Performance Limits and Geometric Properties of Array Localization

Location-aware networks are of great importance and interest in both civil and military applications. This paper determines the localization accuracy of an agent, which is equipped with an antenna array and localizes itself using wireless measurements with anchor nodes, in a far-field environment. In view of the Cram\'er-Rao bound, we first derive the localization information for static scenarios and demonstrate that such information is a weighed sum of Fisher information matrices from each anchor-antenna measurement pair. Each matrix can be further decomposed into two parts: a distance part with intensity proportional to the squared baseband effective bandwidth of the transmitted signal and a direction part with intensity associated with the normalized anchor-antenna visual angle. Moreover, in dynamic scenarios, we show that the Doppler shift contributes additional direction information, with intensity determined by the agent velocity and the root mean squared time duration of the transmitted signal. In addition, two measures are proposed to evaluate the localization performance of wireless networks with different anchor-agent and array-antenna geometries, and both formulae and simulations are provided for typical anchor deployments and antenna arrays.Comment: to appear in IEEE Transactions on Information Theor

Efficient closed-form estimators in multistatic target localization and motion analysis

Object localization is fast becoming an important research topic because of its wide applications. Often of the time, object localization is accomplished in two steps. The first step exploits the characteristics of the received signals and extracts certain localization information i.e. measurements. Some typical measurements include timeof-arrival (TOA), time-difference-of-arrival (TDOA), received signal strength (RSS) and angle-of-arrival (AOA). Together with the known receiver position information, the object location is then estimated in the second step from the obtained measurements. The localization of an object using a number of sensors is often challenged due to the highly nonlinear relationship between the measurements and the object location. This thesis focuses on the second step and considers designing novel and efficient localization algorithms to solve such a problem. This thesis first derives a new algebraic positioning solution using a minimum number of measurements, and from which to develop an object location estimator. Two measurements are sufficient in 2-D and three in 3-D to yield a solution if they are consistent. The derived minimum measurement solution is exact and reduces the computation to the roots of a quadratic equation. The solution derivation also leads to simple criteria to ascertain if the line of positions from two measurements intersects. By partitioning the overdetermined set of measurements first to obtain the individual minimum measurement solutions, we propose a best linear unbiased estimator to form the final location estimate. The analysis supports the proposed estimator in reaching the Cramer-Rao Lower Bound (CRLB) accuracy under Gaussian noise. A measurement partitioning scheme is developed to improve performance when the noise level becomes large. We mainly use elliptic time delay measurements for presentation, and the derived results apply to the hyperbolic time difference measurements as well. Both the 2-D and 3-D scenarios are considered. A multistatic system uses a transmitter to illuminate the object of interest and collects the reflected signal by several receivers to determine its location. In some scenarios such as passive coherent localization or for gaining flexibility, the position of the transmitter is not known. In this thesis, we investigate the use of the indirect path measurements reflected off the object alone, or together with the direct path measurements from the transmitter to receiver for locating the object in the absence of the transmitter position. We show that joint estimation of the object and transmitter positions from both the indirect and direct measurements can yield better object location estimate than using the indirect measurements only by eliminating the dependency of the transmitter position. An algebraic closed-form solution is developed for the nonlinear problem of joint estimation and is shown analytically to achieve the CRLB performance under Gaussian noise over the small error region. To complete the study and gain insight, the optimum receiver placement in the absence of transmitter position is derived, by minimizing the estimation confidence region or the estimation variance for the object location. The performance lost due to unknown transmitter position under the optimum geometries is quantified. Simulations confirm well with the theoretical developments. In practice, a more realistic localization scenario with the unknown transmitter is that the transmitter works non-cooperatively. In this situation, no timestamp is available in the transmitted signal so that the signal sent time is often not known. This thesis next considers the extension of the localization scenario to such a case. More generally, the motion potential of the unknown object and transmitter is considered in the analysis. When the transmitted signal has a well-defined pattern such as some standard synchronization or pilot sequence, it would still be able to estimate the indirect and direct time delays and Doppler frequency shifts but with unknown constant time delay and frequency offset added. In this thesis, we would like to estimate the object and transmitter positions and velocities, and the time and frequency offsets jointly. Both dynamic and partial dynamic localization scenarios based on the motion status of the object and the transmitter are considered in this thesis. By investigating the CRLB of the object location estimate, the improvement in position and velocity estimate accuracy through joint estimation comparing with the differencing approach using TDOA/FDOA measurements is evaluated. The degradation due to time and frequency offsets is also analyzed. Algebraic closed-form solutions to solve the highly nonlinear joint estimation problems are then proposed in this thesis, followed by the analysis showing that the CRLB performance can be achieved under Gaussian noise over the small error region. When the transmitted signal is not time-stamped and does not have a well-defined pattern such as some standard synchronization or pilot sequence, it is often impossible to obtain the indirect and direct measurements separately. Instead, a self-calculated TDOA between the indirect- and direct-path TOAs shall be considered which does not require any synchronization between the transmitter and a receiver, or among the receivers. A refinement method is developed to locate the object in the presence of the unknown transmitter position, where a hypothesized solution is needed for initialization. Analysis shows that the refinement method is able to achieve the CRLB performance under Gaussian noise. Three realizations of the hypothesized solution applying multistage processing to simplify the nonlinear estimation problem are derived. Simulations validate the effectiveness in initializing the refinement estimator

Active Localization using Bernstein Distribution Functions

In this work, we present a framework that enables a vehicle to autonomously localize a target based on noisy range measurements computed from RSSI data. To achieve the mission objectives, we develop a control scheme composed of two main parts: an estimator and a motion planner. At each time step, new estimates of the target's position are computed and used to generate and update distribution functions using Bernstein polynomials. A metric of the efficiency of the estimator is derived based on the Fisher Information Matrix. Finally, the motion planning problem is formulated to react in real time to new information about the target and improve the estimator's performance.Comment: 6 page

Sensor Path Planning for Emitter Localization

The localization of a radio frequency (RF) emitter is relevant in many military and civilian applications. The recent decade has seen a rapid progress in the development of small and mobile unmanned aerial vehicles (UAVs), which offer a way to perform emitter localization autonomously. The path a UAV travels influences the localization significantly, making path planning an important part of a mobile emitter localization system. The topic of this thesis is path planning for a UAV that uses bearing measurements to localize a stationary emitter. Using a directional antenna, the direction towards the target can be determined by the UAV rotating around its own vertical axis. During this rotation the UAV is required to remain at the same position, which induces a trade-off between movement and measurement that influences the optimal trajectories. This thesis derives a novel path planning algorithm for localizing an emitter with a UAV. It improves the current state of the art by providing a localization with defined accuracy in a shorter amount of time compared to other algorithms in simulations. The algorithm uses the policy rollout principle to perform a nonmyopic planning and to incorporate the uncertainty of the estimation process into its decision. The concept of an action selection algorithm for policy rollout is introduced, which allows the use of existing optimization algorithms to effectively search the action space. Multiple action selection algorithms are compared to optimize the speed of the path planning algorithm. Similarly, to reduce computational demand, an adaptive grid-based localizer has been developed. To evaluate the algorithm an experimental system has been built and the algorithm was tested on this system. Based on initial experiments, the path planning algorithm has been modified, including a minimal distance to the emitter and an outlier detection step. The resulting algorithm shows promising results in experimental flights

Cooperative tracking for persistent littoral undersea surveillance

Thesis (Nav. E.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (leaves 39-40).The US Navy has identified a need for an autonomous, persistent, forward deployed system to Detect, Classify, and Locate submarines. In this context, we investigate a novel method for multiple sensor platforms acting cooperatively to locate an uncooperative target. Conventional tracking methods based on techniques such as Kalman filtering or particle filters have been used with great success for tracking targets from a single manned platform; the application of these methods can be difficult for a cooperative tracking scenario with multiple unmanned platforms that have considerable navigation error. This motivates investigation of an alternative, set-based tracking algorithm, first proposed by Detweiler et al. for sensor network localization, to the cooperative tracking problem. The Detweiler algorithm is appealing for its conceptual simplicity and minimal assumptions about the target motion. The key idea of this approach is to compute the temporal evolution of potential target positions in terms of bounded regions that grow between measurements as the target moves and shrink when measurements do occur based on an assumed worst-case bound for uncertainty.(cont.) In this thesis, we adapt the Detweiler algorithm to the scenario of cooperative tracking for persistent undersea surveillance, and explore its limitations when applied to this domain. The algorithm has been fully implemented and tested both in simulation and with postprocessing of autonomous surface craft (ASC) data from the PLUSNet Monterey Bay 2006 experiment. The results indicate that the method provides disappointing performance when applied to this domain, especially in situations where communication links between the autonomous tracking platforms are poor. We conclude that the method is more appropriate for a "large N" tracking scenario, with a large number of small, expendable tracking nodes, instead of our intended scenario with a smaller number of more sophisticated mobile trackers. The method may also be useful as an adjunct to a conventional Bayesian tracker, to reject implausible target tracks and focus computational resources on regions where the target is present.by Robert Derek Scott.S.M.Nav.E

Forecast-Driven Enhancement of Received Signal Strength (RSS)-Based Localization Systems

Real-time user localization in indoor environments is an important issue in ambient assisted living (AAL). In this context, localization based on received signal strength (RSS) has received considerable interest in the recent literature, due to its low cost and energy consumption and to its availability on all wireless communication hardware. On the other hand, the RSS-based localization is characterized by a greater error with respect to other technologies. Restricting the problem to localization of AAL users in indoor environments, we demonstrate that forecasting with a little user movement advance (for example, when the user is about to leave a room) provides significant benefits to the accuracy of RSS-based localization systems. Specifically, we exploit echo state networks (ESNs) fed with RSS measurements and trained to recognize patterns of user’s movements to feed back to the RSS-based localization syste