Magnetic induction based localization for wireless sensor networks in underground oil reservoirs

A non-transitory computer-readable medium storing instructions executable by a computer system to perform operations comprising:

• obtaining a set of distances, wherein the set of distances represents an estimate of distances between a plurality of sensors and at least two anchor devices in a wireless underground sensor network (WUSN) in a hydrocarbon reservoir, and locations of the at least two anchor devices are known;
• establishing an MI-based localization framework by first applying a weighted maximum likelihood estimation (WMLE) and then applying a semi-definite programming (SDP) relaxation to the set of distances and the known locations of the at least two anchor devices;
• after establishing the MI-based localization framework, determining a first set of sensor locations, wherein the determined first set of sensor locations represents a first estimate of locations of the plurality of sensors;
• and
• after determining the first set of sensor locations, determining a second set of sensor locations based on the determined first set of sensor locations, wherein the determined second set of sensor locations represents a second estimate of locations of the plurality of sensors.

A device comprising:

• a memory;
• and
• a processing unit that is arranged to perform operations including:
• obtaining a set of distances, wherein the set of distances represents an estimate of distances between a plurality of sensors and at least two anchor devices in a wireless underground sensor network (WUSN) in a hydrocarbon reservoir, and locations of the at least two anchor devices are known;
• establishing an MI-based localization framework by first applying a weighted maximum likelihood estimation (WMLE) and then applying a semi-definite programming (SDP) relaxation to the set of distances and the known locations of the at least two anchor devices;
• after establishing the MI-based localization framework, determining a first set of sensor locations, wherein the determined first set of sensor locations represents a first estimate of locations of the plurality of sensors;
• and
• after determining the first set of sensor locations, determining a second set of sensor locations based on the determined first set of sensor locations, wherein the determined second set of sensor locations represents a second estimate of locations of the plurality of sensors.