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<p>This study addresses the Degree of Nonlinearity (DON) analysis within the context of nonlinear optimal estimation. Utilizing DON, we investigate the fundamental attributes of diverse discrete-time models applicable in optimal estimation, encompassing both the Traditional Discrete-Time State Space Model (TDTSSM) and the Graphical State Space Model (GSSM). A stochastic approach is adopted as the DON metric to illustrate the nonlinearity degree for systems across varying dimensions. We provide a comparative analysis of the GSSM, which is solved via Factor Graph Optimization (FGO), against the TDTSSM, which is addressed using the Extended Kalman Filter (EKF). This comparison is elucidated through two practical scenarios: radar tracking and the fusion of Global Navigation Satellite System (GNSS) data with Ultra-Wideband (UWB) technology. In both cases, the GSSM exhibits enhanced performance, characterized by significantly lower DON values when contrasted with the TDTSSM. Furthermore, the study reveals that as the temporal window dimension of the GSSM increases, the DON of the system exhibits a decreasing trend. Specifically, for the two problems under consideration, the GSSMs achieve a reduction in DON by 11% and 95%, respectively, compared to the EKF. To facilitate reproducibility and further research, our code and data are publicly available at <a href="https://github.com/zhaoqj23/FE-GUT">https://github.com/zhaoqj23/FE-GUT</a>.</p>

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Degree of nonlinearity analysis for graphical state space model solved by factor graph in radar tracking and GNSS/UWB integration

  • 期刊论文

  • 发表日期：

    2025年7月18日

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  • Houcheng Jiang,
  • Chengxi Zhang,
  • Qijia Zhao,
  • Shaolin Lü

摘要

This study addresses the Degree of Nonlinearity (DON) analysis within the context of nonlinear optimal estimation. Utilizing DON, we investigate the fundamental attributes of diverse discrete-time models applicable in optimal estimation, encompassing both the Traditional Discrete-Time State Space Model (TDTSSM) and the Graphical State Space Model (GSSM). A stochastic approach is adopted as the DON metric to illustrate the nonlinearity degree for systems across varying dimensions. We provide a comparative analysis of the GSSM, which is solved via Factor Graph Optimization (FGO), against the TDTSSM, which is addressed using the Extended Kalman Filter (EKF). This comparison is elucidated through two practical scenarios: radar tracking and the fusion of Global Navigation Satellite System (GNSS) data with Ultra-Wideband (UWB) technology. In both cases, the GSSM exhibits enhanced performance, characterized by significantly lower DON values when contrasted with the TDTSSM. Furthermore, the study reveals that as the temporal window dimension of the GSSM increases, the DON of the system exhibits a decreasing trend. Specifically, for the two problems under consideration, the GSSMs achieve a reduction in DON by 11% and 95%, respectively, compared to the EKF. To facilitate reproducibility and further research, our code and data are publicly available at https://github.com/zhaoqj23/FE-GUT.