Solutions for enhancing parameter identification effects for multivariate equation-error systems in random interference and parameter coupling conditions are considered in this paper. For the purpose of avoiding the impact of colored noises on parameter identification precision, an appropriate filter is utilized to process the autoregressive moving average noise. Then, the filtered system is transformed into a number of sub-identification models based on system output dimensions. Founded on negative gradient search, a new multivariate filtering algorithm employing a partial coupling approach is proposed, and a conventional gradient algorithm is derived for comparison. Parameter identification for multivariate equation-error systems has a high estimation accuracy and an efficient calculation speed with the application of the partial coupling approach and the data filtering method. Two simulations are performed to reveal the proposed method’s effectiveness.