Objectives  In order to solve the problem of the accuracy and efficiency of the noise component of the global navigation satellite system (GNSS) coordinate time series, combined with the equivalent conditional adjustment model and the minimum norm quadratic unbiased estimation method, an equivalent conditional closure error minimum norm component estimation method is proposed.

  Methods  First, we use the equivalent conditional closure error to construct the quadratic variance estimation formula, and combine the conditions of invariance, unbiasedness, and minimum norm criterion to derive the minimum norm estimation formula of the variance-covariance component based on the equivalent conditional closure error. Second, least-squares variance component estimation(LS-VCE) method, minimum norm quadratic unbiased estimate (MINQUE) method and our proposed method are used to calculate the noise amplitude of simulated time series and North American GNSS station coordinate time series respectively, and the calculation time of our method and LS-VCE method are calculated.

  Results and Conclusions  The estimation effect of the MINQUE method is consistent, and its calculation time decreases over 70% of the LS-VCE method, which verifies the correctness and the effectiveness of the proposed method.