A new GNSS-acoustic positioning software implementing multiple positioning functions considering nadir total delays

Earth, Planets and Space

Table 1 GNSS-A positioning functions implemented in SeaGap

Function number	Function name	Mode	Calculation Method	Structure	Equation	Unknown parameters
F1	kinematic_array	Kinematic, array	NLLS	HS-SSS	14	\(\delta {\mathbf{p}}_{i}^{{\text{hor}}}, {C}_{i}\)
F2	static_array	Static, array	NLLS	HS-SSS	16	\(\delta \mathbf{p}, \mathbf{c}\)
F3	static_array_TR	Static, array	NLLS	HS-SSS	16	\(\delta \mathbf{p}, \mathbf{c},{\mathbf{b}}_{0}\)
F4	static_array_grad	Static, array	NLLS	MLGS	17	\(\delta \mathbf{p}, \mathbf{c},{\widetilde{\mathbf{g}}}_{{\text{d}}}\)
F5	static_individual	Static, individual	NLLS	HS-SSS	18	\(\delta {\mathbf{p}}_{k}, \mathbf{c}\)
F6	static_array_mcmcgrad	Static, array	MCMC	SLGS	20, 21	\(\delta \mathbf{p}, \mathbf{c},{\widetilde{\mathbf{g}}}_{{\text{d}}},\boldsymbol{ }D, {\varvec{\upgamma}}\)
F7	static_array_mcmcgradc (F6 with constraints)	Static, array	MCMC	SLGS	20, 21	\(\delta \mathbf{p}, \mathbf{c},{\widetilde{\mathbf{g}}}_{{\text{d}}},\boldsymbol{ }D, {\varvec{\upgamma}}\)

“Mode” includes “Kinematic” (kinematic positioning), “Static” (static positioning), “array” (array positioning), and “individual” (individual transponder positioning). “Calculation Method” is NLLS (non-linear least-squares) or MCMC (Markov Chain Monte Carlo) methods. “Structure” indicates the assumed sound speed structure, which is “HS-SSS” (horizontally stratified sound speed structure), “MLGS” (HS-SSS with multiple layered gradient structure), or “SLGS” (HS-SSS with single layered gradient structure)