Abstract--Achieving reliable ego motion estimation for agile robots, e.g., aerobatic aircraft, remains challenging because most robot sensors fail to respond timely and clearly to highly dynamic robot motions, often resulting in measurement blurring, distortion, and delays. In this paper, we propose an IMU-free and feature-association-free framework to achieve aggressive ego-motion velocity estimation of a robot platform in highly dynamic scenarios by combining two types of exteroceptive sensors, an event camera and a millimeter wave radar, First, we used instantaneous raw events and Doppler measurements to derive rotational and translational velocities directly. Without a sophisticated association process between measurement frames, the proposed method is more robust in texture-less and structureless environments and is more computationally efficient for edge computing devices. Then, in the back-end, we propose a continuous-time state-space model to fuse the hybrid time-based and event-based measurements to estimate the ego-motion velocity in a fixed-lagged smoother fashion. In the end, we validate our velometer framework extensively in self-collected experiment datasets featured by aggressive motion and HDR light conditions. The results indicate that our IMU-free and association-free ego motion estimation framework can achieve reliable and efficient velocity output in challenging environments. Reliable ego-motion estimation is fundamental to autonomous robotic platforms. Early solutions rely on GNSS/INS, while more recent SLAM-based methods integrate diverse sensors such as cameras, LiDARs, and radars, making them more adaptable and widely applicable.

Reliable GNSS positioning in complex environments remains a critical challenge due to non-line-of-sight (NLOS) propagation, multipath effects, and frequent signal blockages. These effects can easily introduce large outliers into the raw pseudo-range measurements, which significantly degrade the performance of global navigation satellite system (GNSS) real-time kinematic (RTK) positioning and limit the effectiveness of tightly coupled GNSS-based integrated navigation system. To address this issue, we propose a two-stage outlier detection method and apply the method in a tightly coupled GNSS-RTK, inertial navigation system (INS), and odometer integration based on factor graph optimization (FGO). In the first stage, Doppler measurements are employed to detect pseudo-range outliers in a GNSS-only manner, since Doppler is less sensitive to multipath and NLOS effects compared with pseudo-range, making it a more stable reference for detecting sudden inconsistencies. In the second stage, pre-integrated inertial measurement units (IMU) and odometer constraints are used to generate predicted double-difference pseudo-range measurements, which enable a more refined identification and rejection of remaining outliers. By combining these two complementary stages, the system achieves improved robustness against both gross pseudo-range errors and degraded satellite measuring quality. The experimental results demonstrate that the two-stage detection framework significantly reduces the impact of pseudo-range outliers, and leads to improved positioning accuracy and consistency compared with representative baseline approaches. In the deep urban canyon test, the outlier mitigation method has limits the RMSE of GNSS-RTK/INS/odometer fusion from 0.52 m to 0.30 m, with 42.3% improvement.

To provide backup and augmentation to global navigation satellite system (GNSS), Doppler shift from Low Earth Orbit (LEO) satellites can be employed as signals of opportunity (SOP) for position, navigation and timing (PNT). Since the Doppler positioning problem is non-convex, local searching methods may produce two types of estimates: a global optimum without notice or a local optimum given an inexact initial estimate. As exact initialization is unavailable in some unknown environments, a guaranteed global optimization method in no need of initialization becomes necessary. To achieve this goal, we propose a certifiably optimal LEO Doppler positioning method by utilizing convex optimization. In this paper, the certifiable positioning method is implemented through a graduated weight approximation (GWA) algorithm and semidefinite programming (SDP) relaxation. To guarantee the optimality, we derive the necessary conditions for optimality in ideal noiseless cases and sufficient noise bounds conditions in noisy cases. Simulation and real tests are conducted to evaluate the effectiveness and robustness of the proposed method. Specially, the real test using Iridium-NEXT satellites shows that the proposed method estimates an certifiably optimal solution with an 3D positioning error of 140 m without initial estimates while Gauss-Newton and Dog-Leg are trapped in local optima when the initial point is equal or larger than 1000 km away from the ground truth. Moreover, the certifiable estimation can also be used as initialization in local searching methods to lower down the 3D positioning error to 130 m.

Recently, gravity has been highlighted as a crucial constraint for state estimation to alleviate potential vertical drift. Existing online gravity estimation methods rely on pose estimation combined with IMU measurements, which is considered best practice when direct velocity measurements are unavailable. However, with radar sensors providing direct velocity data-a measurement not yet utilized for gravity estimation-we found a significant opportunity to improve gravity estimation accuracy substantially. GaRLIO, the proposed gravity-enhanced Radar-LiDAR-Inertial Odometry, can robustly predict gravity to reduce vertical drift while simultaneously enhancing state estimation performance using pointwise velocity measurements. Furthermore, GaRLIO ensures robustness in dynamic environments by utilizing radar to remove dynamic objects from LiDAR point clouds. Our method is validated through experiments in various environments prone to vertical drift, demonstrating superior performance compared to traditional LiDAR-Inertial Odometry methods. We make our source code publicly available to encourage further research and development. https://github.com/ChiyunNoh/GaRLIO

Spinning, frequency-modulated continuous-wave (FMCW) radars with 360 degree coverage have been gaining popularity for autonomous-vehicle navigation. However, unlike 'fixed' automotive radar, commercially available spinning radar systems typically do not produce radial velocities due to the lack of repeated measurements in the same direction and the fundamental hardware setup. To make these radial velocities observable, we modified the firmware of a commercial spinning radar to use triangular frequency modulation. In this paper, we develop a novel way to use this modulation to extract radial Doppler velocity measurements from single raw radar intensity scans without any required data association. We show that these noisy, error-prone measurements contain enough information to provide good ego-velocity estimates, and incorporate these estimates into different modern odometry pipelines. We extensively evaluate the pipelines on over 110 km of driving data in progressively more geometrically challenging autonomous-driving environments. We show that Doppler velocity measurements improve odometry in well-defined geometric conditions and enable it to continue functioning even in severely geometrically degenerate environments, such as long tunnels.

We present a sensor misalignment-tolerant AUV navigation method that leverages measurements from an acoustic array and dead reckoned information. Recent studies have demonstrated the potential use of passive acoustic Direction of Arrival (DoA) measurements for AUV navigation without requiring ranging measurements. However, the sensor misalignment between the acoustic array and the attitude sensor was not accounted for. Such misalignment may deteriorate the navigation accuracy. This paper proposes a novel approach that allows simultaneous AUV navigation, beacon localization, and sensor alignment. An Unscented Kalman Filter (UKF) that enables the necessary calculations to be completed at an affordable computational load is developed. A Nonlinear Least Squares (NLS)-based technique is employed to find an initial solution for beacon localization and sensor alignment as early as possible using a short-term window of measurements. Experimental results demonstrate the performance of the proposed method.

In this paper, we present a fast, lightweight odometry method that uses the Doppler velocity measurements from a Frequency-Modulated Continuous-Wave (FMCW) lidar without data association. FMCW lidar is a recently emerging technology that enables per-return relative radial velocity measurements via the Doppler effect. Since the Doppler measurement model is linear with respect to the 6-degrees-of-freedom (DOF) vehicle velocity, we can formulate a linear continuous-time estimation problem for the velocity and numerically integrate for the 6-DOF pose estimate afterward. The caveat is that angular velocity is not observable with a single FMCW lidar. We address this limitation by also incorporating the angular velocity measurements from a gyroscope. This results in an extremely efficient odometry method that processes lidar frames at an average wall-clock time of 5.64ms on a single thread, well below the 10Hz operating rate of the lidar we tested. We show experimental results on real-world driving sequences and compare against state-of-the-art Iterative Closest Point (ICP)-based odometry methods, presenting a compelling trade-off between accuracy and computation. We also present an algebraic observability study, where we demonstrate in theory that the Doppler measurements from multiple FMCW lidars are capable of observing all 6 degrees of freedom (translational and angular velocity).