Fast Approach to Constructing Normal Equation During the Time of Calculating Height Anomaly Difference by Using Vertical Deflections

Vertical deflections can be used tocalculate height anomaly differences, and determine a regional quasi-geoid under the control of GPS leveling points. But the existing typical methods used for structural equation, the elements in coefficient matrix need to be operated one by one, and all of the elements or those on a diagonal must be saved in internal memory for computing. This usually leads to low-speed processing and high-memory occupancy rates. In order to solve these problems, we propose a novel method in the form of a blocked matrix , then processes sparsely (only saving non-zero elements), and finally integrates all the blocked matrixes. This blocked matrix is considered as operational unit in the further steps. Experiments show that: compared to the typical methods, the computation efficiency of our method has been improved at least 2 orders of magnitudes, this makes our method can quickly solve an adjustment problem intractable by traditional methods of computer configuration. Therefore, our method has great reference value when resolving adjustment problems with regular gridded data.