Spatio-Temporal Constrained Refined Nearest Neighbor Fingerprinting Localization
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摘要: 针对室内指纹定位中降维技术导致的信号与物理空间的几何关联弱化、信号时变引起的在线映射偏差、以及定位过程中伪近邻点干扰等问题，提出时空约束下优选近邻指纹定位算法。在离线降维建库阶段，引入空间关联约束，依据参考点间的物理距离调节低维特征空间结构，加强低维特征与物理坐标的耦合关系；同时设计时变一致约束，促使同一位置不同时刻的指纹在映射后的低维空间中保持聚集，以提升高维信号到低维特征的映射稳定性。在在线定位阶段，融合共享近邻相似度和欧式距离生成邻距相似度，据此构建近邻集，进而采用基于Z-score阈值的迭代优化策略，分析内部相似度分布并剔除伪近邻点，保障近邻质量和定位精度。实验结果表明，所提算法在实测数据集上平均定位误差较基准方法降低至少12.42%，在公开数据集上降低至少7.08%，且在相同误差范围内的累计概率更高。Abstract:
Objective Indoor fingerprint-based localization confronts three critical challenges. Firstly, dimensionality reduction (DR), commonly employed to reduce storage and computational costs, often disrupts the geometric correlation between signal features and physical space, compromising mapping accuracy. Secondly, signal features exhibit temporal variability due to human movement or environmental dynamics. During online mapping, this variability introduces bias, distorting the representation of similarity between target and reference points in the low-dimensional space. Thirdly, pseudo-neighbor interference persists, where environmental noise or imperfect similarity metrics lead to inaccurate neighbor selection, thereby skewing position estimates. To overcome these limitations, this study proposes a Spatio-Temporal Constrained Refined Nearest Neighbor (STC-RNL) fingerprinting localization algorithm, aiming to achieve robust and high-accuracy localization under complex, real-world interference. Methods In the offline phase, a robust DR framework is established by integrating dual constraints into a Multidimensional Scaling (MDS) model. Specifically, a spatial correlation constraint leverages physical distances between reference points, assigning stronger associations to proximate locations to ensure alignment between low-dimensional features and the actual layout. Simultaneously, a temporal consistency constraint clusters multiple temporal signal samples from the same location into a compact region, effectively suppressing feature drift. These constraints, combined with the MDS structure-preserving loss, form the final optimization objective, from which low-dimensional features and an explicit mapping matrix are derived. In the online phase, a progressive refinement mechanism is deployed. An initial candidate set is screened via a Euclidean distance threshold. Subsequently, a hybrid similarity metric is constructed by enhancing shared-neighbor similarity via a Sigmoid-based strategy—which truncates low and smooths high similarities—and then fusing it with Euclidean distance to improve discriminative power for true neighbors. Following this, an iterative Z-score-based filtering strategy is applied to the neighbor set to eliminate outlier reference points that deviate significantly from local group characteristics in both feature and coordinate domains. The final position is estimated through a similarity-weighted average over the refined neighbor set, assigning higher weights to more confident and stable references. Results and Discussions The performance of STC-RNL is comprehensively evaluated on a private ITEC dataset and a public SYL dataset. The introduced spatio-temporal constraints significantly enhance the robustness of the derived mapping matrix under noisy conditions ( Table 2 ). Compared to baseline DR methods, the proposed module reduces the mean localization error by at least 6.30% in high-noise scenarios (Fig. 9 ). In the localization stage, the refined neighbor selection effectively mitigates pseudo-neighbor interference. On the ITEC dataset, STC-RNL achieves an average error of 0.959 m, representing an improvement of 9.61% to 33.68% over SSA-XGBoost and SPSO (Table 3 ). End-to-end system comparisons show that STC-RNL reduces the average error by at least 12.42% on ITEC and by at least 7.08% on SYL (Table 4 ), while its CDF curves demonstrate faster convergence and superior precision, particularly within the 1.2 m range (Fig. 10 ). These results collectively confirm that the algorithm maintains high stability and accuracy, with a notably lower maximum error across datasets.Conclusions The STC-RNL algorithm addresses the issues of structural distortion and mapping bias inherent in traditional DR-based localization. By dual-optimizing the offline feature embedding with spatio-temporal constraints and the online neighbor selection with progressive refinement, the coupling between signal features and physical coordinates is substantially strengthened. The core innovation lies in the synergistic framework that ensures only high-confidence neighbors contribute to the final estimate, thereby enhancing accuracy and robustness in dynamic environments. Experimental validations indicate that the model reduces the average localization error by 12.42%–32.80% on ITEC and by 7.08%–13.67% on SYL compared to baseline algorithms, while exhibiting faster error convergence. For future work, incorporating nonlinear manifold modeling is anticipated to further improve performance in heterogeneous access point environments. -
表 1 不同定位算法性能比较
定位算法 平均定位误差(m) 最小值(m) 最大值(m) SSA-XGBoost 1.340 0.049 4.750 PSO-ELM 1.446 0.082 6.182 SPSO 1.102 0.050 5.064 RDC-WKNN 1.061 0.097 7.039 所提算法 0.959 0.047 3.121 
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表 2 整体算法性能对比
数据集 定位算法 平均定位误差(m) 最小值(m) 最大值(m) 标准差(m) ITEC PCA-KRR 1.427 0.053 5.861 1.075 KPCA-IGBRT 1.129 0.028 3.478 0.904 SANGIRA 1.095 0.010 5.288 0.966 所提算法 0.959 0.047 3.121 0.727 SYL PCA-KRR 4.259 0.652 45.636 4.477 KPCA-IGBRT 4.002 0.118 48.163 4.943 SANGIRA 3.957 0.211 50.927 4.963 所提算法 3.677 0.058 40.950 4.570
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