David Moreno-Salinas

Optimal sensor placement for underwater positioning with uncertainty in the target location

Worldwide, there has been increasing interest in the use of Autonomous Underwater Vehicles (AUVs) to drastically change the means available for ocean exploration and exploitation. Representative missions include marine habitat mapping, pipeline inspection, and archaeological surveying. Central to the operation of some classes of AUVs is the availability of good underwater positioning systems to localize one or more vehicles simultaneously based on information received on-board a support ship or a set of autonomous surface vehicles. In an interesting operational scenario the AUV is equipped with an acoustic pinger and the set of surface vehicles carry a network of acoustic receivers that measure the ranges between the emitter and each of the receivers. Motivated by these considerations, in this paper we address the problem of determining the optimal geometric configuration of an acoustic sensor network at the ocean surface that will maximize the range-related information available for underwater target positioning. It is assumed that the range measurements are corrupted by white Gaussian noise, the variance of which is distance-dependent. Furthermore, we also assume that an initial estimate of the target position is available, albeit with uncertainty. The Fisher Information Matrix and the maximization of its determinant are used to determine the sensor configuration that yields the most accurate “expected” positioning of the target, the position of which is expressed by a probabilistic distribution. It is shown that the optimal configuration lends itself to an interesting geometrical interpretation and that the “spreading” of the sensor configuration depends explicitly on the intensity of the range measurement noise, the probabilistic distribution that defines the target position, and the target depth. Simulation examples illustrate the key results derived.

Optimal Sensor Placement for Multiple Target Positioning with Range-Only Measurements in Two-Dimensional Scenarios

The problem of determining the optimal geometric configuration of a sensor network that will maximize the range-related information available for multiple target positioning is of key importance in a multitude of application scenarios. In this paper, a set of sensors that measures the distances between the targets and each of the receivers is considered, assuming that the range measurements are corrupted by white Gaussian noise, in order to search for the formation that maximizes the accuracy of the target estimates. Using tools from estimation theory and convex optimization, the problem is converted into that of maximizing, by proper choice of the sensor positions, a convex combination of the logarithms of the determinants of the Fisher Information Matrices corresponding to each of the targets in order to determine the sensor configuration that yields the minimum possible covariance of any unbiased target estimator. Analytical and numerical solutions are well defined and it is shown that the optimal configuration of the sensors depends explicitly on the constraints imposed on the sensor configuration, the target positions, and the probabilistic distributions that define the prior uncertainty in each of the target positions. Simulation examples illustrate the key results derived.

Sensor Networks for Optimal Target Localization with Bearings-Only Measurements in Constrained Three-Dimensional Scenarios

In this paper, we address the problem of determining the optimal geometric configuration of an acoustic sensor network that will maximize the angle-related information available for underwater target positioning. In the set-up adopted, a set of autonomous vehicles carries a network of acoustic units that measure the elevation and azimuth angles between a target and each of the receivers on board the vehicles. It is assumed that the angle measurements are corrupted by white Gaussian noise, the variance of which is distance-dependent. Using tools from estimation theory, the problem is converted into that of minimizing, by proper choice of the sensor positions, the trace of the inverse of the Fisher Information Matrix (also called the Cramer-Rao Bound matrix) to determine the sensor configuration that yields the minimum possible covariance of any unbiased target estimator. It is shown that the optimal configuration of the sensors depends explicitly on the intensity of the measurement noise, the constraints imposed on the sensor configuration, the target depth and the probabilistic distribution that defines the prior uncertainty in the target position. Simulation examples illustrate the key results derived.

Optimal Sensor Placement for Acoustic Underwater Target Positioning With Range-Only Measurements

This paper addresses the problem of optimal acoustic sensor placement for underwater target localization in 3-D using range measurements only. By adopting an estimation theoretical framework, the optimal geometric sensor formation that will yield the best achievable performance in terms of target positioning accuracy is computed by maximizing the determinant of an appropriately defined Fisher information matrix (FIM). For mathematical tractability, it is assumed that the measurements of the ranges between the target and a set of acoustic sensors are corrupted with white Gaussian noise. For the sake of completeness, an explicit analytical result for a generic n-sensor network is first obtained for the case when there is no uncertainty in the prior knowledge about the target position. The result is then extended to the practical case where the target is known to lie inside a region of uncertainty. The optimal sensor configuration thus obtained lends itself to an interesting and useful geometrical interpretation. In addition, the “spreading” of the configuration is shown to depend on the number of range measurements, target depth, and the probability distribution function that characterizes the prior knowledge about the target position. Results are also obtained for the problem of optimal sensor placement with constraints, namely, by considering that the sensors can be either located at the sea surface or distributed between the surface and the seabed. The connection between 2-D and 3-D scenarios is clarified. Simulation examples illustrate the key results derived.

Optimal Sensor Placement for Multiple Underwater Target Localization with Acoustic Range Measurements

Worldwide, there is increasing interest in the operation of multiple autonomous underwater vehicles (AUVs) to carry out scientific and commercial missions at sea. For some of the envisioned missions, it is crucial that new methods be developed to localize one more of the vehicles simultaneously, based on acoustic range information received on-board a set of autonomous surface vehicles. As a contribution towards meeting this goal, this paper addresses the problem of computing the optimal geometric configuration of a mobile surface sensor network that will maximize the range-related information available for multiple target localization in three-dimensional space. In contrast to what has so far been published in the literature, we address explicitly the localization problem in 3D using a sensor array located at the sea surface (2D). Furthermore, we incorporate directly in the problem formulation the fact that multiple targets must be localized simultaneously. Clearly, there will be tradeoffs involved in the precision with which each of the targets can be localized; to study them, we resort to techniques that borrow from Pareto optimization and estimation theory. Simulation examples illustrate the key results derived.

Identification of a Surface Marine Vessel Using LS-SVM

The availability of adequate system models to reproduce, as faithfully as possible, the actual behaviour of the experimental systems is of key importance. In marine systems, the changing environmental conditions and the complexity of the infrastructure needed to carry out experimental tests call for mathematical models for accurate simulations. There exist a wide number of techniques to define mathematical models from experimental data. Support Vector Machines (SVMs) have shown a great performance in pattern recognition and classification research areas having an inherent potential ability for linear and nonlinear system identification. In this paper, this ability is demonstrated through the identification of the Nomoto second-order ship model with real experimental data obtained from a zig-zag manoeuvre made by a scale ship. The mathematical model of the ship is identified using Least Squares Support Vector Machines (LS-SVMs) for regression by analysing the rudder angle, surge and sway speed, and yaw rate. The coefficients of the Nomoto model are obtained with a linear kernel function. The model obtained is validated through experimental tests that illustrate the potential of SVM for system identification.

Underwater target positioning with a single acoustic sensor

Abstract The availability of reliable underwater positioning systems to localize one or more vehicles simultaneously based on information received on-board a support ship or an autonomous surface vessel is key to the operation of some classes of AUVs. Furthermore, there is considerable interest in reducing the number of sensors involved in acoustic navigation/positioning systems to reduce the costs involved and the time consumed in the deployment, callibration, and recovery phases. Motivated by these considerations, in this paper we address the problem of single underwater target positioning based on measurements of the ranges between the target and a moving sensor at the sea surface, obtained via acoustic ranging devices. In particular, and speaking in loose terms, we are interested in determining the optimal geometric trajectory of the surface sensor that will, in a well defined sense, maximize the range-related information available for underwater target positioning. To this effect, an appropriate Fisher Information Matrix is defined and its determinant is maximized to yield the sensor trajectory that maximizes the accuracy of the target position estimate that can possibly be obtained with any unbiased estimator. It is shown that the optimal trajectory depends on the relative velocity of the sensor, the sampling time between measurements, and the number of measurements acquired for the FIM computation. Simulation examples illustrate the key results derived.

Nonlinear Control for Trajectory Tracking of a Nonholonomic RC-Hovercraft with Discrete Inputs

This work studies the problem of trajectory tracking for an underactuated RC-hovercraft, the control of which must be done by means of discrete inputs. Thus, the aim is to control a vehicle with very simple propellers that produce only a discrete set of control commands, and with minimal information about the dynamics of the actuators. The control problem is approached as a cascade control problem, where the outer loop stabilizes the position error, and the inner loop stabilizes the orientation of the vehicle. Stability of the controller is theoretically demonstrated and the robustness of the control law against disturbances and noise is established. Simulation examples and experiments on a real setup validate the control law showing the real system to be robust against disturbances, noise, and outdated dynamics.

Semiphysical Modelling of the Nonlinear Dynamics of a Surface Craft with LS-SVM

One of the most important problems in many research fields is the development of reliable mathematical models with good predictive ability to simulate experimental systems accurately. Moreover, in some of these fields, as marine systems, these models play a key role due to the changing environmental conditions and the complexity and high cost of the infrastructure needed to carry out experimental tests. In this paper, a semiphysical modelling technique based on least-squares support vector machines (LS-SVM) is proposed to determine a nonlinear mathematical model of a surface craft. The speed and steering equations of the nonlinear model of Blanke are determined analysing the rudder angle, surge and sway speeds, and yaw rate from real experimental data measured from a zig-zag manoeuvre made by a scale ship. The predictive ability of the model is tested with different manoeuvring experimental tests to show the good performance and prediction ability of the model computed.

Optimal Sensor Trajectories for Mobile Underwater Target Positioning with Noisy Range Measurements

Abstract There is considerable interest in reducing the number of sensors/beacons involved in underwater positioning/navigation systems since this has the potential to drastically reduce the costs and the time spent in deploying, calibrating, and recovering acoustic equipment at sea. Motivated by these considerations, we address the problem of single underwater target positioning based on acoustic range measurements between the target and a moving sensor at the sea surface. In particular, the goal of the present work is to compute optimal geometric trajectories for the surface sensor that will, in a well defined sense, maximize the range-related information available for underwater target positioning and tracking. To this effect, the Fisher Information Matrix and the maximization of its determinant are used to determine the sensor trajectory that yields the most accurate positioning of the target, while the latter describes a preplanned trajectory. It is shown that the optimal trajectory depends on the velocity of the sensor, the velocity and trajectory of the target, the sampling time between measurements, the measurement error model, and the number of measurements used to compute the FIM. Simulation examples illustrate the key results derived.