Seafloor transponder coordinates are determined by measurements between a ship-borne GNSS-acoustic transducer and the transponder. Differencing techniques can be applied to eliminate the impact of measurement biases for precise positioning effectively. The problem is that the correlations between differenced measurements must be adequately considered in the covariance matrix, which might cause a great number of calculations. This paper presents a set of conversion formulae to derive the differenced solution from the undifferenced model without nuisance parameters, and then we propose a dimension-reduction algorithm to fast solve the Gauss–Markov model augmented with nuisance parameters. The equivalence of the differenced and undifferenced solution is discussed within a wider range. It shows that: (1) the undifferenced solution can be converted into the differenced solution with only a few additional calculations; (2) there are a class of differencing schemes which are completely equivalent to each other having unique differencing equivalence weight (DEW) matrix; (3) the proposed algorithm is more efficient and has a good numerical stability relative to the blocking–stacking algorithm and the one-by-one elimination. The simulation and the real trial performed in a 3000-m depth sea area verified the proposed results.

海底转发器坐标由船载 GNSS 声学传感器和转发器之间的测量确定。可以应用差分技术来消除测量偏差对精确定位的影响。问题是必须在协方差矩阵中充分考虑差分测量之间的相关性，这可能会导致大量计算。本文提出了一组转换公式来从无扰动参数的无差分模型中推导出差分解，然后我们提出了一种降维算法来快速求解带有扰动参数的高斯-马尔可夫模型。在更广泛的范围内讨论了差分和非差分解的等价性。它表明：(1) 只需少量额外计算，即可将非差分解转换为差分解；(2) 存在一类完全等价的差分方案，它们具有唯一的差分等价权(DEW)矩阵；(3)所提出的算法相对于block-stacking算法和一一消除算法效率更高，具有良好的数值稳定性。在 3000 米深的海域进行的模拟和实际试验验证了所提出的结果。(3)所提出的算法相对于block-stacking算法和一一消除算法效率更高，具有良好的数值稳定性。在 3000 米深的海域进行的模拟和实际试验验证了所提出的结果。(3)所提出的算法相对于block-stacking算法和一一消除算法效率更高，具有良好的数值稳定性。在 3000 米深的海域进行的模拟和实际试验验证了所提出的结果。