⚡ electrical engineering

RIS Nearfield Position and Velocity Estimation Using a Validated Propagation Model

This paper proposes a robust modified three-step algorithm for nearfield position and velocity estimation using a validated 1-bit RIS propagation model, demonstrating that accounting for antenna patterns and moving beyond far-field assumptions significantly reduces errors to 7 mm and 0.12 m/s at a 2-meter distance.

Original authors: Thomas Zemen, Musa Furkan Keskin, Moustafa Rahal, Thomas Wilding, Hamed Radpour, Markus Hofer, Benoit Denis, Henk Wymeersch

Published 2026-02-16

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CC BY 4.0

Original authors: Thomas Zemen, Musa Furkan Keskin, Moustafa Rahal, Thomas Wilding, Hamed Radpour, Markus Hofer, Benoit Denis, Henk Wymeersch

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are in a large, cluttered warehouse (an indoor industrial setting). You are trying to find a moving robot (the User Equipment, or UE) that is hiding behind a giant wall. You can't see the robot directly because the wall blocks your view.

However, you have a special "smart mirror" (the RIS or Reconfigurable Intelligent Surface) mounted on the ceiling. This isn't just a normal mirror; it's made of thousands of tiny, adjustable tiles that can bounce radio waves off the wall and around the corner to find the robot.

This paper is about teaching that smart mirror how to not only find where the robot is, but also how fast it's moving, even when the robot is very close to the mirror.

Here is the breakdown of their discovery using simple analogies:

1. The Problem: The "Far-Field" Mistake

In the past, scientists tried to locate objects using these mirrors by assuming the object was far away, like a star in the sky. When you look at a star, the light rays hitting your eyes are perfectly parallel. This is called the Far-Field assumption.

But in a factory, the robot might be just a few meters away. When you are close to a lightbulb, the light rays hitting your eyes are spreading out in a curve, not parallel. This is the Near-Field.

The authors found that using the old "Far-Field" math (assuming parallel rays) when the robot is close causes the location estimate to go haywire. It's like trying to use a flat map to navigate a mountain; the map works for a flat plain, but fails miserably when the terrain curves.

2. The Solution: A Three-Step "Search and Refine" Game

To fix this, the team created a new, smarter algorithm that works in three stages, like a detective narrowing down a suspect's location:

Step 1: The Rough Sketch (Grid Search)
Instead of guessing the robot's location based on the "flat map" (Far-Field) math, they use a "curved map" (Near-Field) math. They scan a 3D grid of possible spots (up/down, left/right, near/far) to find the best starting guess.
- The Fix: They realized the old method was too sloppy for close distances. Their new method scans the 3D space properly, giving a much better starting point.
Step 2: The Quick Correction (Closed-Form)
Once they have a rough guess, they use a quick mathematical formula to nudge the guess closer to the truth. It's like taking a rough sketch and quickly erasing the obvious mistakes.
Step 3: The Final Polish (Gradient Descent)
Finally, they run a high-precision computer search that fine-tunes the location and speed until the error is tiny. This is like using a magnifying glass to make the final adjustments.

3. The "Real World" Reality Check

Many computer simulations pretend that radio waves bounce off a perfect, invisible surface. But in the real world, the "smart mirror" has physical tiles, and the antennas have specific shapes that focus the signal like a flashlight beam (this is the Antenna Pattern).

The authors tested their system using a realistic model that includes these physical imperfections. They found that:

Ignoring the shape of the antennas makes the location estimate slightly worse (like trying to aim a flashlight with a cracked lens).
However, even with these imperfections, their new algorithm is incredibly accurate.

The Results: How Good Is It?

They tested this in a simulated 3-meter by 3-meter room. When the robot was 2 meters away from the smart mirror:

Position Error: They could pinpoint the robot's location within 7 millimeters (about the thickness of a credit card).
Velocity Error: They could calculate the robot's speed within 0.12 meters per second (a very slow walking pace).

Why Does This Matter?

This technology is a game-changer for Industry 4.0 (smart factories).

Safety: If a robot is moving near a human, the system can track it precisely even if they are behind a machine or a wall.
Efficiency: You don't need expensive cameras or GPS (which doesn't work indoors) to track hundreds of moving parts. You just need this "smart mirror" to bounce signals around.

In a nutshell: The paper says, "Stop using old, flat-map math for close-up tracking. Use our new 3-step, curved-map algorithm, and you can track moving objects in a factory with the precision of a surgeon's scalpel, even when they are hiding behind walls."

1. Problem Statement

The paper addresses the challenge of estimating the position and velocity of a User Equipment (UE) in Non-Line-of-Sight (NLOS) indoor scenarios using Reconfigurable Intelligent Surfaces (RIS).

Context: In industrial automation and control, direct Line-of-Sight (LOS) between the Base Station (BS) and UE is often blocked. RISs can create a bypass by reflecting signals, but accurately localizing the UE in the Near-Field (NF) of the RIS is difficult.
Specific Challenges:
- Existing algorithms often rely on Far-Field (FF) assumptions (planar wavefronts), which fail at short distances where spherical wavefronts dominate.
- Previous methods may not account for realistic antenna patterns (BS, RIS unit cells, and UE), leading to inaccuracies.
- There is a need for robust algorithms that work with practical, compound RIS structures (multiple tiles) rather than idealized single arrays.

2. Methodology

The authors propose a modified three-step estimation algorithm based on a single snapshot of received pilot symbols, utilizing a realistic numerical propagation model validated by empirical measurements.

A. System and Signal Model

Setup: A BS, a passive reflective RIS (composed of $M$ elements), and a moving UE. The LOS between BS and UE is blocked.
Propagation Model: The paper uses a validated model (from references [6]–[8]) that includes:
- Antenna Patterns: Directional gains for the BS horn, UE monopole, and RIS unit cells.
- Geometry: The channel coefficient accounts for the specific distances from the BS to the RIS element and from the RIS element to the UE.
- Reflection: 1-bit phase control per RIS unit cell.
Signal Simplification: The received signal is modeled to isolate the phase terms dependent on position ( $p$ ) and velocity ( $v$ ), assuming small-scale mobility and constant amplitude over the observation window.

B. The Modified Algorithm

The authors refine the multi-step algorithm proposed in prior work [4] to handle near-field conditions more robustly:

Step 1: Robust 3D Grid Search (GS):
- Previous Approach: Used a 2D GS for azimuth/elevation based on FF assumptions, followed by a line search for range. This failed at short distances.
- Proposed Approach: A 3D Grid Search in azimuth ( $\phi$ ), elevation ( $\theta$ ), and range ( $r$ ) using the full Near-Field (NF) expression. This avoids the error propagation caused by invalid FF assumptions at close range.
Step 2: Closed-Form (CF) Refinement:
- Uses linearization of the RIS phase response to calculate position and velocity offsets ( $p_\delta, v_\delta$ ) based on the current estimates. This step iteratively refines the initial grid search results.
Step 3: 6D Gradient Descent:
- A final optimization step starting from the refined estimates to minimize the projection error of the received signal vector onto the null space of the channel model, yielding the final Maximum Likelihood (ML) estimates for position and velocity.

3. Key Contributions

Algorithmic Improvement: Demonstrated that the initial FF-based grid search is not robust for short distances (near-field). Proposed and analyzed a 3D Near-Field Grid Search as a superior initialization step.
Realistic Validation: Evaluated the algorithm using a validated propagation model that includes realistic antenna patterns and a compound RIS structure (4 tiles, 508 elements total), rather than idealized isotropic models.
Performance Analysis: Quantified the impact of antenna patterns on estimation error and provided a detailed breakdown of error contributions from each algorithmic step (GS, CF, Gradient Descent).

4. Simulation Results

The authors simulated a $3\text{m} \times 3\text{m}$ Area of Interest (AOI) at a height of $z = -0.5\text{m}$ with a center frequency of 23.8 GHz.

Accuracy at 2 meters:
- Position Error: Achieved 7 mm (RMS).
- Velocity Error: Achieved 0.12 m/s (RMS).
Impact of Antenna Patterns:
- Simulations showed that including realistic antenna patterns increases the estimation error compared to an idealized model (where patterns are set to 1). However, the error remains within acceptable limits for industrial applications.
Distance Dependency:
- Errors increase with distance from the RIS due to signal attenuation and the decay of near-field wavefront curvature effects.
- For distances $< 1.2\text{m}$ , errors slightly increase/flattened due to limitations in the closed-form refinement expressions derived for small displacements.
Algorithm Steps:
- The Near-Field Grid Search (GS NF) significantly outperformed the Far-Field approach (GS FF) for distances $< 2\text{m}$ .
- The Closed-Form (CF) and 6D Gradient Descent steps provided the final convergence.
- A "fine" grid search step was found to be unnecessary, as the CF and 6D steps converged to the same result regardless of whether the initial GS was coarse or fine.

5. Significance

Practical Applicability: The results demonstrate that RIS-aided localization is viable for industrial automation and control scenarios where high precision (millimeter-level) is required in NLOS environments.
Model Fidelity: The paper highlights the critical importance of using validated propagation models that include antenna patterns. Ignoring these patterns leads to optimistic but unrealistic performance predictions.
Algorithm Robustness: By shifting from Far-Field to Near-Field assumptions in the initialization step, the proposed method ensures reliable localization even when the UE is very close to the RIS, a common scenario in indoor deployments.
Hardware Feasibility: The use of a compound RIS with 1-bit phase control (low complexity hardware) achieving high precision proves that cost-effective RIS prototypes can support advanced sensing tasks.