Daniel Viegas

Distributed state estimation for linear multi-agent systems with time-varying measurement topology

This paper addresses the problem of distributed state estimation in formations of vehicles with time-varying measurement topology. One or more vehicles have access to measurements of their own state, while the rest must rely on measurements relative to other vehicles in the vicinity and limited communication to estimate their own state, and it is assumed that the vehicles may gain or lose access to some measurements over time. The proposed solution consists in the implementation of a local state observer on-board each vehicle, and the effects of changes in the measurement topology on the estimation error dynamics are studied resorting to switched systems theory. Sufficient conditions for exponential stability of the global estimation error dynamics are presented for two different switching laws. The results are applied to the practical case of a formation of Autonomous Underwater Vehicles (AUVs), and simulation results are presented that validate the proposed solution.

Decentralized H2 observers for position and velocity estimation in vehicle formations with fixed topologies

Abstract This paper addresses the problem of decentralized state estimation in fixed topology formations of vehicles with applications to Autonomous Underwater Vehicles (AUVs). In the envisioned scenario, each vehicle in the formation estimates its own state relying only on locally available measurements and data communicated by neighboring agents, requiring lower computational and communication loads than centralized solutions. A method for designing local state observers featuring global error dynamics that converge globally asymptotically to zero is detailed, and an algorithm for improving its performance under stochastic disturbances and Gaussian uncertainties is presented. The proposed algorithm minimizes the H 2 norm of the global estimation error dynamics, expressed as an optimization problem subject to Bilinear Matrix Inequality (BMI) constraints. To assess the performance of the solution, realistic simulation results are presented and discussed for several formation topologies.

Position and Velocity Filters for ASC/I-AUV Tandems Based on Single Range Measurements

This paper proposes novel cooperative navigation solutions for an Intervention Autonomous Underwater Vehicle (I-AUV) working in tandem with an Autonomous Surface Craft (ASC). The I-AUV is assumed to be moving in the presence of constant unknown ocean currents, and aims to estimate its position relying on measurements of its range to the ASC. Two different scenarios are considered: in the first scenario, the ASC transmits its position and velocity to the I-AUV, and the I-AUV has access to readings of its velocity relative to the water. In the second scenario, the ASC transmits only its position, and the I-AUV has access to measurements of its velocity relative to the ASC. In both cases, it is assumed that an Attitude and Heading Reference System (AHRS) mounted on-board the I-AUV provides measurements of its attitude and angular velocity. A sufficient condition for observability and a method for designing state observers with Globally Asymptotically Stable (GAS) error dynamics are presented for both problems. Finally, simulation results are included and discussed to assess the performance of the proposed solutions in the presence of measurement noise.

Decentralized range-based linear motion estimation in acyclic vehicle formations with fixed topologies

The problem of decentralized state estimation in formations of autonomous vehicles is addressed in this paper. A reduced number of agents in the formation have access to absolute position measurements, while the rest must rely on range measurements to neighboring agents and local sensing and communication capabilities to estimate their own position and velocity. A method for designing local state estimators for each of the agents is presented such that the resulting decentralized state estimator features globally exponentially stable error dynamics when the graph associated with the formation is acyclic. Realistic simulation results are presented and discussed to assess the performance of the proposed solution under the influence of measurement noise.

Linear motion observers for ASC/AUV tandems based on single range readings

This paper proposes novel cooperative navigation strategies for an Intervention Autonomous Underwater Vehicle (I-AUV) working in tandem with an Autonomous Surface Craft (ASC). The proposed solutions rely on single range readings and two different scenarios are considered: in the first, the I-AUV is assumed to be moving in the presence of unknown constant ocean currents and the ASC transmits its inertial position and velocity, while the I-AUV measures its velocity relative to the water; in the second case, the ASC transmits its inertial position and the I-AUV is assumed to measure its velocity relative to the ASC. Necessary and sufficient observability conditions are derived for both problems and globally asymptotically stable (GAS) filters are developed. Although inspired in marine robotics, the proposed methods apply to other mobile platforms as they are based on the general motion kinematics in 3-D. Finally, to assess the performance of the proposed solutions, realistic simulation results are presented and discussed.

GAS decentralized navigation filters in a continuous-discrete fixed topology framework

This paper addresses the problem of state estimation in formations of autonomous vehicles. The approach considered here consists in the implementation of a local state observer in each vehicle relying only on locally available measurements and data communicated by neighboring agents, resulting in a decentralized state observer which features lower computational and communication loads than comparable centralized solutions. A method for computing observer gains which yield globally asymptotically stable error dynamics is presented for fixed topology formations, as well as an iterative algorithm for improving the decentralized estimators performance when the measurements are corrupted by noise. The proposed framework is particularized to the practical case of a formation of Autonomous Underwater Vehicles (AUVs), and a continuous-discrete formulation is achieved for the local state observers, to take into account the difference in sampling rates between on-board instrumentation and positioning systems. To assess the performance of the solution, simulation results are presented and discussed for different formation topologies.

Position and velocity filters for intervention AUVs based on single range and depth measurements

This paper proposes novel cooperative navigation solutions for an Intervention Autonomous Underwater Vehicle (I-AUV) working in tandem with an Autonomous Surface Craft (ASC). The I-AUV is assumed to be moving in the presence of constant unknown ocean currents, and aims to estimate its position relying on measurements of its range to the ASC and of its depth relatively to the sea level. Two different scenarios are considered: in one, the ASC transmits its position and velocity to the I-AUV, while in the other the ASC transmits only its position, and the I-AUV has access to measurements of its velocity relative to the ASC. A sufficient condition for observability and a method for designing state observers with Globally Asymptotically Stable (GAS) error dynamics are presented for both problems. Finally, simulation results are included and discussed to assess the performance of the proposed solutions in the presence of measurement noise.

Discrete-time distributed Kalman filter design for multi-vehicle systems

This paper addresses the problem of distributed state estimation in a multi-vehicle framework. In the scenario envisioned in this work, each vehicle aims to estimate its own state by implementing a local state observer which relies on locally available measurements and limited communication with other vehicles in the vicinity. The dynamics of the problem are formulated as a more general discrete-time Kalman filtering problem with a sparsity constraint on the gain and, based on this formulation, a method for computation of steady-state observer gains for arbitrary fixed measurement topologies is introduced. The proposed method consists in the optimization of the time-varying distributed Kalman filter over a finite time window to approximate steady-state behavior and compute well-performing steady-state observer gains. To assess the performance of the proposed solution, simulation results are detailed for the practical case of a formation of Autonomous Underwater Vehicles (AUVs).

On the stability of the continuous-time Kalman filter subject to exponentially decaying perturbations

Abstract This paper details the stability analysis of the continuous-time Kalman filter dynamics for linear time-varying systems subject to exponentially decaying perturbations. It is assumed that estimates of the input, output, and matrices of the system are available, but subject to unknown perturbations which decay exponentially with time. It is shown that if the nominal system is uniformly completely observable and uniformly completely controllable, and if the state, input, and matrices of the system are bounded, then the Kalman filter built using the perturbed estimates is a suitable state observer for the nominal system, featuring exponentially convergent error dynamics.

Nonlinear observability and observer design through state augmentation

This paper addresses the problems of observability analysis and state observer design for nonlinear systems based on the study of linear systems which mimic their dynamics. It is shown that, if a nonlinear system can be related to a linear system through an appropriate transformation of the state variables, the observability analysis of the linear system can determine observability or non-observability of the nonlinear system, depending on the properties of the state transformation function. Conditions are also derived for state observers for the linear systems to double as state observers for the original nonlinear systems, as well as retaining exponential stability properties. To illustrate the usefulness of those results, several application examples are detailed.