高斯过程回归误差标定辅助的室内惯性测量单元与超宽带融合定位算法研究

马鑫鹏; 陈宇; 崔志成; 李兴广; 崔炜

doi:10.11999/JEIT241145

高斯过程回归误差标定辅助的室内惯性测量单元与超宽带融合定位算法研究

doi: 10.11999/JEIT241145 cstr: 32379.14.JEIT241145

长春理工大学电子信息工程学院长春 130022

基金项目: 吉林省科技发展计划项目(20220203066SF)

详细信息

作者简介:
马鑫鹏：男，硕士，研究方向为室内UWB与IMU融合定位

陈宇：女，副教授，研究方向为计算机视觉

崔志成：男，硕士，研究方向为室内视觉与UWB融合定位

李兴广：男，教授，研究方向为智能信息处理

崔炜：男，副教授，研究方向为人工智能和模式识别

通讯作者:
陈宇　assma@163.com

中图分类号: TN967.2
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出版历程
- 收稿日期: 2024-12-30
- 修回日期: 2025-07-28
- 网络出版日期: 2025-08-05

Research on Fusion Localization Algorithm of Indoor UWB and IMU Assisted by GPR Error Calibration

Changchun University of Science and Technology, School of Electronic information Engineering, Changchun 130022, China

Funds: Jilin Province Science and Technology Development Plan Project (20220203066SF)

摘要

摘要: 室内环境下超宽带(UWB)误差标定困难，静态和动态目标在视距和非视距情况下的定位精度均难以保证。为此该文提出了一种高斯过程回归(GPR)误差标定辅助的室内惯性测量单元(IMU)与UWB融合定位算法(GIU-EKF)。在视距情况下通过对视距环境UWB测距误差进行采样分析，建立GPR误差标定模型关联二维坐标与测距误差。使用误差标定模型计算所有坐标点UWB测距值的概率分布集合，利用待测点范围内的坐标样本及其归一化概率计算测距拟合值，实时抑制视距环境测距误差。当UWB测距增量超过阈值判别为非视距环境。非视距情况下通过子级扩展卡尔曼滤波器(EKF)融合UWB信息和短时IMU信息实时修正运动过程中测距值的非视距误差，并将其送入主EKF实现运动状态估计更新。实验结果表明，在视距情况下标签处于静态和动态时经GPR粗差修正后的定位误差较修正前分别下降64%和58%，GIU-EKF算法在论文所述的3种非视距环境下对低速运动目标能保持稳健的运动状态估计，平均定位误差达到7.5 cm；运动速度为0.2～0.8 m/s的标签，定位误差小于10 cm。
- 室内定位 /
- 超宽带误差标定 /
- 高斯过程回归 /
- 扩展卡尔曼滤波器 /
- 惯性测量单元短时估计
Abstract: Objective Ultra-WideBand (UWB) ranging in confined indoor environments is prone to coarse ranging errors and Gaussian noise, which substantially degrade localization accuracy for both static and dynamic targets, even under Line-of-Sight (LOS) conditions. In addition, during indoor operations of wheeled vehicles, obstacles often obstruct the LOS between onboard UWB tags and anchors, resulting in Non-Line-of-Sight (NLOS) propagation. NLOS-induced interference results in abrupt fluctuations in range measurements, which severely compromise the estimation of the vehicle’s motion state. Methods To address these challenges, this study proposes a Gaussian Process Regression (GPR)-calibrated indoor UWB/Inertial Measurement Unit (IMU) fusion localization algorithm (GIU-EKF). The proposed approach offers two key features. First, a UWB ranging error model for the entire two-dimensional localization area is established by collecting UWB measurements at a limited set of reference points under LOS conditions. This model is applied to correct LOS-related ranging biases. Second, by leveraging the low short-term drift characteristics of inertial measurements, the algorithm fuses IMU and UWB data to mitigate NLOS ranging errors. Results and Discussions Under LOS conditions, a GPR-based error calibration model is constructed by sampling and analyzing UWB ranging deviations at known reference coordinates. This model captures the statistical association between two-dimensional spatial positions and the corresponding ranging errors. For any queried location, the model generates a set of probabilistic range estimates, with the final range value obtained by weighting nearby sample points according to their normalized likelihoods. This enables real-time suppression of LOS-related ranging errors. A threshold-based detection mechanism identifies NLOS conditions when the UWB range increment exceeds a predefined threshold. In NLOS scenarios, a subordinate Extended Kalman Filter (EKF) fuses UWB range data with short-term IMU measurements to compensate for NLOS-induced ranging errors during motion. The corrected range data are then incorporated into a primary EKF to update the vehicle’s motion state estimation. Experimental results demonstrate that the proposed GPR-based coarse error correction reduces localization errors by 64% and 58% for static and dynamic tags under LOS conditions, respectively. In three representative NLOS scenarios, the GIU-EKF algorithm maintains reliable motion state estimation for low-speed targets, achieving an average localization error of 7.5 cm. For tags moving at speeds between 0.2 m/s and 0.8 m/s, localization errors remain below 10 cm. The robustness of the proposed algorithm under extreme conditions is also validated. As shown in Section 4.3.2, the algorithm maintains stable velocity vector estimation even when the wheeled vehicle experiences alternating occlusions between single-anchor and multi-anchor configurations. Under low-speed conditions (2.2 cm/s), the localization error remains as low as 6.7 cm. Section 4.3.3 further verifies the algorithm’s convergence capability under large initial deviations. When subjected to initial heading errors between 5° and 50°, or a combined 1.5-meter position offset and 10° heading deviation, the proposed method consistently converges to the true position within a 2-meter travel distance. Conclusions This study presents a GPR-assisted indoor UWB/IMU fusion localization algorithm. By independently suppressing LOS and NLOS ranging errors from four UWB anchors, the proposed approach enhances localization accuracy in complex indoor environments. Under LOS conditions, a GPR-based correction mitigates coarse UWB ranging errors. In NLOS scenarios, short-term inertial estimates compensate for anomalous UWB measurements. A subordinate EKF adaptively balances observation uncertainties from the two sensing modalities, maintaining motion state observability when the tag moves slowly in confined spaces. This design avoids long-term drift accumulation, which is often observed in tightly coupled systems that treat IMU data as a strong prior, particularly when using low-cost inertial sensors. Experimental results demonstrate that the proposed algorithm achieves sub-10 cm localization accuracy under both LOS and NLOS conditions. During low-speed operations, the system maintains convergence of both velocity and position estimates. Furthermore, even with significant initial motion state biases, the algorithm consistently converges to the true trajectory. These findings indicate that the proposed method effectively meets the operational requirements of mobile robots in narrow indoor environments. However, practical application still requires further attention to two key aspects: efficient and autonomous collection of coordinate samples for GPR model training, and integration of real-time localization outputs with vehicle path planning and motion control systems.
- Indoor localization /
- Ultra-WideBand (UWB) error calibration /
- Gaussian Process Regression (GPR) /
- Extended Kalman Filter (EKF) /
- Short-term Inertial Measurement Unit (IMU) estimation

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图 1 融合定位模型架构

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图 2 实验设备与场景

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图 3 LOS定位数据采集轨道

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图 4 运动目标NLOS定位数据采集轨道

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图 5 基站C误差标定模型

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图 6 静态定位结果

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图 7 LOS运动目标定位

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图 8 NLOS环境定位结果

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图 9 轨道2 IMU修正前后测距值

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图 10 速度与位置估计

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图 11 初始状态异常实验

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表 1 4个基站高斯模型优化后的核参数和对应的误差函数值

基站	$ {\mathrm{\sigma }}_{\mathrm{l}} $	$ {\sigma }_{\mathrm{f}} $	$ \sigma $	$ \beta $	$ {E}_{\mathrm{r}\mathrm{m}\mathrm{s}\mathrm{e}} $ (cm)
A	500	46.49	80	–259.84	6.499
B	600	21.28	63	–143.58	5.217
C	550	24.57	52	–215.22	5.160
D	550	30.79	78	–217.79	4.863

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表 2 各基站修正前后测距误差RMS(cm)

基站编号	轨道1		轨道2		轨道3		轨道4
基站编号	修正前/后	下降(%)	修正前/后	下降(%)	修正前/后	下降(%)	修正前/后	下降(%)
A	25.0/5.8	77	26.3/4.6	83	33.6/5.7	83	21.3/10.5	51
B	16.7/12.1	28	12.8/10.3	20	22.4/10.6	53	15.5/3.8	75
C	23.6/3.2	86	20.2/3.2	84	16.5/13.1	21	17.1/5.8	66
D	22.8/7.1	69	26.4/5.9	78	23.1/3.8	84	26.2/4.2	84

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表 3 4条轨道定位误差RMS(cm)

轨道编号	LS		EKF
轨道编号	修正前/后	下降(%)	修正前/后	下降(%)
1	33.8/17.5	48	27.8/12.1	56
2	30.4/15.4	49	28.6/7.7	73
3	44/31.2	29	16.9/11.1	34
4	16.4/5	70	18.9/5.8	69
误差均值	29.3/14.3	-	22.4/8.8	-

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表 4 NLOS环境4条轨道3种定位算法定位误差RMS(cm)

轨道编号	GP-LS	GP-EKF	GIU-EKF
1	16.8	10.8	9.8
2	17.2	28.9	5.4
3	34.6	8.1	8.2
4	7.4	9.6	6.9

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表 5 不同速度下定位误差RMS(cm)

速度(cm/s)	2.2	22	44	66	88
本文算法	6.7	6.3	6.4	6.5	6.2
传统算法	24.8	23.6	24.1	25.7	26.4

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