Frequency selection for indoor ranging using compressive sensing

Nowadays, indoor ranging and localization have become necessary in daily life. Due to the multi-path propagation and noise in the indoor environment, phase domain ranging method using multi-frequency has been proposed which achieves accurate estimation of indoor target. However, as the indoor communication is usually carried on Bluetooth Low Energy (BLE) or Zigbee, high efficiency is indispensable in the face of limited bandwidth and measuring time. Thus, in this thesis, we aim to reduce the number of frequencies used in the ranging while keeping an acceptable estimation accuracy. We at first build the signal model and study the ambiguity range of the problem. Then based on the estimation theory and the concept of compressive sensing (CS) theory, we take the Cramer Rao Lower Bound (CRLB) and the matrix coherence as the criteria and select the optimal subset on given tone set. To test the performance of selected subset, we utilize gridless reconstruction algorithms, noiseless global matched filter (NL-GMF) and atomic norm minimization (ANM), to estimate target distance with the subset in both simulated data and real data and provide the mean square error (MSE), the estimation probability and the successful estimation probability in various estimation conditions.