Pedro Tiago Martins Batista

Single range aided navigation and source localization: Observability and filter design

This paper addresses the problems of navigation and source localization by mobile agents based on the range to a single source, in addition to relative velocity readings. The contribution of the paper is two-fold: (i) necessary and sufficient conditions on the observability of the nonlinear system are derived, which are useful for trajectory planning and motion control of the agent; and (ii) a nonlinear system, which given the input and output of the system is regarded as linear time-varying, is proposed and a Kalman filter is applied to successfully estimate the system state. Simulation results are presented in the presence of realistic measurement noise that illustrate the performance achieved with the proposed solution.

Sensor-Based Globally Asymptotically Stable Filters for Attitude Estimation: Analysis, Design, and Performance Evaluation

This technical note presents the design, analysis, and performance evaluation of a novel globally asymptotically stable (GAS) filter for attitude estimation. The design is sensor-driven and departs from traditional solutions as no explicit representations of the attitude are considered. The proposed solution yields unique estimates and it does not suffer from drawbacks such as singularities, topological limitations for achieving global stabilization, or unwinding phenomena. The performance of the overall attitude estimation solution is evaluated with the design and implementation of an Attitude and Heading Reference System (AHRS) based on a single low-cost Inertial Measurement Unit. The performance of the proposed AHRS is assessed experimentally using a high precision motion rate table, which provides ground truth signals for comparison with the resulting estimates.

Accelerometer Calibration and Dynamic Bias and Gravity Estimation: Analysis, Design, and Experimental Evaluation

Tri-axial linear accelerometers are key components in a great variety of applications and, in particular, in navigation systems. Nonidealities such as scale factors, cross coupling, bias, and other higher-order nonlinearities affect the output of this sensor, leading, in general, to prohibitive errors. On the other hand, these coefficients are often slowly time-varying, which renders offline calibration less effective. One such coefficient that usually varies greatly over time and between power-ons is the bias. This paper details the calibration of an accelerometer unit and presents also a dynamic filtering solution for the bias, which also includes the estimation of the gravity in body-fixed coordinates. Simulation and experimental results obtained with a motion rate table are presented and discussed to illustrate the performance of the proposed algorithms.

On the observability of linear motion quantities in navigation systems

Abstract Navigation systems are a key element in a large variety of mobile platforms, where the correct knowledge of their position and attitude is essential in most applications. This paper focuses on the observability of linear motion quantities (position, linear velocity, linear acceleration, and accelerometer bias). It presents necessary and sufficient conditions, with a clear physical insight, for the observability of these variables in 3-D. The analysis provided is based on kinematic models, which are exact and intrinsic to the motion of a rigid-body, and different cases are presented depending on the assumptions made on the sensor suite that is available on-board.

Discrete-Time Complementary Filters for Attitude and Position Estimation: Design, Analysis and Experimental Validation

This paper develops a navigation system based on complementary filtering for position and attitude estimation, with application to autonomous surface crafts. Using strapdown inertial measurements, vector observations, and global positioning system (GPS) aiding, the proposed complementary filters provide attitude estimates in Euler angles representation and position estimates in Earth frame coordinates, while compensating for rate gyro bias. Stability and performance properties of the proposed filters under operating conditions usually found in oceanic applications are derived, and the tuning of the filter parameters in the frequency domain is emphasized. The small computational requirements of the proposed navigation system make it suitable for implementation on low-power hardware and using low-cost sensors, providing a simple yet effective multirate architecture suitable to be used in applications with autonomous vehicles. Experimental results obtained in real time with an implementation of the proposed algorithm running on-board the DELFIMx catamaran, an autonomous surface craft developed at ISR/IST for automatic marine data acquisition, are presented and discussed.

Position USBL/DVL sensor-based navigation filter in the presence of unknown ocean currents

This paper presents a novel approach to the design of globally asymptotically stable (GAS) position and velocity filters for Autonomous Underwater Vehicles (AUVs) based directly on the sensor readings of an Ultra-short Baseline (USBL) acoustic array system and a Doppler Velocity Log (DVL). The proposed methodology is based on an equivalent linear time-varying (LTV) system that fully captures the dynamics of the nonlinear system, allowing for the use of powerful linear system analysis and filtering design tools that yield GAS filter error dynamics. Numerical results using Monte Carlo simulations and comparison to the Bayesian Cramer Rao Bound (BCRB) reveal that the performance of the proposed filter is tight to this theoretical estimation error lower bound. In comparison with other approaches, the present solution achieves the same level of performance of the Extended Kalman Filter (EKF), which does not offer GAS guarantees, and outperforms other classical filtering approaches designed in inertial coordinates instead of the body-fixed coordinate frame.

Brief paper: A GES attitude observer with single vector observations

This paper proposes a globally exponentially stable (GES) observer for attitude estimation based on a single time-varying reference vector, in inertial coordinates, and corresponding vector, in body-fixed coordinates, in addition to angular velocity readings. The proposed solution is computationally efficient and, in spite of the fact that the observer does not evolve on the Special Orthogonal Group SO(3), an explicit solution on SO(3) is also provided, whose error is shown to converge exponentially fast to zero for all initial conditions. The distinct roles of the inertial and the corresponding body-fixed vectors on the observability of the system are also examined and simulation results are shown that illustrate the performance of the proposed attitude observer in the presence of low-grade sensor specifications.

Globally Asymptotically Stable Sensor-Based Simultaneous Localization and Mapping

This paper presents the design, analysis, and experimental validation of a globally asymptotically stable (GAS) filter for simultaneous localization and mapping (SLAM), with application to unmanned aerial vehicles. The SLAM problem is formulated in a sensor-based framework and modified in such a way that the underlying system structure can be regarded as linear time varying for observability analysis and filter design purposes, from which a linear Kalman filter with GAS error dynamics follows naturally. The performance and consistency validation of the proposed sensor-based SLAM filter are successfully assessed with real data, acquired indoors, using an instrumented quadrotor.

A Sensor-Based Controller for Homing of Underactuated AUVs

A new sensor-based homing integrated guidance and control law is presented to drive an underactuated autonomous underwater vehicle (AUV) toward a fixed target, in three dimensions, using the information provided by an ultrashort baseline (USBL) positioning system. The guidance and control law is first derived using quaternions to express the vehicles attitude kinematics, which are directly obtained from the time differences of arrival (TDOA) measured by the USBL sensor. The dynamics are then included resorting to backstepping techniques. The proposed Lyapunov-based control law yields global asymptotic stability in the absence of external disturbances and is further extended, keeping the same properties, to the case where constant known ocean currents affect the dynamics of the vehicle. Finally, a globally exponentially stable nonlinear TDOA and range-based observer is introduced to estimate the ocean current and uniform asymptotic stability is obtained for the overall closed-loop system. Simulations are presented illustrating the performance of the proposed solutions.

Sensor-based complementary globally asymptotically stable filters for attitude estimation

This paper presents the design, analysis, and performance evaluation of a new class of globally asymptotically stable filters for attitude estimation. The design is based directly on the sensor measurements as opposed to traditional solutions that resort to parameterizations of the attitude, e.g., Euler angles, quaternions, or rotation matrices, and therefore it does not have problems such as singularities, unwinding phenomena, or topological limitations for achieving global asymptotic stability. The proposed solution includes the estimation of gyros biases, incomplete sensor measurements, systematic tuning procedures, and also allows for the inclusion of frequency weights to model colored noise on the different sensing devices. Finally, and due to the inherent structure, the filters are complementary. Simulation results are included that illustrate the achievable performance in the presence of realistic measurements provided by a low-cost, low-power sensor suite.