# High-Accuracy Wave Direction Estimation Using Kalman Fusion of Interferometric Measurements and Energy Field Reconstruction

## TL;DR

A new method fuses interferometric and energy-based measurements to accurately estimate wave direction, improving performance in noisy and complex environments.

## Contribution

The novel multi-rate Kalman fusion strategy combines high-rate interferometric and low-rate energy-based data for robust wave direction estimation.

## Key findings

- The fusion method achieves azimuth and elevation RMSEs of 0.0069° and 0.006°, significantly reducing high-frequency fluctuations.
- The proposed method improves capture efficiency from approximately 0.988 and 0.998 for individual methods to nearly unity for the fusion output.

## Abstract

We propose a high-accuracy wave-direction estimation framework that fuses interferometric phase-based angle measurements with energy-field reconstruction. We develop a multi-rate Kalman fusion strategy to improve robustness and precision over single-source methods, validated under varying SNR and multi-target scenarios.

What are the main findings?
A high-accuracy wave-direction estimation framework is developed by fusing interferometric phase-based angle measurements with energy-field reconstruction, exploiting their complementary strengths.A multi-rate Kalman fusion strategy effectively integrates high-rate interferometric observations and low-rate energy-based constraints, achieving improved accuracy and robustness under low SNR and multi-target conditions.

A high-accuracy wave-direction estimation framework is developed by fusing interferometric phase-based angle measurements with energy-field reconstruction, exploiting their complementary strengths.

A multi-rate Kalman fusion strategy effectively integrates high-rate interferometric observations and low-rate energy-based constraints, achieving improved accuracy and robustness under low SNR and multi-target conditions.

What are the implications of the main findings?
The proposed fusion paradigm provides a practical and generalizable solution for reliable direction estimation in array-based remote sensing and electromagnetic sensing systems operating in noisy and complex environments.The proposed method can reduce sensitivity to measurement noise and scene complexity, supporting more stable pointing for applications such as microwave sensing links and space-based remote measurement scenarios.

The proposed fusion paradigm provides a practical and generalizable solution for reliable direction estimation in array-based remote sensing and electromagnetic sensing systems operating in noisy and complex environments.

The proposed method can reduce sensitivity to measurement noise and scene complexity, supporting more stable pointing for applications such as microwave sensing links and space-based remote measurement scenarios.

Microwave wireless power transfer (MWPT) for space solar power stations (SSPS) requires high-precision beam pointing in order to maintain effective aperture coupling and transmission efficiency under platform motion and disturbances. This paper proposes a dual-link beam pointing estimation framework that integrates guidance-link interferometric angle-of-arrival (AoA) measurements with power-link energy-field reconstruction. The interferometric chain provides high-rate azimuth and elevation observations for dynamic tracking, while the energy-field reconstruction estimates the energy-centroid displacement from the received-aperture power distribution to correct steady-state pointing bias. A Kalman filter (KF) is developed to fuse the asynchronous multi-rate measurements, yielding continuous and robust pointing estimates for closed-loop beam control. Simulation results show that the proposed fusion method achieves azimuth and elevation RMSEs of 0.0069° and 0.006° with interferometric and energy-centroid error levels of approximately 0.05° and 0.02°, respectively, significantly reducing high-frequency fluctuations. In addition, a sensitivity model is established to quantify the impact of angular errors on capture efficiency. The expected efficiency improves from approximately 0.988 and 0.998 for the individual methods to nearly unity for the fusion output. Quantitative accuracy thresholds corresponding to different efficiency requirements are further derived, providing practical guidelines for SSPS MWPT system design.