Determination of time delay for precise bathymetric survey

Abstract

Now tide- independent bathymetric system is widely used in hydrographic survey and improves effectively single-beam bathymetric accuracy relative to the traditional bathymetric method. While time delay (TD), which exists between GPS RTK and single-beam sounding system, often leads to the positioning and sounding solution non synchronization and decreases the accuracy of final result. TD mainly originates from the lingering output of GPS RTK solution due to its interior algorithm, satellites number, radio signal processing mode and logging data model. Large numbers of experiments have proved that time delay may reach 0.2 second at least and 1.2 second at most. Generally, TD is determined by comparing sounding solutions with positioning solutions measured as vessel going by an anchored buoy in a to-and-fro surveying way with different velocities. However, this method may bring obvious error in the determination due to buoy movement. Therefore the following three methods are studied and presented in the paper. We first study method of characteristic point pairs. Looking for a characteristic inshore seabed, we implemented a to-and-fro measurement along a planning line. The characteristic terrain of the seabed can be found easily in the two profiles. For a characteristic aim on seabed, we can find a pair of characteristic points in the two profiles. According to the two horizontal positions, depths and time of the characteristic point pair, we can calculate the TD. For different characteristic points, we can also determine their time delays. Then the TD of the system is the mean of TDs of all point pairs. Determined TD by the above method needs to choose characteristic point pairs manually. In the following, we will study an automatic determination method, which is method of maximum similarity of profiles. High-sampling rate makes the to-and-fro profiles present seabed topography subtly and continuously. If we think the two profiles are two curves of A and B, we can determine TD in virtue of similarity coefficient R of them. If we fix profile A and move profile B, we can get a series of similarity coefficient R(d). If we move a displacement of d, R reaches maximum or is close to 1, then the d is the displacement resulted from TD. If v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> and v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> are mean vessel velocity in to-and- fro measurements, then TD can be acquired through the calculating of d divided by the sum of v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> and v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> . The method can automatically calculate TD, while we must implement a fro-and- to measurement. In the following, we present a more convenient method which is Method of Consistent Vertical Motion of Vessel. Both of heave derived from MRU and GPS height from GPS RTK take the same role in monitoring the vessel vertical motion. If we correct the two signals to the same position, such as reference point(RP) in vessel frame system(VFS), we can get two time series dh <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">heave-RP</sup> and h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GPS-RP</sup> . Taking similar method shown in method of maximum similarity of profiles, we can acquire TD by fixing time series dh <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">heave-RP</sup> and moving time series h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GPS-RP</sup> in time scale. If we move a time ? and make similarity coefficient R(?) reach maximum, then the ? is also time delay of the system. The method of time delay determination can be implemented at any time and by any way. While an important mention, which time length [0 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> ] of the time series used for determining time delay is not the whole time length of dh <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">heave-RP</sup> or h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GPS-RP</sup> , but only part of it, needs to be clarified. As concerning frequency characters of the two time series, time series h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GPS-RP</sup> , veritably reflects entire- frequency vertical motion, while dh <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">heave-RP</sup> is only valid in presenting high-frequency vertical motion. Thus, the time length of both time series should be within 60 second of their common period. we used the three methods in an experiment of time delay detection, and acquire very consistent time delay and high accuracy of time delay determination. Finally, we analyze the characters of the three methods. Method of characteristic point pairs and method of maximum similarity of profiles need to implement to-and-fro profile measurements in data sampling. The two methods are simple in calculation, while accuracy of the determination of TD will become weak with the decreasing of sampling density and point- pair correlative degree. Method of consistent motion has simplicity in implement and high accuracy in the determination of time delay. Thus we recommend it as an optimum method for determining TD.