The underwater dynamic navigation based on the sectional observation system generates multi-source and heterogeneous data, creating crossed or forked tracks due to asynchronous time delay and unknown system errors. This makes it difficult to represent continuous navigation processes and identify local characteristic points. To address this issue, a functional reconstruction algorithm for underwater data fusion is proposed.

The polynomial constraint fusion (PCF) method and the spline function fusion (SFF) method are employed to process track data collected via sectional observations. These methods effectively integrate the full underwater track and address issues such as discontinuous dynamic parameter sequences and ambiguous data in overlapping section.

Numerical simulations show that both PCF and SFF methods can capture the main characteristics of underwater dynamic motion and produce accurate and continuous tracks. Compared with the general data fusion (GDF) method, the PCF and SFF yield smoother and more continuous data series, enabling a more precise representation of motion in overlapping regions. Compared with the moving average filter algorithm, the fusion processing results based on the functional reconstruction algorithm and the filter algorithm both show an optimizing performance in accuracy and smoothness. In terms of velocity and acceleration consistency, the functional reconstruction algorithm is better than the filter algorithm. Verified by sea trials, the SFF and the PCF were used to obtain the re-analysis track in the observed section with velocity estimation errors within 5% at the characteristic points, and also obtain the predicted track in subsequent sections with errors within 15%.

The proposed method shows application values for processing multi-source and heterogeneous data in complex underwater motion scenarios, and is also effective for the short-term underwater navigation estimation.