## 1 Introduction  
With the development of smart cities and Internet of Things (IoT) technology, there is a high application demand for indoor location services. High-precision indoor positioning systems are the basis for providing high-quality location services [1] and are different from traditional positioning techniques, which rely on the strength of signals received by the target object to meet the indoor high-precision demand. Ultra-wideband (UWB) positioning is a new type of short-range and high-rate wireless communication technology [2] that adopts the carrier-free spread spectrum technology, which uses an impact pulse with a very low duty cycle as the information carrier. It has a strong anti-jamming ability and can reach a centimeter-level positioning accuracy [3]. However, UWB signals are easily reflected, diffracted, or blocked during transmission, resulting in signal weakness. In addition, multipath interference and the non-light-of-sight (NLOS) phenomenon also cause large errors in the positioning results. There are three main positioning technologies for UWB: RSSI technology, AOA technology, and TOA/TDOA technology [4]. UWB position estimation methods are divided into two kinds [5]: estimating the position of the point to be measured based on the existing measurement information, or optimally estimating the position based on the existing redundant measurement information. For example, [PERSON] et al. [6] proposed an algorithm based on time-of-arrival (TOA) ranging information to estimate the entire region of target existence and select the center of mass of the region as the estimation result. [PERSON] et al. [7] used Kalman filtering to process UWB ranging data, which increased the localization accuracy by 21.96%. However, the Kalman filter algorithm was used under the premise that the model is a linear Gaussian model, which can optimally estimate the linear Gaussian system state and reduce its robustness in the case of complex environmental noise. To reduce the nonlinear error problem, Canadian scholar [PERSON] proposed a nonlinear filtering tracking cubature Kalman filtering (CKF) algorithm based on the spherical-radial cubature rule [8], achieving significantly superior accuracy and efficiency to those of other filters. [PERSON] et al. [9] used the three-dimensional spherical-radial rule for the CKF algorithm to approximate the Gaussian system with Taylor series third-order accuracy under non-Gaussian noise conditions. It obtained better numerical accuracy. [PERSON] et al. [10] proposed a new positioning algorithm based on the current statistics (CS) model and CKF algorithm for the nonlinear tracking problem in traditional UWB indoor positioning. The algorithm improves the positioning accuracy of UWB indoor positioning. [PERSON] et al. [11] designed an adaptive square root cubature Kalman filter (ASRCKF) positioning algorithm to solve the problem of target tracking in the research field, and the modified algorithm achieved a positioning accuracy of 15 cm in the dynamic tracking environment. However, the CKF algorithm often reduces the numerical accuracy when calculating the estimated mean square deviation because it does not satisfy the positive definiteness [12]. In addition, it is not adaptive, which will significantly impact or even cause divergence in the filtering performance when the model does not match the target. This study uses the CKF algorithm to process UWB localization data based on the squared range difference (SRD) model of distance, which is fundamental to the time difference of arrival (TDOA) algorithm, to address the problem of accuracy degradation in UWB dynamic moving target localization. Moreover, this paper proposes an improved adaptive algorithm by combining the Sigmoid function and the singular value decomposition (SVD) method to address the poor positioning accuracy under non-line-of-sight conditions. The Sigmoid adaptive function is used to update the measurement noise matrix, and singular value decomposition is used to decompose the covariance estimation.