Noisy Position Measurements Research Articles

Polynomial Regression on Lie Groups and Application to SE(3).

In this paper, we address the problem of estimating the position of a mobile such as a drone from noisy position measurements using the framework of Lie groups. To model the motion of a rigid body, the relevant Lie group happens to be the Special Euclidean group SE(n), with n=2 or 3. Our work was carried out using a previously used parametric framework which derived equations for geodesic regression and polynomial regression on Riemannian manifolds. Based on this approach, our goal was to implement this technique in the Lie group SE(3) context. Given a set of noisy points in SE(3) representing measurements on the trajectory of a mobile, one wants to find the geodesic that best fits those points in a Riemannian least squares sense. Finally, applications to simulated data are proposed to illustrate this work. The limitations of such a method and future perspectives are discussed.

Event-Triggered Adaptive Fuzzy Setpoint Regulation of Surface Vessels With Unmeasured Velocities Under Thruster Saturation Constraints

This article investigates the event-triggered adaptive fuzzy output feedback setpoint regulation control for the surface vessels. The vessel velocities are noisy and small in the setpoint regulation operation and the thrusters have saturation constraints. A high-gain filter is constructed to obtain the vessel velocity estimations from noisy position and heading. An auxiliary dynamic filter with control deviation as the input is adopted to reduce thruster saturation effects. The adaptive fuzzy logic systems approximate vessel’s uncertain dynamics. The adaptive dynamic surface control is employed to derive the event-triggered adaptive fuzzy setpoint regulation control depending only on noisy position and heading measurements. By the virtue of the event-triggering, the vessel’s thruster acting frequencies are reduced such that the thruster excessive wear is avoided. The computational burden is reduced due to the differentiation avoidance for virtual stabilizing functions required in the traditional backstepping. It is analyzed that the event-triggered adaptive fuzzy setpoint regulation control maintains position and heading at desired points and ensures the closed-loop semi-global stability. Both theoretical analyses and simulations with comparisons validate the effectiveness and the superiority of the control scheme.

Dynamic model identification for CNC machine tool feed drives from in-process signals for virtual process planning

Virtual process planning offers advantages in terms of predicting servo and contouring errors ahead of time, and taking corrective action by modifying the program or CNC parameters. Successful application of virtual process planning requires accurate models that capture the dynamics of feed drives. Identification of such models is typically time consuming.This paper presents a pole search method used in conjunction with least squares (LS) projection technique for identifying virtual machine tool drives. Compared to earlier research published in rapid identification, and the generic system identification method (i.e., a two-stage instrumental variable method), the parameter convergence has been improved significantly. This is achieved by reducing the number of unknown variables solved during LS estimation from eight to four (corresponding to each candidate pole triplet), and by avoiding the use of noisy position measurements and their time derivatives in the LS matrix pseudo-inversion. As a result, virtual feed drive models can be constructed using only in-process gathered data, without interrupting a machine tool's production for dedicated identification tests. Effectiveness of the new method is demonstrated in simulations and experimental case studies on two different machine tools, a gear grinding machine, and a 5-axis machining center. With the new method, servo errors can be predicted during the process planning stage to within 1-2% of closeness of their actual (experimental) values.

Discrete-time sliding mode observer for the state estimation of a manoeuvring target

This article addresses the problem of estimating the position, velocity, and acceleration of a manoeuvring target from noisy position measurements. A discrete-time sliding mode observer is designed to handle unmeasured disturbance input and measurement noise. A first-order linear dynamics is considered for target acceleration. The acceleration input command and the pole of the first-order acceleration dynamics are considered to be unknown parameters with known upper bounds. A finite non-zero boundary layer is employed to reduce the chattering phenomenon typically associated with sliding mode observers. Analysis of estimation error dynamics is presented for the case where the discrete-time sliding mode observer is operating outside the boundary layer and also within the boundary layer. An algorithm is developed for obtaining the observer gain vector that guarantees the stability of the error dynamics. Numerical simulations and experimental results are presented to validate the stability and performance of the proposed observer.

Coverage Control for Heterogeneous Mobile Sensor Networks Subject to Measurement Errors

The coverage control problem of a circle by a mobile sensor network affected by bounded measurement errors is addressed in this paper. The mobile sensors are assumed to have different maximum velocities. Our main objective is to study the effect of measurement errors on the coverage cost function, which is defined as the largest time for the sensor network to arrive at any point on the circle. Coverage control laws with input constraints are developed based on the noisy position measurements among sensors, under which the mobile sensor network converges to a neighborhood of the optimal configuration. Furthermore, the conditions for the sensors to preserve their spatial order on the circle are derived in order to avoid collision among sensors. An upper bound on the limit of the coverage cost function as time goes to infinity is also given.

A Load Transportation Nonlinear Control Strategy Using a Tilt-Rotor UAV

This paper proposes a nonlinear control strategy to solve the trajectory tracking problem of a tilt-rotor Unmanned Aerial Vehicle (UAV) when transporting a suspended load. For the present study, the aim of the control system is to track a desired trajectory of the aircraft with load’s swing-free, even in the presence of external disturbances, parametric uncertainties, unmodeled dynamics, and noisy position measurements with lower sampling frequency than the controller. The whole system modeling is obtained through the Euler-Lagrange formulation considering the dynamics of the tilt-rotor UAV coupled to the suspended load. As for the nonlinear control strategy, an inner-loop control is designed based on input-output feedback linearization combined with the dynamic extension approach to stabilize the attitude and altitude of the UAV assuming nonlinearities, while an outer-loop control law is designed for guiding the aircraft with reduced load swing. The linearized dynamics are controlled using linear mixed H2/H∞ controllers with pole placement constraints. The solution is compared to two simpler control systems: the first one considers the load as a disturbance to the system but does not avoid its swing; the second one is a previous academic result with a three-level cascade strategy. Finally, in order to deal with the problem of position estimation in presence of unknown disturbances and noisy measurements with low sampling frequency, a Linear Kalman Filter with Unknown Inputs is designed for estimating both the aircraft’s translational position and translational disturbances. Simulation results are carried out to corroborate the proposed control strategy.

An Integrated Likelihood Formulation for Characterizing the Proximity of Position Measurements to Road Segments

The analysis of spatial proximity between objects can yield useful insights for a variety of problems. A common application is found in map matching problems, where noisy position measurements collected from a receiver on a network-bound mobile object is analyzed for estimating the original road segments traversed by the object. Motivated by this problem, we take a detailed look at proximity measures that quantify the spatial closeness between points and curves in non-deterministic problems, where the given points are noisy observations of a stochastic process defined on a given set of curves. Starting with a critical review of traditional pointwise approaches, we introduce the integral proximity measure for quantifying proximity, so as to better represent the statistical likelihoods of a process’ states. Assuming a generic stochastic model with additive noise, we discuss the correct proximity function for the proximity measures, and the relationship between a posteriori probabilities of the process and the proximity measures for a comparison of both measures. Later, we prove that the proposed measure can provide better inferences about the process’ states, when the process is under the influence of uncorrelated bivariate Gaussian noise. Finally, we conduct an extensive Monte Carlo analysis, which shows significant inference improvements over traditional proximity measures, particularly under high noise levels and dense road settings.

Robust adaptive gain higher order sliding mode observer based control-constrained nonlinear model predictive control for spacecraft formation flying

This work deals with the development of a decentralized optimal control algorithm, along with a robust observer, for the relative motion control of spacecraft in leader-follower based formation. An adaptive gain higher order sliding mode observer has been proposed to estimate the velocity as well as unmeasured disturbances from the noisy position measurements. A differentiator structure containing the Lipschitz constant and Lebesgue measurable control input, is utilized for obtaining the estimates. Adaptive tuning algorithms are derived based on Lyapunov stability theory, for updating the observer gains, which will give enough flexibility in the choice of initial estimates. Moreover, it may help to cope with unexpected state jerks. The trajectory tracking problem is formulated as a finite horizon optimal control problem, which is solved online. The control constraints are incorporated by using a nonquadratic performance functional. An adaptive update law has been derived for tuning the step size in the optimization algorithm, which may help to improve the convergence speed. Moreover, it is an attractive alternative to the heuristic choice of step size for diverse operating conditions. The disturbance as well as state estimates from the higher order sliding mode observer are utilized by the plant output prediction model, which will improve the overall performance of the controller. The nonlinear dynamics defined in leader fixed Euler-Hill frame has been considered for the present work and the reference trajectories are generated using Hill-Clohessy-Wiltshire equations of unperturbed motion. The simulation results based on rigorous perturbation analysis are presented to confirm the robustness of the proposed approach.

Hybrid Observer Combining Measurements of Different Fidelities

Abstract: A signal-based hybrid observer combining measurements of different fidelities is proposed for position and velocity estimation of marine vessels. The concept assumes that noisy position measurements are available only sporadically at a non-constant sampling rate. Predictions of position between the samples are provided by integrating acceleration measurements, which are available at a high rate (approximated to be continuous sampling). Estimates with smaller variance are computed by averaging multiple observer copies of the position. This work is a continuation of the observer proposed in Brodtkorb et al. (2015). The main contributions of this paper is extending the observer to the more realistic scenario where linear velocity and angular acceleration measurements are not available. A simulation study showed that the observer performed well in closed loop with a controller conducting dynamic positioning operations of a marine vessel.

Navigating with highly precise odometry and noisy GPS: a case study

Abstract: For linear systems, the Kalman filter perfectly handles rank deficiencies in the process noise covariance matrix, i.e., deterministic information. Yet, in a nonlinear setting this poses great challenges to the extended Kalman filter (EKF). In this paper we consider a simplified nonlinear car model with deterministic dynamics, i.e., perfect odometry, and noisy position measurements. Simulations evidence the EKF, when used as a nonlinear observer, 1- fails to correctly encode the physical implications of the deterministic dynamics 2- fails to converge even for arbitrarily small initial estimation errors. On the other hand, the invariant (I)EKF, a variant of the EKF that accounts for the symmetries of the problem 1- correctly encodes the physical implications of the deterministic information 2-is mathematically proved to (almost) globally converge, with explicit convergence rates, whereas the EKF does not even locally converge in our simulations. This study more generally suggests the IEKF is way more natural than the EKF, for high precision navigation purposes.

Global adaptive estimation of joint velocities in robotic manipulators

This study presents a method for global estimation of joint velocities in robotic manipulators. The authors consider a non-minimal model of a robotic manipulator and design an adaptive observer capable of handling uncertainties in robot dynamics. Smoothness of the dynamics of the proposed observer allows its easy implementation in comparison with non-smooth observers. Dimension of the proposed observer is shown to be at least 3n where n stands for the manipulator's degrees of freedom. This number is less than the dimension of most existing globally convergent adaptive observers. Global asymptotic convergence of state estimates to their true values is achieved under no persistency of excitation condition. Furthermore, under noisy position and force measurements, the proposed observer guarantees ultimate boundedness of estimation errors. Simulation results illustrate low noise sensitivity of the proposed observer in comparison with non-smooth observers.

Real-Time Target Tracking for Autonomous UAVs in Adversarial Environments: A Gradient Search Algorithm

This paper presents a rule-based intelligent guidance strategy for autonomous pursuit of mobile targets by unmanned aerial vehicles (UAVs) in an area with threats, obstacles, and restricted regions. The probabilistic threat exposure map (PTEM) is used as the mathematical formulation of the area of operation for the guidance strategy to make intelligent decisions based on a set of defined rules. The rules are developed for three objectives in the order of priority as: 1) avoid obstacles/restricted regions; 2) maintain the target proximity; 3) minimize UAV threat exposure level. A least-square estimation and kinematic relations are used to estimate/predict the target states based on noisy position measurements. The work presented herein addresses the same problem as in a previous work by the authors, and aims at improving the computational efficiency without compromising the performance. Simulation results of several pursuit scenarios demonstrate the full capabilities of the strategy and the improvement over the previous work

Experimental Evaluation of Tracking Algorithms Used for the Determination of Fish Behavioral Statistics

The fine-scale swimming behavior of fish can now be studied because of the development of sophisticated measurement devices such as multibeam sonar and stereo video systems. However, even with these sensors, improved methods are still required to generate quality estimates of swimming speeds and turn rates. Biologists have commonly relied on pointwise differentiation of noisy position measurements while engineers have focused on Bayesian algorithms to track underwater vehicles. A comparative evaluation of the performance of these tracking algorithms for the analysis of fine-scale behavior of fish was performed using a data set of 100 fish tracks recorded simultaneously with a multibeam sonar and a stereo video camera system. The segmenting track identifier, a non-Bayesian curve fitting and segmenting tracker, is shown to be most effective for tracking the unpredictable and complex horizontal motion of fish while a Kalman smoother using a constant-velocity model is shown to be most effective for tracking the more predictable and piecewise linear vertical motion of fish. Both are shown to be more effective than pointwise differentiation. Criteria for selecting an appropriate algorithm for a given motion study are provided

DYNAMIC POSITIONING CONTROL OF SHIPS VIA RELAY OBSERVER DESIGN

ABSTRACTA dynamically positioned ship maintains its position (fixed location or predetermined track) exclusively by means of active thrusters. In this paper, a control scheme for dynamic positioning control of ships using a relay observer design is presented. Our analysis relies on nonsmooth strict Lyapunov functions to demonstrate global asymptotic stability of the closed‐loop system equilibrium. Using simulation results we illustrate the good performance of the proposed scheme under noisy ship position measurements.

Tracking multiple and dynamic objects with an extended particle filter and an adapted k-means clustering algorithm

The work presented is related to the research area of autonomous navigation for mobile robots in unstructured, heavy crowded and highly dynamic environments. One of the main involved tasks in this researching area is the obstacle tracking module that has been successfully developed with different kind of probabilistic algorithms. The reliability that these techniques have shown estimating position with noisy measurements make them the most adequate to the mentioned problem, but their high computational cost has made them only useful with few and structured objects. In this paper a computational simple solution based on a multimodal (or extended) particle filter is proposed to track multiple and dynamic obstacles in an unstructured environment and based on the noisy position measurements taken from sonar sensors.

Passive nonlinear observer design for ships using lyapunov methods: full-scale experiments with a supply vessel

Dynamic positioning (DP) and tracking systems for ships are usually designed under the assumption that the kinematic equations can be linearized about a set of predefined constant yaw angles, typically 36 operating points in steps of 10°, to cover the whole heading envelope. This is necessary when applying linear (Kalman filter)theory and gain scheduling techniques. However, global exponential stability (GES) cannot be guaranteed if linear theory is used. In this paper a nonlinear observer is derived. The observer is proven to be passive and GES. The number of tuning parameters is reduced to a minimum by using passivity theory. This results in a simple and intuitive tuning procedure. The proposed observer includes features like estimation of both the low-frequency position and velocity of the ship from noisy position measurements, bias state estimation (environmental disturbances) and wave filtering. The nonlinear passive observer has been simulated on a computer model of a supply vessel and implemented on full-scale ships with excellent results.

Advanced guidance laws for acceleration-constrained missile, randomly maneuvering target and noisy measurements

Explicit, closed-form formulae of advanced guidance laws for a linear, time-invariant, acceleration-constrained arbitrary-order missile, and a linear, time-invariant, arbitrary-order, randomly maneuvering target with noisy position measurements are derived. Two approaches are presented. The first approach derives the optimal guidance law for a quadratic objective. The solution is the guidance law for deterministic system with limiting on the commanded acceleration applied on the estimated state. The limiting function in this case is the saturation function. The second approach derives a control law called the average input guidance law. This approach is based on the idea of applying the average of the input that would have been applied to the plant if the noises were known. The solution has similar structure. It is the guidance law for deterministic system with limiting on the commanded acceleration applied on the estimated state. The limiting function in this case is from the family of describing functions of the saturation function. The formulas of the different guidance laws are given in terms of the transfer function of the missile and acceleration constraint, the shaping filter of the maneuver of the target, responses to initial conditions, error variance matrix of the estimated state and weights in the criterion. It is demonstrated by simulations that although the optimal guidance law has improved performance in terms of the miss distance, the suboptimal average input guidance law consumes less energy.

On optimal smoothing and derivative estimation from noisy displacement data in biomechanics

Estimating derivatives from noisy displacement data is a notoriously ill-posed problem in signal processing and biomechanics. Following the work of Wood and Jennings (1978) and Hatze (1979, 1981), the present paper describes the use of optimally regularized, natural quintic splines for estimating smoothed positions, velocities, and accelerations from equidistantly sampled, noisy position measurements. It appears that the nature of the boundary conditions of the data is of some importance, since various algorithms used hitherto result in artefacts throughout the data if the true derivatives at the record ends differ significantly from zero. Natural quintic splines do not suffer from this disadvantage below the third derivative. The ill-posed character of movement analysis has some interesting implications for movement synthesis and optimization, similar to the indeterminacy of muscular co-contraction from merely external, biomechanical measurements.

Velocity Estimation from Position Outputs of a Three-Dimensional Radar

Kalman filtering equations to obtain estimates of velocity from radar position information are defined. In a track-while-scan operation, a three-dimensional radar sensor measures range, bearing, and elevation (r, θ, ø) of an airborne target at uniform sampling intervals of time T. The noisy position measurements are converted to x, y, z coordinates and put through a Kalman filter to obtain x, y, z velocity components. The filtering equations together with steady-state error estimates are given.