Long Baseline LBL positioning

Long baseline (LBL) positioning is a standard in underwater navigation. First used in the 1960's and 1970's (Hunt, Marquet, Moller, Peal, Smith, & Spindel, 1974), the foundational idea of using acoustic transponders moored to the seafloor has been used to fix the position of a wide spectrum underwater assets: submersibles, towed instrumentation, ROVs and AUVs. Fig. 4 illustrates the basic LBL method for use with an AUV. For each navigation cycle the vehicle measures the two-way time-of-flight for an acoustic signal sent round trip between the platform and fixed transponders on the seafloor. Position is determined by multilateration, typically implemented as a non-linear least-squares solution to the spherical positioning equations.

Due to the particular challenges and constraints of working in marine environments, a large variety of range-based positioning solutions have been put into practice. The ability to precisely measure the range between two acoustic nodes is the foundation of any such solution. For example, short baseline (SBL) techniques are equivalent to the LBL positioning except that the transponders are in closer proximity, often mounted to the surface ship or platform (Milne, 1983) (Smith & Kronen, 1997). Wired configurations are used in small environments and allow one-way range measurement (Bingham, Mindell, Wilcox, & Bowen, 2006). Such solutions can be particularly useful for confined environments such as small test tank (Kinsey, Smallwood, & Whitcomb, 2003).

There are many implementations of the basic LBL positioning method. Commerical systems are available to provide support for scientific, military and industry application. Typical systems operate at frequencies near 10 kHz with maximum ranges of 5-10 km and range resolution between 0.5 and 3 m1. Specific purpose systems are also available for small-scale high-resoution positioning2 or even subsea geodetics.

Fig. 5 is a conceptual sketch of the method of spherical positioning which can be generalized with a stochastic measurement model. Each spherical positioning solution is based on observing individual range values (zr.) between known fixed beacon locations (xb.) and an unknown mobile host position (xh) where the individual range measurements is indexed by i.

We consider the additive noise in each measurement (wr.) as an independent, zero-mean, Gaussian variable with variance ff,?.

1 Examples include solutions from Teledyne Benthos, Sonardyne International Ltd. and LinkQuest Inc.

2 Examples include solutions from Desert Star Systems or Marine Sonics Technology, Ltd.

Fig. 4. Illustration of long baseline (LBL) positioning of an AUV in an instrumented environment. Three transponders are shown moored to the seafloor. Three time-of-flight range observations are represented by dashed lines between the seafloor transponders and the mobile host, in this case an autonomous underwater vehicle.

Fig. 4. Illustration of long baseline (LBL) positioning of an AUV in an instrumented environment. Three transponders are shown moored to the seafloor. Three time-of-flight range observations are represented by dashed lines between the seafloor transponders and the mobile host, in this case an autonomous underwater vehicle.

Fig. 5. Illustration of a standalone spherical positioning solution, shown in two dimensions. Each of the three transponders is represented by a mark at the center of the three circles

(x6.). By measuring a range from each transponder we know the radius of each circle. With three ranges the position is estimated by the intersection of the three circles.

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