Compensation of INS Errors based on LBL References in a Quadratic Sound-Speed-Profile

In this paper, compensation of an inertial navigation system (INS) errors based on position references from a long baseline (LBL) acoustic positioning system is presented. This problem arises form the inherent tendency of an INS to accumulate errors over the time. To mitigate this drawback, the INS needs to be corrected in certain period using an accurate reference. In terrestrial and aerial applications, these references are mostly provided by the global positioning systems (GPS). In the absence of GPS in the water, its aforementioned role can be taken by due to their resemblance in terms of configurations and working principles. However, since propagation speed of an underwater acoustic wave is not necessarily constant, its trajectory-the raytrace-henceforth may not be linear. When this is the case, the well-developed methods and technique in the GPS community cannot be directly borrowed and implemented to a LBL. The main contribution of this paper is to deal with deal with the above INS/LBL navigation while taking the characteristic of underwater acoustic wave into account. Specifically, it is considered interactions between an autonomous underwater vehicle (AUV) and a LBL in a region where its sound-speed-profile (SSP) can be approximated as a quadratic function of depth. When a time-of-flight (ToF) measurement occur between an acoustic transponder and the AUV, the horizontal pseudorange between these two points is then estimated by calculating its Snell parameter. Once pseudoranges from all transponders are available, the so-called pseudorange-differences method can be used to compute the subject horizontal position. Subsequently, the INS as primer navigation aid can use this reference to compensate the errors. By simulation, we demonstrate that the LBL can provide the position reference with averaged errors less than 2 m.