrated that the proposed RAMF-HMISG algorithm outperforms other variants of the algorithm, such as zero-filling, masked-only, robust-only, and fixed filtered ones, in terms of smaller parameter-estimation errors under the simultaneous colored noise, missing outputs, and impulsive perturbations. The evaluation further covered a higher-order three-input three-output system, missing-output probabilities up to $ 50\% $, several noise levels, coloring coefficients and impulsive intensities, a component-wise ablation of the two adaptive laws, a scalability study of the adaptive mechanisms, and a numerical verification of the excitation and mismatch conditions used in the analysis. The applicable boundary of the common-filter assumption was also quantified for channel-dependent coloring.