In ultra-wideband indoor positioning, due to the complex indoor environment, the communication between each anchor node and the positioning node will be subject to different degrees of interference, and the more interfered data will seriously affect the positioning accuracy, so it is necessary to screen the anchor nodes. Aiming at the above problems, an ultra-wideband indoor positioning anchor node selection method based on received signal strength indication(RSSI) is proposed. Firstly, the RSSI between the anchor nodes is calculated using the interpolation method and optimized by Gaussian process regression to obtain the initial RSSI estimation value. Secondly, this estimation value is Taylor-expanded at the anchor node position and the path loss factor to obtain the Fisher matrix with the RSSI information, and then, the Cramér-Rao lower bound(CRLB) of the RSSI is obtained. Then, all the anchor nodes are selected by the method, and the RSSI of the anchor nodes is obtained. Then, all the anchor node selected state combinations(selected as 1 and unselected as 0) are substituted into the CRLB formula, and the traces of the CRLB are solved by semidefinite relaxation. Finally, the selected state combination corresponding to the minimum trace is the selection result. The experimental results show that compared with the algorithm without anchor node selection, this method improves the positioning accuracy in X, Y, and Z directions by 37.6%, 32.2%, and 38.8%, respectively, and it is close to the anchor node selection result of the exhaustive method. In addition, the proposed algorithm adopts an unsupervised approach without obtaining a priori data, which has high practical application value.