UAV Path Optimization for Angle-Only Self-Localization and Target Tracking Based on the Bayesian Fisher Information Matrix.

In this paper, new path optimization algorithms are developed for uncrewed aerial vehicle (UAV) self-localization and target tracking, exploiting beacon (landmark) bearings and angle-of-arrival (AOA) measurements from a manoeuvring target. To account for time-varying rotations in the local UAV coordinates with respect to the global Cartesian coordinate system, the unknown orientation angle of the UAV is also estimated jointly with its location from the beacon bearings. This is critically important, as orientation errors can significantly degrade the self-localization performance. The joint self-localization and target tracking problem is formulated as a Kalman filtering problem with an augmented state vector that includes all the unknown parameters and a measurement vector of beacon bearings and target AOA measurements. This formulation encompasses applications where Global Navigation Satellite System (GNSS)-based self-localization is not available or reliable, and only beacons or landmarks can be utilized for UAV self-localization. An optimal UAV path is determined from the optimization of the Bayesian Fisher information matrix by means of A- and D-optimality criteria. The performance of this approach at different measurement noise levels is investigated. A modified closed-form projection algorithm based on a previous work is also proposed to achieve optimal UAV paths. The performance of the developed UAV path optimization algorithms is demonstrated with extensive simulation examples.

3D TDOA Emitter Localization Using Conic Approximation.

This paper develops a new time difference of arrival (TDOA) emitter localization algorithm in the 3D space, employing conic approximations of hyperboloids associated with TDOA measurements. TDOA measurements are first converted to 1D angle of arrival (1D-AOA) measurements that define TDOA cones centred about axes connecting the corresponding TDOA sensor pairs. Then, the emitter location is calculated from the triangulation of 1D-AOAs, which is formulated as a system of nonlinear equations and solved by a low-complexity two-stage estimation algorithm composed of an iterative weighted least squares (IWLS) estimator and a Taylor series estimator aimed at refining the IWLS estimate. Important conclusions are reached about the optimality of sensor-emitter and sensor array geometries. The approximate efficiency of the IWLS estimator is also established under mild conditions. The new two-stage estimator is shown to be capable of outperforming the maximum likelihood estimator while performing very close to the Cramer Rao lower bound in poor sensor-emitter geometries and large noise by way of numerical simulations.

Optimal Geometries for AOA Localization in the Bayesian Sense.

This paper considers the optimal sensor placement problem for angle-of-arrival (AOA) target localization in the 2D plane with a Gaussian prior. Optimal sensor locations are analytically determined for a single AOA sensor using the D- and A-optimality criteria and an approximation of the Bayesian Fisher information matrix (BFIM). Optimal sensor placement is shown to align with the minor axis of the prior covariance error ellipse for both optimality criteria. The approximate BFIM is argued to be valid for a sufficiently small prior covariance compared with the target range. Optimal sensor placement results obtained for Bayesian target localization are extended to manoeuvring target tracking. For sensor trajectory optimization subject to turn-rate constraints, numerical search methods based on the D- and A-optimality criteria as well as a new closed-form projection algorithm that aims to achieve alignment with the minor axis of the prior error ellipse are proposed. It is observed that the two optimality criteria generate significantly different optimal sensor trajectories despite having the same optimal sensor placement for the localization of a stationary target. Analysis results and the performance of the sensor trajectory optimization methods are demonstrated with simulation examples. It is observed that the new closed-form projection algorithm achieves superior tracking performance compared with the two numerical search methods.

Robust Instant Angle Speed Measurement for Internal Combustion Engines-A Novel Sensing Suite and Methodology.

This paper presents the development and implementation of a novel robust sensing and measurement system that achieves fine granularity and permits new insights into operation of rotational machinery. Instant angle speed measurements offer a wealth of useful information for complex machines in which the motion is the result of multidimensional, internal, and external interactions. The implementation of the proposed system was conducted on an internal combustion engine. The internal combustion engine crankshaft's angular velocity is the result of the integration of all variables of motor and resisting forces. The crankshaft angular velocity variation also reflects the interaction between the internal thermodynamic cycle of the engine and the plant it powers. To minimise the number of variables, we used for our experiments an aero piston engine for small air-vehicles-a well-made and reliable powerplant-connected to a propeller. This paper presents the need for a better sensing and measurement system. Then, we show the development of the system, the measurement protocol and process, recording and analysis of the data, and results of some experiments. We then demonstrate the possibilities this sensing suite can achieve-a deeper insight into the operation of the machine-by performing high-quality analyses of engine cycles, well beyond capabilities in the state of the art. This system can be generalised for other rotational machines and equipment.

Optimal Maneuvering for Autonomous Vehicle Self-Localization.

We consider the problem of optimal maneuvering, where an autonomous vehicle, an unmanned aerial vehicle (UAV) for example, must maneuver to maximize or minimize an objective function. We consider a vehicle navigating in a Global Navigation Satellite System (GNSS)-denied environment that self-localizes in two dimensions using angle-of-arrival (AOA) measurements from stationary beacons at known locations. The objective of the vehicle is to travel along the path that minimizes its position and heading estimation error. This article presents an informative path planning (IPP) algorithm that (i) uses the determinant of the self-localization estimation error covariance matrix of an unscented Kalman filter as the objective function; (ii) applies an l-step look-ahead (LSLA) algorithm to determine the optimal heading for a constant-speed vehicle. The novel algorithm takes into account the kinematic constraints of the vehicle and the AOA means of measurement. We evaluate the performance of the algorithm in five scenarios involving stationary and mobile beacons and we find the estimation error approaches the lower bound for the estimator. The simulations show the vehicle maneuvers to locations that allow for minimum estimation uncertainty, even when beacon placement is not conducive to accurate estimation.

Closed-Form Pseudolinear Estimators for DRSS-AOA Localization.

This paper investigates the hybrid source localization problem using differential received signal strength (DRSS) and angle of arrival (AOA) measurements. The main advantage of hybrid measurements is to improve the localization accuracy with respect to a single sensor modality. For sufficiently short wavelengths, AOA sensors can be constructed with size, weight, power and cost (SWAP-C) requirements in mind, making the proposed hybrid DRSS-AOA sensing feasible at a low cost. Firstly the maximum likelihood estimation solution is derived, which is computationally expensive and likely to become unstable for large noise levels. Then a novel closed-form pseudolinear estimation method is developed by incorporating the AOA measurements into a linearized form of DRSS equations. This method eliminates the nuisance parameter associated with linearized DRSS equations, hence improving the estimation performance. The estimation bias arising from the injection of measurement noise into the pseudolinear data matrix is examined. The method of instrumental variables is employed to reduce this bias. As the performance of the resulting weighted instrumental variable (WIV) estimator depends on the correlation between the IV matrix and data matrix, a selected-hybrid-measurement WIV (SHM-WIV) estimator is proposed to maintain a strong correlation. The superior bias and mean-squared error performance of the new SHM-WIV estimator is illustrated with simulation examples.

An Image Focusing Method for Sparsity-Driven Radar Imaging of Rotating Targets.

This paper presents a new image focusing algorithm for sparsity-driven radar imaging of rotating targets. In the general formulation of off-grid scatterers, the sparse reconstruction algorithms may result in blurred and low-contrast images due to dictionary mismatch. Motivated by the natural clustering of atoms in the sparsity-based reconstructed images, the proposed algorithm first partitions the atoms into separate clusters, and then the true off-grid scatterers associated with each cluster are estimated. Being a post-processing technique, the proposed algorithm is computationally simple, while at the same time being capable of producing a sharp and correct-contrast image, and attaining a scatterer parameter estimation performance close to the Cramér⁻Rao lower bound. Numerical simulations are presented to corroborate the effectiveness of the proposed algorithm.