Interval analysis techniques for field mapping and geolocation

Yan Cui, Purdue University


Field mapping and estimation become a challenging problem, with their various applications on non-linear estimation, geolocation, and positioning systems. In this research, we develop novel algorithms based on interval analysis and introduce a solution for autonomous map construction, field mapping, geolocation, and simultaneous localization and mapping (SLAM), providing applications on indoor geolocation and other potential areas. Generally, the localization algorithm includes a quasi-state estimation and a dynamic estimation. Quasi-static estimation collects each single measurement and give a group of estimation intervals on the pre-constructed field map. Results from quasi-static estimation are processed into the dynamic estimation algorithm, having properties of removing redundant intervals while keep the best estimation results. Sizes of estimation from quasi-static estimation are proved to be related to the resolution of the map and the quality of the sensor. Based on quasi-state estimation algorithm, we develop an algorithm to fuse different type of measurements and discuss the condition when this algorithm an be applied effectively. Having theoretical guarantees, we apply these algorithms to augment the accuracy of cell phone geolocation by taking advantage of local variations of magnetic intensity. Thus, the sources of disturbances to magnetometer readings caused indoors are effectively used as beacons for localization. We construct a magnetic intensity map for an indoor environment by collecting magnetic field data over each floor tile. We then test the algorithms without position initialization and obtain indoor geolocation to within 2m while slowly walking over a complex path of 80 meters. The geolocation errors are smaller in the vicinity of large magnetic disturbances. After fusing the magnetometer measurement with inertial measurements on the cell phone, the algorithm yields even smaller geolocation errors of under 50cm for a moving user. The map construction and geolocation algorithms are then extended to realize the SLAM, with hierarchical structure of estimation update and localization update. When a new user steps into a random map, the dead reckoning algorithm with assistance of IMU and Kalman filter provides initial estimation of position on the map, which coordinates the corresponding reading of magnetic field intensity as well as all other sources such as WiFi received signal strength (RSS), to construct an initial map. Based on the initial map, we then apply the localization algorithm to estimate new geolocations consequently and fuse the estimation intervals both from IMU and from crowd-sourced field maps to reduce the estimation size and eventually revise the map as well as the geolocation. In this research, we have built up mathematical model and developed mathematical solutions with corresponding theories and proofs. Our theoretical results connect geolocation accuracy to combinations of sensor and map properties.




Chiu, Purdue University.

Subject Area

Mechanical engineering|Robotics|Computer science

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