This paper studies motion estimation of moving energy emitters using passive sensors. The emitters may be light, acoustic, or radio sources. While the bearing vector pointing from the sensor to the emitter can be easily obtained, existing approaches mainly rely on the bearing-only motion estimation method. However, this method suffers from a fundamental limitation that the sensor must have lateral motion to ensure observability. Unfortunately, this lateral motion requirement often conflicts with the sensor's desired motion in many tasks. In this paper, we point out that the received signal strength, which can also be obtained easily in many ways, can greatly enhance motion estimation. Surprisingly, this strength information has not been well explored so far. Here, we propose a new bearing-strength method to fully exploit both the bearing and strength measurements. Our theoretical analysis shows that the system observability is significantly enhanced in the sense that the lateral motion condition is not required anymore. Real-world experimental results verify the proposed method and the theoretical analysis. It is notable that the benefit of the proposed method comes with no additional cost since it simply utilizes the received strength information that has not been fully exploited in the past.
This letter proposes a novel distributed bearing-based pose estimator for time-varying multi-robot systems. The method uses angles computed from body-frame bearings to estimate the robots' positions in R3 without knowledge of their orientations. The orientations in SO(3) are recovered from the estimated positions, the bearings, and the bearing derivatives. The proposed observer only requires the (directed) sensing topology to be \textit{angle-rigid}, a weaker condition than the commonly used ones like bearing rigidity. Local uniform exponential stability of the proposed observer is established under the assumption of persistently exciting motions for a subset of robots. Simulations are presented and discussed to evaluate the scheme's effectiveness and practicality.
J. Francisco Presenza, Leonardo J. Colombo, Ignacio Mas +1
Sensing ego-velocity estimation is fundamental to state estimation in visually degraded environments, where camera- and LiDAR-based pipelines can become unreliable. Millimetre-wave radar is well suited to these conditions because it provides direct Doppler velocity sensing and remains robust to poor illumination, textureless scenes, and airborne particulates. However, conventional radar ego-velocity pipelines typically apply constant false alarm rate (CFAR) thresholding to convert dense radar spectra into sparse point clouds, prematurely discarding sub-threshold returns that may still retain useful Doppler motion cues. We present Dense Soft Weighting, an analytic radar front-end that maps every range-Doppler cell to a continuous confidence metric rather than enforcing a binary detection threshold. Ego-velocity is then estimated using a deterministic robust weighted least-squares formulation, while the same weighted measurements provide a closed-form, measurement-derived velocity covariance for integration with a shared inertial back-end. The method requires no platform-specific training data or learning-based uncertainty model, supporting transfer across single-chip radar configurations. Across two public datasets and one self-collected dataset, Dense Soft Weighting reduces mean absolute pose error by 31-45% relative to the strongest CFAR point-cloud baseline under an identical inertial back-end, while running in real time on embedded hardware.
Bearing-odometry-based cooperative localization has attracted increasing research interest due to its minimal infrastructure requirements, low communication bandwidth and broad applicability in complex environments. However, existing 6-DoF approaches still face challenges in rapidly obtaining accurate and reliable inter-robot pose estimation, as the system is prone to observability degeneracy under specific motion patterns. To address these issues, we first propose a closed-form 4-DoF inter-robot pose estimator, which relaxes nonlinear constraints for rotations estimation and employs error projection for translations estimation. We then conduct a theoretical analysis of the system's observability, identifying degeneracy under two typical motion patterns: collinear and shape-preserving formations. The analysis further shows that the proposed 4-DoF system requires less stringent motion excitation for observability, enabling reliable estimation under a broader range of cooperative maneuvers. Furthermore, an observability test module is introduced to autonomously determine the optimal estimation instant, eliminating reliance on a predefined fixed-length sliding window. Extensive simulations and real-world experiments demonstrate that the proposed algorithm achieves higher estimation accuracy with significantly low computational cost, and the observability test module ensures estimation reliability while minimizing the data collection interval.