GPS-denied Navigation: Attitude, Position, Linear Velocity, and Gravity Estimation with Nonlinear Stochastic Observer (2104.09920v2)

Abstract: Successful navigation of a rigid-body traveling with six degrees of freedom (6 DoF) requires accurate estimation of attitude , position, and linear velocity. The true navigation dynamics are highly nonlinear and are modeled on the matrix Lie group of SE2(3). This paper presents novel geometric nonlinear continuous stochastic navigation observers on SE2(3) capturing the true nonlinearity of the problem. The proposed observers combines IMU and landmark measurements. It efficiently handles the IMU measurement noise. The proposed observers are guaranteed to be almost semi-globally uniformly ultimately bounded in the mean square. Quaternion representation is provided. A real-world quadrotor measurement dataset is used to validate the effectiveness of the proposed observers in its discrete form. Keywords: Inertial navigation, stochastic system, Brownian motion process, stochastic filter algorithm, stochastic differential equation, Lie group, SE(3), SO(3), pose estimator, position, attitude, feature measurement, inertial measurement unit, IMU.

• The paper introduces a continuous geometric nonlinear stochastic observer that integrates IMU data to estimate vehicle states in GPS-denied environments.
• It employs the matrix Lie group SE₂(3) and quaternion representation to model 6 DoF dynamics and mitigate low-cost sensor noise.
• Experimental validation on a quadrotor dataset demonstrates high estimation accuracy and robust performance under constrained conditions.

Analysis of "GPS-denied Navigation: Attitude, Position, Linear Velocity, and Gravity Estimation with Nonlinear Stochastic Observer"

The paper "GPS-denied Navigation: Attitude, Position, Linear Velocity, and Gravity Estimation with Nonlinear Stochastic Observer," presented by Hashim A. Hashim, introduces a novel approach for achieving navigation in environments where GPS signals are unavailable. The focus is on developing sophisticated nonlinear stochastic observers capable of providing accurate estimations of a vehicle's attitude, position, linear velocity, and gravity, crucial for autonomous navigation systems.

The research explores the true nonlinear dynamics associated with navigation tasks. These dynamics are elegantly modeled using the matrix Lie group $\mathbb{SE}_{2}(3)$, which encapsulates the complex interdependencies between different motion states of a vehicle operating with six degrees of freedom (6 DoF). The methodology leverages integrated measurement data from inertial sensors, specifically IMUs, complemented by additional landmark observations within the vehicle's vicinity.

A significant contribution of this work is the design of continuous geometric nonlinear stochastic observers. These observers are mathematically rigorous and are constructed to integrate IMU data, compensating for noise levels intrinsic to low-cost sensors through stochastic filtering techniques. The observers' design guarantees that estimation errors remain almost semi-globally uniformly ultimately bounded in the mean square, ensuring robust performance even in stochastic environments where the underlying model parameters could be varying.

The experimental validation segment of the paper employs a quadrotor dataset from real-world measurements, which showcases the practicality of these observers. Results from the experiments illustrate the observers' ability to maintain high accuracy in estimate convergence and reliability over extended periods and under conditions with limited sampling rates. The use of quaternion representation complements the matrix formulation, providing additional computational efficiency and facilitating smoother implementation in a discrete form suited for real-time applications.

In terms of theoretical implications, this work extends the applicability of nonlinear stochastic control theories to practical navigation problems, offering a structured approach to tackling the challenges posed by sensor noise and the lack of direct velocity measurements. It also opens avenues for refining stochastic filter algorithms on special Euclidean groups, which can be extended to various robotics and aerospace applications.

Moving forward, this paper lays a foundation for further investigations into enhanced sensor fusion techniques and adaptive algorithms capable of dealing with even more complex noise patterns and dynamic environments. Peer researchers and developers in fields such as robotics, aeronautics, and autonomous systems stand to gain significantly from these insights, particularly in developing resilient navigation systems that function autonomously across GPS-denied settings. The advancement toward low-cost, reliable navigation solutions remains an exciting trajectory underscored by this research's findings.