# Combining Dilution of Precision and Kalman Filtering for UWB Positioning in a Narrow Space
## 1 Introduction  
In recent years, with the development of the Internet of Things (IoT), virtual reality and smart home technology, the demand for indoor location services has increased [1, 2]. Low-cost, high-precision indoor positioning solutions have become the key to many IoT applications [3, 4, 5]. The ranging technology of ultra-wideband (UWB) has the advantages of a short pulse interval and high temporal resolution, which can achieve centimeter-level ranging accuracy [1, 6]. Therefore, UWB has become a common technology for indoor positioning in recent years [7]. Furthermore, a series of studies have been carried out on the UWB positioning mechanism, including channel model [8], multipath component estimation [9] and non-line-of-sight (NLOS) identification [10]. However, most studies have not focused on a special scene such as a narrow space. Most application scenes contain the narrow space, such as coalmine roadway, shaft, tunnel, corridor, etc. [11], whose structural characteristics can be summarized as follows: the space is long and narrow, and the side wall is limited [12]. Owing to these special structure characteristics, the positioning is more challenging in the narrow space compared with the general indoor environment. Firstly, in the narrow space, the electromagnetic wave propagation will have various reflections, transmissions, refractions and keyhole effects, resulting in channel deterioration and ranging errors [13; 14]. Secondly, the narrow space limits the layout of the positioning base station, which means the base station layout is impossible to be ideal for positioning [15]. Therefore, it is difficult to obtain a high positioning accuracy for UWB positioning in a narrow indoor space. Improving the positioning accuracy in the narrow space will push the UWB positioning to a wider range of application scenes [16]. DOP is an important indicator to describe the position accuracy obtained from a satellite constellation [17; 18], which is closely related to the satellite network structure. In the indoor environment, it contains the knowledge of positioning accuracy under specific base station network and scene characteristics [19]. In recent years, DOP has also become an important indicator of the geometric location distribution and accuracy of base stations in indoor positioning. The applicability of DOP in an indoor time difference of an arrival (TDOA) positioning system is analyzed in [20]. The results showed that, in the case of a low signal-to-noise ratio, the DOP values can be used as a reference index for the optimization of base station configuration. In [21], the base station layout schemes in different scenes were simulated to minimize the positioning error and maximize the coverage of the positioning area. Similarly, in [22], the optimal positioning scheme was obtained by weighting the geometric dilution of precision (GDOP) values, thereby minimizing the influence of the NLOS error in the position estimation process. Most of the previous studies only analyzed the characteristics of the geometric structure between the positioning source and the positioning node by employing DOP values, which gave the corresponding base station layout optimization strategy. However, they did not, in turn, use the DOP numerical analysis model to improve the positioning accuracy and stability of the existing positioning algorithm in a narrow space. The Kalman filter (KF) algorithm is an optimal regression data processing algorithm [23; 24]. It has been widely used to estimate the optimal state in various fields of engineering, such as robotics, target tracking, navigation, signal processing and communication [25; 26; 27]. In the study of indoor positioning, the estimation position of the tag is mainly optimized by KF. In [28], the particle swarm optimization algorithm was used to optimize the parameters of KF to improve the ranging accuracy of UWB. However, this technique was only applicable to one-dimensional ranging.