An adaptive boundaries technique (ABT) yielded by the geometrical properties of celestial triangles is proposed to deal with problems resulting from ex-meridian or meridian sights when the Sumner method is used. Due to the trial-and-error characteristic of the Sumner method, an iteration method is introduced to improve numerical accuracy. Combining the ABT and the iteration method into the Sumner method, this modified Sumner method (MSM) is developed so that it successfully determines the astronomical vessel position (AVP). Especially when the non-simultaneous sights condition is encountered, based on the running fix concept, middle-latitude sailing is adopted to translate Sumner points to the fix time for determining the AVP. A program developed using the proposed approach is implemented to solve the AVP problem. Three benchmark examples are conducted to validate the accuracy and versatility of the proposed approach.

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