Near-Field Positioning and Attitude Sensing Based on Electromagnetic Propagation Modeling

TL;DR

This work develops a physics-based electromagnetic propagation model (EPM) to enable joint near-field positioning and attitude sensing, treating the UE as an extended source whose current distribution encodes pose. By partitioning the distance domain with Phase Ambiguity Distance $d_{ ext{PA}}$ and Spacing Constraint Distance $d_{ ext{SC}}$, the authors derive region-specific, closed-form solutions for $(z_t,t_z)$ in the noise-free case and provide provable performance bounds under noise. They establish two globally informative bounds, the ZZB and the ECRB, and show how these bounds depend on SNR, carrier frequency, array size, and priors, with explicit expressions and asymptotic behavior. Numerical results confirm millimeter-level position accuracy and sub-0.1 attitude accuracy at practical SNRs, and illustrate the tighter, globally valid ZZB relative to the high-SNR ECRB. The methodology and bounds offer a solid theoretical foundation for high-precision near-field sensing and ISAC scenarios, with strong implications for IoT, smart environments, and 5G/B5G systems.

Abstract

Positioning and sensing over wireless networks are imperative for many emerging applications. However, since traditional wireless channel models over-simplify the user equipment (UE) as a point target, they cannot be used for sensing the attitude of the UE, which is typically described by the spatial orientation. In this paper, a comprehensive electromagnetic propagation modeling (EPM) based on electromagnetic theory is developed to precisely model the near-field channel. For the noise-free case, the EPM model establishes the non-linear functional dependence of observed signals on both the position and attitude of the UE. To address the difficulty in the non-linear coupling, we first propose to divide the distance domain into three regions, separated by the defined Phase ambiguity distance and Spacing constraint distance. Then, for each region, we obtain the closed-form solutions for joint position and attitude estimation with low complexity. Next, to investigate the impact of random noise on the joint estimation performance, the Ziv-Zakai bound (ZZB) is derived to yield useful insights. The expected Cramér-Rao bound (ECRB) is further provided to obtain the simplified closed-form expressions for the performance lower bounds. Our numerical results demonstrate that the derived ZZB can provide accurate predictions of the performance of estimators in all signal-to-noise ratio (SNR) regimes. More importantly, we achieve the millimeter-level accuracy in position estimation and attain the 0.1-level accuracy in attitude estimation.

Figures (11)

• Figure 1: Illustration of the far-field UPW, near-field SWM, and near-field EPM. Fig. \ref{['fig:jsac11']} shows the far-field UPW and near-field SWM in the 2D view, where the approximation process of transition from a spherical wavefront to a planar wavefront is truncated due to space limitations. Fig. \ref{['fig:jsac12']} illustrates the near-field EPM based on 3D electromagnetic propagation theory, where the UE is considered as a dipole as an example.
• Figure 2: Illustration of the joint position and attitude estimation system.
• Figure 3: RERRs versus the normalized $z_{\mathsf{t}}$. Without loss of generality, we set that $\lambda=0.01~\textrm{m}$, $x_{\mathsf{r}}=0~\textrm{m}$, $y_{\mathsf{r}}=10\lambda$, and $t_z=\sqrt{0.1}$, $\sqrt{0.5}$, or $\sqrt{0.9}$.
• Figure 4: Illustration of the UE distance domain division, where $\mathbf{p}_{\mathsf{t1}}$ is located at the near-field boundary defined by the Fraunhofer distance$d_{\mathsf{F}}$, $\mathbf{p}_{\mathsf{t2}}$ is located at the boundary defined by the Phase ambiguity distance$d_{\mathsf{PA}}$, and $\mathbf{p}_{\mathsf{t3}}$ is located at the boundary defined by the Spacing constraint distance$d_{\mathsf{SC}}$.
• Figure 5: MSEs versus SNR for the joint estimates of $z_{\mathsf{t}}$ and $t_z$, with $z_{\mathsf{t}} \sim \mathcal{U}[3~\textrm{m}, 5~\textrm{m}]$, $t_{z} \sim \mathcal{U}[0, 1)$, $\lambda=0.1~\textrm{m}$, $D_{\mathsf{r}}=5~\textrm{m}$, and $l_{\mathsf{s}}=0.1~\textrm{m}$. $\mathrm{ZZB}\left(z_{\mathsf{t}}\right)$ and $\mathrm{ZZB}\left(t_{z}\right)$ are computed based on \ref{['eq:ZZBz']} and \ref{['eq:ZZBtz']}, $\mathrm{ECRB}\left(z_{\mathsf{t}}\right)$ and $\mathrm{ECRB}\left(t_{z}\right)$ are computed based on \ref{['eq:ECRBYT']} and \ref{['eq:ECRBT']}, and $\mathrm{MAP}\left(z_{\mathsf{t}}\right)$ and $\mathrm{MAP}\left(t_{z}\right)$ are obtained from Monte Carlo simulations.

Theorems & Definitions (15)

• Definition 1: Parameters to be estimated
• Remark 1: EPM contains SWM
• Remark 2: EPM provides attitude information
• Proposition 1: Phase ambiguity distance $d_{\mathsf{PA}}$ and Spacing constraint distance $d_{\mathsf{SC}}$
• Remark 3: Summary of closed-form solutions
• Lemma 1: ZZB preliminaries for $\bm{\xi}$
• Lemma 2: Minimum error probability
• Proposition 2: ZZB expressions for $\bm{\xi}$
• Corollary 1: Asymptotic analysis of ZZB
• Corollary 2: ZZB for the attitude-only estimation