Consistent localization of cooperative multi-robot systems during navigation presents substantial challenges. This paper proposes a fault-tolerant, multi-modal localization framework for multi-robot systems on matrix Lie groups. We introduce novel stochastic operations to perform composition, differencing, inversion, averaging, and fusion of correlated and non-correlated estimates on Lie groups, enabling pseudo-pose construction for filter updates. The method integrates a combination of proprioceptive and exteroceptive measurements from inertial, velocity, and pose (pseudo-pose) sensors on each robot in an Extended Kalman Filter (EKF) framework. The prediction step is conducted on the Lie group$\mathbb {SE}_{2}(3) \times \mathbb {R}^{3} \times \mathbb {R}^{3}$, where each robot's pose, velocity, and inertial measurement biases are propagated. The proposed framework uses body velocity, relative pose measurements from fiducial markers, and inter-robot communication to provide scalable EKF update across the network on the Lie group$\mathbb {SE}(3) \times \mathbb {R}^{3}$. A fault detection module is implemented, allowing the integration of only reliable pseudo-pose measurements from fiducial markers. We demonstrate the effectiveness of the method through experiments with a network of wheeled mobile robots equipped with inertial measurement units, wheel odometry, and ArUco markers. The comparison results highlight the proposed method's real-time performance, superior efficiency, reliability, and scalability in multi-robot localization, making it well-suited for large-scale robotic systems.

This work, based on the standard unscented Kalman filter (UKF), proposes a modified UKF for highly non‐linear stochastic systems, assuming that the associated probability distributions are normal. In the standard UKF with 2 n + 1 sample points, the estimated mean and covariance match the true mean and covariance up to the third order, besides, there exists a scaling parameter that plays a crucial role in minimising the fourth‐order errors. The proposed method consists of a computationally efficient formulation of the unscented transform that incorporates , , constant parameters to scale sample points such that the order errors are minimised. The scaling parameters are obtained by solving a set of algebraic equations. Through rigorous analytical processes and numerical simulations, it is demonstrated that the new filter provides consistent estimates and the estimation error of the modified UKF is smaller than that of the standard UKF. With the help of a well‐studied case, univariate non‐stationary growth model, the authors evaluate the estimation performance of the new technique using 4 n + 1 sample points over 100 independent runs.

This study deals with the problem of track‐to‐track fusion in a sensor network when the correlation terms between the estimates of the agents are unknown. The proposed method offers an upper bound for the optimal minimum variance fusion rule through construction of the correlation terms according to an optimisation scheme. In general, the upper bound filter provides an estimate that is more conservative than the optimal estimate generated by the minimum variance fusion rule, while at the same time is less conservative than one obtained by the widely used covariance intersection method. From the geometrical viewpoint, the upper bound filter results in the inscribed largest volume ellipsoid within the intersection region defined by the ellipsoids corresponding to the fused estimates while the covariance intersection leads to the external minimum volume ellipsoid over the intersection region. The authors demonstrate the superiority of the proposed method through analysing estimation error and consistency of the fusion filter over Monte‐Carlo simulations for a multi‐dimensional system.