Regression Assisted Matrix Completion for Reconstructing a Propagation Field with Application to Source Localization

This paper develops a regression assisted matrix completion method to reconstruct the propagation field for received signal strength (RSS) based source localization without prior knowledge of the propagation model. Existing matrix completion methods did not exploit the fact that the uncertainty of each observed entry is different due to the reality that the sensor density may vary across different locations. This paper proposes to employ local polynomial regression to increase the accuracy of matrix completion. First, the values of selected entries of a matrix are estimated via interpolation from local measurements, and the interpolation error is analyzed. Then, a matrix completion problem that is aware of the different uncertainty of observed entries is formulated and solved. It is demonstrated that the proposed method significantly improves the performance of matrix completion, and as a result, increases the localization accuracy from the numerical results.