Optimal Measurement Location Planning for Localizing Underwater Transponders
Jesse Garcia, Jay A. Farrell, Zak (Zaher) M. Kassas, University of California, Riverside
Navigation has become ubiquitous in our daily lives over the past decades thanks in part to the accessibility and abundance of GPS/GNSS signals in the environment. These signals, however, be- come severely attenuated underwater and are unusable for navigation at depths greater than three feet. Vehicles navigating underwater can utilize networks of pre-deployed underwater transponders, surface vehicles, or resurfacing strategies to reduce drift inherent with inertial navigation. These solutions are far from optimal in situations where stealth and covertness are required or when the environment is not accessible beforehand (i.e disaster situations or naval mine hunting operations). A group of heterogeneous marine vehicles can overcome these limitations by collaboratively navi- gating the uncertain underwater environment. An initial piece of this research is presented herein, wherein an autonomous underwater vehicle (AUV) is tasked with optimally localizing a set of static underwater transponders (UTs) to aid in navigation once submerged.
One aspect of this problem is where the AUV should place itself to generate the most useful measurement data. This closely relates to the optimal sensor placement problem. Many works provide approaches based on the D-optimality criterion, or maximization of the log-determinant of the Fisher information matrix (FIM), as it yields the maximum reduction in target location uncertainty , . An alternative, computationally efficient, optimization criterion based on in- novation maximization is developed in . A collaborative sensor placement strategy is developed in , wherein a network of coordinated ASVs attempt to optimally place themselves to localize a single UT. The work of  introduces a piecewise concave geometric optimization strategy for planar sensor placement when localizing a single terrestrial RF transmitter based on pseudorange measurements. The authors of  proceed to generalize this method to handle a multiple trans- mitter environment. It is important to note that approaches in  and  consider the placement of all sensors simultaneously, while that of  considers the placement of a single additional sensor in the environment.
While the above papers consider planar sensor placement, a 3D sensor placement strategy be- comes viable in underwater and aerial applications. Additional complexities here result from the fact that, once submerged, an underwater vehicle is deprived of GNSS signals and accurate posi- tioning information about itself. This forces a reliance on onboard inertial sensor suites that provide rapidly decaying self-positioning estimates due to integral effects. Aided navigation and simultane- ous localization and mapping (SLAM) techniques can be used to mitigate this decay. Approaches to this problem for underwater scenarios are developed in  for SONAR based terrain aided nav- igation (TAN). The authors of  provide criteria to ensure observability of the nonlinear system when ranging to a single acoustic beacon. Similar scenarios are examined in  for aerial vehicles in GNSS denied environments using pseudorange measurements to a number of RF transmitters.
This article considers a framework for acoustic target localization and optimal measurement location planning. An AUV (operating on the surface) navigates in an environment containing a network of fixed UTs at unknown locations. The AUV makes acoustic range measurements to a subset of these UTs that are within acoustic range. The AUV’s task is twofold: (1) estimate the location of the UTs in the environment, and (2) determine the successive measurement locations that will yield the most information during each successive measurement cycle. Step (2) enhances the solutions to (1). At an unknown time, the AUV will submerge to depth and begin navigating autonomously without access to GNSS signals. The AUV will now act in a SLAM-type fashion using range measurements to the UTs to aid its inertial navigation system, while improving the location estimates of each UT in the environment. We handle the localization problem via maximum a-posteriori (MAP) estimation. While surfaced, successive acoustic measurements are planned according to the D-optimality criterion, which optimizes a function of the Fisher information matrix (FIM). We demonstrate an algebraic simplification to this optimization problem for the case when only one UT is being localized, and develop a generalization for the case when localizing multiple UTs. Theory, simulations, and experimental results demonstrating the proposed approach will be presented. Experiments will take place at SPAWAR Systems Center Pacific’s (SSC Pac) Transdec pool.
 D. Salinas-Moreno, N.Crasta, M. Ribiero, B. Bayat, A. Pascoal, and J. Aranda, “Integrated motion planning, control, and estimation for range-based marine vehicle positioning and target localization,” IFAC Conference on Control Applications in Marine Systems, vol. 49, no. 23, pp. 34 – 40, September 2016.
 Z. Kassas and T. Humphreys, “Motion planning for optimal information gathering in opportunistic navigation systems,” AIAA Guidance, Navigation, and Control Conference, pp. 4551 – 4565, August 2013.
 Z. Kassas, T. Humphreys, and A. Arapostathis, “Greedy motion planning for simultaneous signal landscape mapping and receiver localization,” IEEE Journal of Selected Topics in Signal Processing, vol. 9, no. 2, pp. 246 – 258, March 2015.
 B. Ferriera, A. Matos, H. Campos, and N. Cruz, “Localization of a sound source: optimal positioning of sensors carried on autonomous surface vehicles,” IEEE Marine Technological Society OCEANS, pp. 1 – 8, September 2013.
 J. Morales and Z. Kassas, “Optimal collaborative mapping of terrestrial transmitters: Receiver placement and performance characterization,” IEEE Transactions on Aerospace and Electronic Systems, 2017, accepted.
 F. Teixeira, J. Quintas, and A. Pascoal, “AUV terrain-aided doppler navigation using complementary filtering,” IFAC Conference on Maneuvering and Control of Marine Craft, vol. 45, pp. 313 – 318, September 2012.
 P. Batista, C. Silvestre, and P. Oliveira, “Single range aided navigation and source localization: Observability and filter design,” Systems & Control Letters, vol. 60, no. 8, pp. 665 – 673, June 2011.
 J. Morales, P. Roysdon, and Z. Kassas, “Signals of opportunity aided inertial navigation,” ION Global Navigation Satellite Systems Conference, pp. 1492 – 1501, September 2016.