Efficient Estimation of Variance and Covariance Components: A Case Study for GPS Stochastic Model Evaluation

The variance and covariance component estimation (VCE) has been extensively investigated. However, in real application, the bottleneck problem is the huge computation burden, particularly when many variance and covariance components are involved for many heterogeneous observations. The objective of this paper is to develop a new method allowing the efficient estimation of variance and covariance components. The core of the new method is to construct an orthogonal complement matrix of the coefficient matrix in a Gauss-Markov model using only the coefficient matrix itself. Therefore, the constructed matrix and the computed discrepancies of measurements with each other, which are the essential inputs for the VCE, are invariant in the iterative procedure of computing the variance and covariance components. As a result, the computation efficiency is significantly improved. As a case study, we apply the new method to evaluate the GPS stochastic model with 15 variance and covariance components demonstrating its superior performance. Comparing with the traditional VCE method, the equivalent results are achievable, and the computation efficiency is improved by 34.2%. In the future, much more sensors will be available, and plentiful data can be acquired. Therefore, the new method will be very promising to efficiently estimate the variance and covariance components of the measurements from the different sensors and reasonably balance their contributions to the fused solution, benefiting the higher time-resolution solutions.