UWB (Ultra Wide Band) refers to a system with a bandwidth of over 500 MHz or a bandwidth of 20% of the center frequency. It is robust against channel fading and has a wide signal bandwidth. Using the IR-UWB based ranging system, it is possible to obtain decimeter-level ranging accuracy. Furthermore, IR-UWB system enables acquisition over glass or cement with high resolution. In recent years, IR-UWB-based ranging chipsets have become cheap and popular, and it has become possible to implement positioning systems of several tens of centimeters. The system can be configured as one-way ranging (OWR) positioning system for fast ranging and TWR (two-way ranging) positioning system for cheap and robust ranging. On the other hand, the ranging based positioning system has a limitation on the number of terminals for localization because it takes time to perform a communication procedure to perform ranging. To overcome this problem, code multiplexing and channel multiplexing are performed. However, errors occur in measurement due to interference between channels and code, multipath, and so on. The measurement filtering is used to reduce the measurement error, but more fundamentally, techniques for removing these measurements should be studied. First, the TWR based positioning was analyzed from a stochastic point of view and the effects of outlier measurements were summarized. The positioning algorithm for analytically identifying and removing single outlier is summarized and extended to three dimensions. Through the simulation, we have verified the algorithm to detect and remove single outliers.