1. A system for reconstructing sensor data in a rotor system of a rotary wing aircraft having a number of aircraft states, comprising: a plurality of rotor blades of the rotor system of the rotary wing aircraft; a plurality of sensors mounted to each of the plurality of rotor blades, the plurality of sensors sensing at least one of loads and motion characteristics in the corresponding one of the one or more of the plurality of rotor blades and generate a number of sensor samples on each rotor revolution; and an analysis unit to generate, through a processor, reconstructed sensor data from the sensor data using numerical analysis for low-rank matrices, wherein the plurality of sensors are wireless sensors to transmit the sensor data from the corresponding one of the one or more of the plurality of rotor blades to the analysis unit; wherein the plurality of sensors includes a number of sensors with the number of sensors multiplied by the number of sensor samples for each sensor generated on each rotor revolution being greater than the number of aircraft states; wherein the analysis unit generates the reconstructed sensor data by generating a matrix with the sensor data and performing numerical methods for low-rank matrices, wherein the reconstructed sensor data corrects for corrupted wireless transmissions from the wireless sensors; wherein the analysis unit further generates a fault-free matrix, a fault matrix, and a noise matrix from the matrix generated with the sensor data; wherein each row of the matrix contains sensor data generated in one revolution of the rotor system for each of the plurality of sensors, and the number of rows corresponds to a plurality of revolutions of the rotor system; wherein each column of the matrix contains data sampled from one of the plurality of sensors at a selected rotor azimuth location; wherein sensor data is sampled at multiple azimuth positions through a single revolution of the rotor system; and a data output unit operable to output the reconstructed sensor data to fault detection system.