In this paper we propose a modular nonlinear least squares filtering approach for systems composed of independent subsystems. The state and error covariance estimate of each subsystem is updated independently, even when a relative measurement simultaneously depends on the states of multiple subsystems. We integrate the Covariance Intersection (CI) algorithm as part of our solution in order to prevent double counting of information when subsystems share estimates with each other. An alternative derivation of the CI algorithm based on least squares estimation makes this integration possible. We particularise the proposed approach to the robot-landmark localization problem. In this problem, noisy measurements of the bearing angle to a stationary landmark position measured relative to the SE(2) pose of a moving robot couple the estimation problems for the robot pose and the landmark position. In a randomized simulation study, we benchmark the proposed modular method against a monolithic joint state filter to elucidate their respective trade-offs. In this study we also include variants of the proposed method that achieve a graceful degradation of performance with reduced communication and bandwidth requirements.

We address the problem of sparse selection of visual features for localizing a team of robots navigating an unknown environment, where robots can exchange relative position measurements with neighbors. We select a set of the most informative features by anticipating their importance in robots localization by simulating trajectories of robots over a prediction horizon. Through theoretical proofs, we establish a crucial connection between graph Laplacian and the importance of features. We show that strong network connectivity translates to uniformity in feature importance, which enables uniform random sampling of features and reduces the overall computational complexity. We leverage a scalable randomized algorithm for sparse sums of positive semidefinite matrices to efficiently select the set of the most informative features and significantly improve the probabilistic performance bounds. Finally, we support our findings with extensive simulations.

This article studies the distributed estimation problem of a multi-agent system with bounded absolute and relative range measurements. Parts of the agents are with high-accuracy absolute measurements, which are considered as anchors; the other agents utilize lowaccuracy absolute and relative range measurements, each derives an uncertain range that contains its true state in a distributed manner. Different from previous studies, we design a distributed algorithm to handle the range measurements based on extended constrained zonotopes, which has low computational complexity and high precision. With our proposed algorithm, agents can derive their uncertain range sequentially along the chain topology, such that agents with low-accuracy sensors can benefit from the high-accuracy absolute measurements of anchors and improve the estimation performance. Simulation results corroborate the effectiveness of our proposed algorithm and verify our method can significantly improve the estimation accuracy. Keywords: Set-membership estimation, constrained zonotope, absolute and relative measurements.

In this paper, we focus on the distributed set-membership filtering (SMFing) problem for a multi-agent system with absolute (taken from agents themselves) and relative (taken from neighbors) measurements. In the literature, the relative measurements are difficult to deal with, and the SMFs highly rely on specific set descriptions. As a result, establishing the general distributed SMFing framework having relative measurements is still an open problem. To solve this problem, first, we provide the set description based on uncertain variables determined by the relative measurements between two agents as the foundation. Surprisingly, the accurate description requires only a single calculation step rather than multiple iterations, which can effectively reduce computational complexity. Based on the derived set description, called the uncertain range, we propose two distributed SMFing frameworks: one calculates the joint uncertain range of the agent itself and its neighbors, while the other only computes the marginal uncertain range of each local system. Furthermore, we compare the performance of our proposed two distributed SMFing frameworks and the benchmark -- centralized SMFing framework. A rigorous set analysis reveals that the distributed SMF can be essentially considered as the process of computing the marginal uncertain range to outer bound the projection of the uncertain range obtained by the centralized SMF in the corresponding subspace. Simulation results corroborate the effectiveness of our proposed distributed frameworks and verify our theoretical analysis.

In this article, we focus on the cooperative state estimation problem of a multi-agent system. Each agent is equipped with absolute and relative measurements. The purpose of this research is to make each agent generate its own state estimation with only local measurement information and local communication with neighborhood agents using Set Membership Filter(SMF). To handle this problem, we analyzed centralized SMF framework as a benchmark of distributed SMF and propose a finite-horizon method called OIT-Inspired centralized constrained zonotopic algorithm. Moreover, we put forward a distributed Set Membership Filtering(SMFing) framework and develop a distributed constained zonotopic algorithm. Finally, simulation verified our theoretical results, that our proposed algorithms can effectively estimate the state of each agent.

This paper considers the problem of distributed cooperative localization (CL) via robot-to-robot measurements for a multi-robot system. We propose a distributed consistent CL algorithm. The key idea is to perform the EKF-based state estimation in a transformed coordinate system. Specifically, a coordinate transformation is constructed by decomposing the state-propagation Jacobian by which the correct observability properties are guaranteed. Moreover, the transformed state-propagation Jacobian becomes an identity matrix which is more suitable for distribution. In the proposed algorithm, a server-based framework is adopted to distributely estimate the robot pose in which each robot propagates its pose estimations and the server maintains the correlations. To reduce communication costs, only when the multi-robot system takes a robot-to-robot relative measurement, the robots and the server exchange information to update the pose estimations and the correlations. In addition, no assumptions are made about the type of robots or relative measurements. The proposed algorithm has been validated by experiments and shown to outperform the state-of-art algorithms in terms of consistency and accuracy.

Human vision is often guided by instinctual commonsense such as proportions and contours. In this paper, we explore how to use the proportion as the key knowledge for designing a privacy algorithm that detects human private parts in a 3D scan dataset. The Analogia Graph is introduced to study the proportion of structures. It is a graph-based representation of the proportion knowledge. The intrinsic human proportions are applied to reduce the search space by an order of magnitude. A feature shape template is constructed to match the model data points using Radial Basis Functions in a non-linear regression and the relative measurements of the height and area factors. The method is tested on 100 datasets from CAESAR database. Two surface rendering methods are studied for data privacy: blurring and transparency. It is found that test subjects normally prefer to have the most possible privacy in both rendering methods. However, the subjects adjusted their privacy measurement to a certain degree as they were informed the context of security.