Performance Analysis of Bearings-only Tracking Problems for Maneuvering Target and Heterogeneous Sensor Applications

State estimation, i.e. determining the trajectory, of a maneuvering target from noisy measurements collected by a single or multiple passive sensors (e.g. passive sonar and radar) has wide civil and military applications, for example underwater surveillance, air defence, wireless communications, and self-protection of military vehicles. These passive sensors are listening to target emitted signals without emitting signals themselves which give them concealing properties. Tactical scenarios exists where the own position shall not be revealed, e.g. for tracking submarines with passive sonar or tracking an aerial target by means of electro-optic image sensors like infrared sensors. This estimation process is widely known as bearings-only tracking. On the one hand, a challenge is the high degree of nonlinearity in the estimation process caused by the nonlinear relation of angular measurements to the Cartesian state. On the other hand, passive sensors cannot provide direct target location measurements, so bearings-only tracking suffers from poor target trajectory estimation accuracy due to marginal observability from sensor measurements. In order to achieve observability, that means to be able to estimate the complete target state, multiple passive sensor measurements must be fused. The measurements can be recorded spatially distributed by multiple dislocated sensor platforms or temporally distributed by a single, moving sensor platform. Furthermore, an extended case of bearings-only tracking is given if heterogeneous measurements from targets emitting different types of signals, are involved. With this, observability can also be achieved on a single, not necessarily moving platform. In this work, a performance bound for complex motion models, i.e. piecewisely maneuvering targets with unknown maneuver change times, by means of bearings-only measurements from a single, moving sensor platform is derived and an efficient estimator is implemented and analyzed. Furthermore, an observability analysis is carried out for targets emitting acoustic and electromagnetic signals. Here, the different signal propagation velocities can be exploited to ensure observability on a single, not necessarily moving platform. Based on the theoretical performance and observability analyses a distributed fusion system has been realized by means of heterogeneous sensors, which shall detect an event and localize a threat. This is performed by a microphone array to detect sound waves emitted by the threat as well as a radar detector that detects electromagnetic emissions from the threat. Since multiple platforms are involved to provide increased observability and also redundancy against possible breakdowns, a WiFi mobile ad hoc network is used for communications. In order to keep up the network in a breakdown OLSR (optimized link state routing) routing approach is employed

Tracking the Tracker from its Passive Sonar ML-PDA Estimates

Target motion analysis with wideband passive sonar has received much attention. Maximum likelihood probabilistic data-association (ML-PDA) represents an asymptotically efficient estimator for deterministic target motion, and is especially well-suited for low-observable targets; the results presented here apply to situations with higher signal to noise ratio as well, including of course the situation of a deterministic target observed via clean measurements without false alarms or missed detections. Here we study the inverse problem, namely, how to identify the observing platform (following a two-leg motion model) from the results of the target estimation process, i.e. the estimated target state and the Fisher information matrix, quantities we assume an eavesdropper might intercept. We tackle the problem and we present observability properties, with supporting simulation results.Comment: To appear in IEEE Transactions on Aerospace and Electronic System

Nonlinear Control of a Flexible Rotor Magnetic Bearing System: Robustness and the Indefinate Model

Previously published control strategies for magnetic bearings primarily focus on linear optimal control techniques. While these methods afford many advantages, conspicuously absent from the literature are detailed attempts at nonlinear control. Here, we obtain the equations of motion of an overhung flexible rotor supported in magnetic bearings with two different levels of model sophistication. We derive a generic nonlinear controller in the manner of feedback linearization, and compare the eigenanalysis and transient response of the two rotor models under the action of this >perfect model> controller. We then proceed to obtain a robust nonlinear controller through the sliding mode technique and demonstrate that robustness by implementing it on an uncertain model.Center for Electromechanic

Stochastic Real-time Optimal Control for Bearing-only Trajectory Planning

A method is presented to simultaneously solve the optimal control problem and the optimal estimation problem for a bearing-only sensor. For bearing-only systems that require a minimum level of certainty in position relative to a source for mission accomplishment, some amount of maneuver is required to measure range. Traditional methods of trajectory optimization and optimal estimation minimize an information metric. This paper proposes constraining the final value of the information states with known time propagation dynamics relative to a given trajectory which allows for attainment of the required level of information with minimal deviation from a general performance index that can be tailored to a specific vehicle. The proposed method does not suffer from compression of the information metric into a scalar, and provides a route that will attain a particular target estimate quality while maneuvering to a desired relative point or set. An algorithm is created to apply the method in real-time, iteratively estimating target position with an Unscented Kalman Filter and updating the trajectory with an efficient pseudospectral method. Methods and tools required for hardware implementation are presented that apply to any real-time optimal control (RTOC) system. The algorithm is validated with both simulation and flight test, autonomously landing a quadrotor on a wire

Novel passive localization algorithm based on double side matrix-restricted total least squares

AbstractIn order to solve the bearings-only passive localization problem in the presence of erroneous observer position, a novel algorithm based on double side matrix-restricted total least squares (DSMRTLS) is proposed. First, the aforementioned passive localization problem is transferred to the DSMRTLS problem by deriving a multiplicative structure for both the observation matrix and the observation vector. Second, the corresponding optimization problem of the DSMRTLS problem without constraint is derived, which can be approximated as the generalized Rayleigh quotient minimization problem. Then, the localization solution which is globally optimal and asymptotically unbiased can be got by generalized eigenvalue decomposition. Simulation results verify the rationality of the approximation and the good performance of the proposed algorithm compared with several typical algorithms