Shapes from Echoes: Uniqueness from Point-to-Plane Distance Matrices

We study the problem of localizing a configuration of points and planes from the collection of point-to-plane distances. This problem models simultaneous localization and mapping from acoustic echoes as well as the notable "structure from sound" approach to microphone localization with unknown sources. In our earlier work we proposed computational methods for localization from point-to-plane distances and noted that such localization suffers from various ambiguities beyond the usual rigid body motions; in this paper we provide a complete characterization of uniqueness. We enumerate equivalence classes of configurations which lead to the same distance measurements as a function of the number of planes and points, and algebraically characterize the related transformations in both 2D and 3D. Here we only discuss uniqueness; computational tools and heuristics for practical localization from point-to-plane distances using sound will be addressed in a companion paper.Comment: 13 pages, 13 figure

Cooperative positioning studies based on WLANs

Location information and location-based service have gained importance in recent years because, based on their concept, a new business market has been opened which encompass emergency services, security, monitoring, tracking, logistics, etc. Nowadays, the most developed positioning systems, namely the Global Navigation Satellite Systems (GNSS), are meant for outdoor use. In order to integrate outdoor and indoor localization in the same mobile application, several lines of research have been created for the purpose of investigating the possibility of wireless network technologies and of overcoming the challenges faced by GNSS in performing localization and navigation in indoor environments. The benefit in using wireless networks is that they provide a minimally invasive solution which is based on software algorithms that can be implemented and executed in the Mobile Station (MS) or in a Location Server connected to the network. This thesis focuses on the development of localization approaches based on Received Signal Strength (RSS) and applied in WLANs. Such approaches demonstrated in recent research advances that RSS-based localization algorithms are the simplest existing approaches due to the fact that the RSSs are most accessible existing measurements. RSS measurements can be used with two main algorithms, which are addressed in this thesis: Fingerprinting method (FP) and Pathloss method (PL). These two methods can be applied in both cooperative and non-cooperative algorithms. Such algorithms are evaluated here in terms of Root Mean Square Error (RMSE) for both simulated and real-field data

Heading drift mitigation for low-cost inertial pedestrian navigation

The concept of autonomous pedestrian navigation is often adopted for indoor pedestrian navigation. For outdoors, a Global Positioning System (GPS) is often used for navigation by utilizing GPS signals for position computation but indoors, its signals are often unavailable. Therefore, autonomous pedestrian navigation for indoors can be realized with the use of independent sensors, such as low-cost inertial sensors, and these sensors are often known as Inertial Measurement Unit (IMU) where they do not rely on the reception of external information such as GPS signals. Using these sensors, a relative positioning concept from initialized position and attitude is used for navigation. The sensors sense the change in velocity and after integration, it is added to the previous position to obtain the current position. Such low-cost systems, however, are prone to errors that can result in a large position drift. This problem can be minimized by mounting the sensors on the pedestrian’s foot. During walking, the foot is briefly stationary while it is on the ground, sometimes called the zero-velocity period. If a non-zero velocity is then measured by the inertial sensors during this period, it is considered as an error and thus can be corrected. These repeated corrections to the inertial sensor’s velocity measurements can, therefore, be used to control the error growth and minimize the position drift. Nonetheless, it is still inadequate, mainly due to the remaining errors on the inertial sensor’s heading when the velocity corrections are used alone. Apart from the initialization issue, therefore, the heading drift problem still remains in such low-cost systems. In this research, two novel methods are developed and investigated to mitigate the heading drift problem when used with the velocity updates. The first method is termed Cardinal Heading Aided Inertial Navigation (CHAIN), where an algorithm is developed to use building ‘heading’ to aid the heading measurement in the Kalman Filter. The second method is termed the Rotated IMU (RIMU), where the foot-mounted inertial sensor is rotated about a single axis to increase the observability of the sensor’s heading. For the CHAIN, the method proposed has been investigated with real field trials using the low-cost Microstrain 3DM-GX3-25 inertial sensor. It shows a clear improvement in mitigating the heading drift error. It offers significant improvement in navigation accuracy for a long period, allowing autonomous pedestrian navigation for as long as 40 minutes with below 5 meters position error between start and end position. It does not require any extra heading sensors, such as a magnetometer or visual sensors such as a camera nor an extensive position or map database, and thus offers a cost-effective solution. Furthermore, its simplicity makes it feasible for it to be implemented in real-time, as very little computing capability is needed. For the RIMU, the method was tested with Nottingham Geospatial Institute (NGI) inertial data simulation software. Field trials were also undertaken using the same low-cost inertial sensor, mounted on a rotated platform prototype. This method improves the observability of the inertial sensor’s errors, resulting also in a decrease in the heading drift error at the expense of requiring extra components

Heading drift mitigation for low-cost inertial pedestrian navigation

The concept of autonomous pedestrian navigation is often adopted for indoor pedestrian navigation. For outdoors, a Global Positioning System (GPS) is often used for navigation by utilizing GPS signals for position computation but indoors, its signals are often unavailable. Therefore, autonomous pedestrian navigation for indoors can be realized with the use of independent sensors, such as low-cost inertial sensors, and these sensors are often known as Inertial Measurement Unit (IMU) where they do not rely on the reception of external information such as GPS signals. Using these sensors, a relative positioning concept from initialized position and attitude is used for navigation. The sensors sense the change in velocity and after integration, it is added to the previous position to obtain the current position. Such low-cost systems, however, are prone to errors that can result in a large position drift. This problem can be minimized by mounting the sensors on the pedestrian’s foot. During walking, the foot is briefly stationary while it is on the ground, sometimes called the zero-velocity period. If a non-zero velocity is then measured by the inertial sensors during this period, it is considered as an error and thus can be corrected. These repeated corrections to the inertial sensor’s velocity measurements can, therefore, be used to control the error growth and minimize the position drift. Nonetheless, it is still inadequate, mainly due to the remaining errors on the inertial sensor’s heading when the velocity corrections are used alone. Apart from the initialization issue, therefore, the heading drift problem still remains in such low-cost systems. In this research, two novel methods are developed and investigated to mitigate the heading drift problem when used with the velocity updates. The first method is termed Cardinal Heading Aided Inertial Navigation (CHAIN), where an algorithm is developed to use building ‘heading’ to aid the heading measurement in the Kalman Filter. The second method is termed the Rotated IMU (RIMU), where the foot-mounted inertial sensor is rotated about a single axis to increase the observability of the sensor’s heading. For the CHAIN, the method proposed has been investigated with real field trials using the low-cost Microstrain 3DM-GX3-25 inertial sensor. It shows a clear improvement in mitigating the heading drift error. It offers significant improvement in navigation accuracy for a long period, allowing autonomous pedestrian navigation for as long as 40 minutes with below 5 meters position error between start and end position. It does not require any extra heading sensors, such as a magnetometer or visual sensors such as a camera nor an extensive position or map database, and thus offers a cost-effective solution. Furthermore, its simplicity makes it feasible for it to be implemented in real-time, as very little computing capability is needed. For the RIMU, the method was tested with Nottingham Geospatial Institute (NGI) inertial data simulation software. Field trials were also undertaken using the same low-cost inertial sensor, mounted on a rotated platform prototype. This method improves the observability of the inertial sensor’s errors, resulting also in a decrease in the heading drift error at the expense of requiring extra components