Bounded-error Estimation Research Articles

Localization of Partially Hidden Moving Targets Using a Fleet of UAVs via Bounded-Error Estimation

Localization of Partially Hidden Moving Targets Using a Fleet of UAVs via Bounded-Error Estimation

Robust Extended Kalman Filtering for Systems With Measurement Outliers

Outliers can be caused by sensor errors, model uncertainties, changes in the ambient environment, data loss, or malicious cyberattacks to contaminate the measurement process of many nonlinear dynamic systems. When the extended Kalman filter (EKF) is applied to such systems for state estimation, the outliers can seriously reduce the estimation accuracy. This brief proposes an innovation saturation mechanism to make the EKF robust against outliers. This mechanism applies a saturation function to the innovation process that the EKF leverages to correct the state estimation. As such, when outliers occur, the distorted innovation is saturated, so as not to undermine the state estimation. The mechanism features an adaptive adjustment of the saturation bounds. The design leads to the development of robust EKF approaches for both continuous- and discrete-time systems. The stability of the proposed approaches when applied to linear systems is characterized, showing that they are capable of performing bounded-error estimation in the presence of bounded outlier disturbances in this case. A simulation study about mobile robot localization is presented to illustrate the efficacy of the proposed design. Compared to existing methods, the proposed approaches can effectively reject outliers of various magnitudes, types, and durations, at significant computational efficiency and without requiring additional measurement redundancy.

Finite horizon constrained control and bounded-error estimation in the presence of missing data

In this paper, we propose an optimization-based design technique for constrained control and bounded-error state estimation for affine systems in the presence of intermittent measurements. We treat the affine system as a switched system where the measurement equation switches between two modes based on whether a measurement exists or is missing, and model potential missing data patterns with a finite-length language that constrains the feasible mode sequences. Then, we introduce a novel property, equalized recovery, that generalizes the equalized performance property and that allows us to tolerate missing observations. By utilizing Q-parametrization, we show that a finite horizon optimal estimator/controller can be constructed using time-based and prefix-based approaches, where the latter implicitly estimates the specific missing data pattern (i.e., mode sequence), within the given language, according to the prefix observed so far. We illustrate with numerical examples that the proposed approaches can provide desirable performance guarantees.

Bounded-error target localization and tracking in presence of decoys using a fleet of UAVs

Abstract This paper addresses the problem of searching and tracking of an a priori unknown number of targets spread over some geographical area using a fleet of UAVs. State perturbations and measurement noises are assumed to belong to bounded sets. In the monitored geographical area, some decoys may be erroneously considered as targets when observed under specific conditions. A robust bounded-error estimation approach is proposed to evaluate, at each time step, sets guaranteed to contain the actual state of already localized true targets and decoys. A set containing the states of targets still to be discovered is also evaluated. These sets are used to determine the control inputs of UAVs so as to minimize the estimation uncertainty at future time steps. Simulations involving several UAVs show that the proposed robust set-membership estimator is able to estimate the state of all actual targets and to efficiently identify and eliminate decoys.

A robust set approach for mobile robot localization in ambient environment

Mobile robot localization consists in estimating the robot coordinates using real-time measurements. In ambient environment context, data can come both from the robot on-board sensors and from environment objects, mobile or not, able to sense the robot. The paper considers localization problem as a nonlinear bounded-error estimation of the state vector. The components of the state vector are the robot coordinates as well as the 2D position and orientation. The approach based on interval analysis can satisfy the needs of ambient environment by easily taking account a heterogeneous set and a variable number of measurements. Bounded-error state estimation can be an alternative to particle filtering which is sensitive to non-consistent measures, large measure errors, and drift of evolution model. The paper addresses the theoretical formulation of the set-membership approach and the application to the estimation of the robot localization. Additional treatments are added to the estimator in order to meet more realistic conditions. Treatments aim at reducing the effects of disruptive events: outliers, model inaccuracies or model drift and robot kidnapping. Simulation results show the contribution of each step of the estimator.

Guaranteed confidence region characterization for source localization using RSS measurements

Abstract This paper considers source localization in a Wireless Sensor Network (WSN) from Received Signal Strength (RSS) measurements. Its aim is to characterize confidence regions (CR) of the search space to which the source parameters (location, reference power, path loss exponent) are guaranteed to belong with a pre-specified probability level. The Leave-out Sign-dominant Correlation Regions (LSCR) method is adapted to this source localization context. LSCR defines CR considering very mild assumptions on the measurement noise corrupting the RSS readings. The confidence level may be arbitrarily chosen and the LSCR approach is valid even when very few measurements are available (non-asymptotic regime). The CR, as defined by LSCR may be non-convex or even non-connected sets. Their characterization is performed via interval analysis, which provides inner and outer approximations of CR. The CR obtained via LSCR are compared to set estimates obtained using (robust) bounded-error estimation techniques, as well as to more classical confidence ellipsoids derived from Cramer-Rao lower bounds.

Bounded-error optimal experimental design via global solution of constrained min–max program

We present an improvement of existing methods for globally solving optimal experimental design (OED) for bounded-error estimation based on a bilevel formulation from Mukkala et al. (2017). The proposed solution method for the min–max program is based on our method for generalized semi-infinite programs (via restriction of the right-hand side). The algorithm employed has the advantage that it guarantees a global solution for the OED assuming the global solution of two subproblems. To obtain a feasible solution only the lower-level problem has to be solved globally. In case of a local solution of the upper-level problem, the solution is still feasible though it is an upper bound of the global solution. The min–max method for OED is illustrated with four examples: two simple chemical reactions, BET-adsorption and a reformulated predator-prey system. The benefits of global methods are shown along with the limitations of state-of-the-art global solvers.

Global optimization for low-dimensional switching linear regression and bounded-error estimation

The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local optimization heuristics without global optimality guarantees or with guarantees valid only under restrictive conditions, the proposed approach always yields a solution with a certificate of global optimality. This approach relies on a branch-and-bound strategy for which we devise lower bounds that can be efficiently computed. In order to obtain scalable algorithms with respect to the number of data, we directly optimize the model parameters in a continuous optimization setting without involving integer variables. Numerical experiments show that the proposed algorithms offer a higher accuracy than convex relaxations with a reasonable computational burden for hybrid system identification. In addition, we discuss how bounded-error estimation is related to robust estimation in the presence of outliers and exact recovery under sparse noise, for which we also obtain promising numerical results.

A multihypothesis set approach for mobile robot localization using heterogeneous measurements provided by the Internet of Things

Mobile robot localization consists in estimation of robot pose by using real-time measurements. The Internet of Things (IoT) adds a new dimension to this process by enabling communications with smart objects at anytime and anywhere. Thus data used by localization process can come both from the robot on-board sensors and from environment objects, mobile or not, able to sense the robot. The paper considers localization problem as a nonlinear bounded-error estimation of the state vector whose components are the robot coordinates. The approach based on interval analysis is able to answer the constraints of IoT by easily taking account a heterogeneous set and a variable number of measurements. Bounded-error state estimation can be an alternative to other approaches, notably particle filtering which is sensible to non-consistent measures, large measure errors, and drift of robot evolution model. The theoretical formulation of the set-membership approach and the application to the estimation of the robot localization are addressed first. In order to meet more realistic conditions the way of reducing the effect of environment model inaccuracies, evolution model drift, outliers and disruptive events such as robot kidnapping is introduced. By integrating these additional treatments to the set-membership approach we propose a bounded-error estimator using multihypothesis tracking. Simulation results show the contribution of each step of the estimator. Real experiments focus on global localization and specific treatments for synchronizing measurements and processing outliers.

Set-membership estimation of fiber laser physical parameters from input–output power measurements

The problem of fiber laser parameters estimation from input–output transient power measurements is considered in the paper. The proposed procedure is based on a suitable laser model obtained from the rate and propagation equations. By proper manipulation of the simplified laser equations, the estimation problem is formulated in the bounded error estimation framework, where a priori information on physical parameters can be properly taken into account. First the so-called feasible parameter set is defined. Then, the problem of optimally picking a single model from the set is formulated in terms of central conditional estimation and solved by exploiting recent results by the authors. Properties of the proposed solution are discussed. The proposed algorithm is tested on a set of simulated data obtained from a commercial laser simulator.

Kernel Characterization of an Interval Function

This paper proposes a set-membership approach to characterize the kernel of an interval-valued function. In the context of a bounded-error estimation, this formulation makes it possible to embed all uncertainties of the problem inside the interval function and thus to avoid bisections with respect to all these uncertainties. To illustrate the principle of the approach, two testcases taken from robotics will be presented. The first testcase deals with the characterization of all loops of a mobile robot from proprioceptive measurements only. The second testcase is the localization of a robot from range-only measurements.

Cooperative guidance laws for maneuvering target interceptions

This study addresses the design of cooperative guidance laws for interceptor missiles. A polyhedric bounded-error estimation of the target position is employed, based only on the assumption that the target acceleration and measurement noise remain within known bounds. This prediction of the maneuvering target trajectory is then incorporated into a model predictive control scheme to derive the missile guidance law. The cases of both single and multiple targets are investigated. Simulation results are presented to illustrate the proposed approach.

Dynamic Parameters Estimation Based on Set Inversion and Interval Analysis Algorithm

In the paper, an approach, based on bounded-error estimation via interval analysis, is presented to identify viscous damping coefficient and Coulomb friction coefficient of such-rod pumping system of directional well. The approach assumes the error of colleted output data of suck-rod pumping system is bounded. Hence, the problem of parameter estimation can be viewed as that of set inversion, which will be effectively solved via interval analysis. The main advantage of the proposed method in comparison with the traditional estimation methods is that, as it is global, it bypasses the problem of initialization. Moreover, the method avoids amount error due to transformation of measurement output data. An identification example is given to show the correctness and efficiency of the proposed method.

Mobile robot localization by multiangulation using set inversion

This work is about solving the global localization issue for mobile robots operating in large and cooperative environments. It tackles the problem of estimating the pose of a robot in the environment using real-time data either from the robot on-board sensors or/and from the sensors in the environment or/and the real-time data coming from other robots. The paper focuses on the 3-DOF localization of a mobile robot that is to say the estimation of the robot coordinates (xmr, ymr, θmr) in a 2D-environment.The interest of this method lies on the ability to easily integrate a large variety of sensors, from the roughest to the most complex one. The method takes into account the following constraints: a flexible number of measurements, generic goniometric measurements, a statistical knowledge on the measurements limited to the tolerance, and the fact the measurements are acquired both from the robot onboard sensors and the environment sensors. The approach is able to integrate a heterogeneous set of measurements; not only generic goniometric measurements but also range, position given by a tactile tile, complex shape, and dead reckoning measurements. The way that outliers and environment model inaccuracies can be taken into account is described.The problem of nonlinear bounded-error estimation is viewed as a set inversion. The paper presents the theoretical formulation of the localization method in a bounded-error context and the parameter estimation based on interval analysis. Simulation results as well as real experiments show the interest of the method in a cooperative environment context.

A Multiple-Hypothesis Map-Matching Method Suitable for Weighted and Box-Shaped State Estimation for Localization

The goal of map-matching algorithms is to identify the road taken by a vehicle and to compute an estimate of the vehicle position on that road using a digital map. In this paper, a map-matching algorithm based on interval analysis and the belief function theory is proposed. The method combines the outputs from existing bounded-error estimation techniques with piecewise rectangular roads that are selected using evidential reasoning. A set of candidate roads is first defined at each time step using the topology of the map and a similarity criterion, and a mass function on the set of candidate roads is computed. An overall estimate of the vehicle position is then derived after the most probable candidate road has been selected. This method allows multiple road junction hypotheses to efficiently be handled and can cope with missing data. In addition, the implementation of the method is quite simple, because it is based on geometrical properties of boxes and rectangular road segments. Experiments with simulated and real data demonstrate the ability of this method to handle junction situations and to compute an accurate estimate of the vehicle position.

Guaranteed estimation of the parameters of nonlinear continuous‐time models: Contributions of interval analysis

AbstractThis paper is about guaranteed parameter estimation in two contexts, namely bounded‐error and optimal estimation. In bounded‐error estimation, one looks for the set of all parameter vectors that are consistent with some prior bounds on the errors deemed acceptable between the model behavior and that of the system. In optimal estimation, one looks for the set of all parameter vectors that minimize some cost function quantifying the discrepancy between the behaviors of the system and its model. In both cases, guaranteed means that proven statements are made about the set of interest. The situation is made much more difficult when the model output is assumed to depend nonlinearly in the parameters to be estimated and when dealing with continuous‐time models, as here. Important tools based on interval analysis (IA) that contribute to allowing guaranteed estimation in these challenging conditions are presented. Some are absolutely classical in the context of IA but not so well known in the community of parameter estimation at large. Others have been developed recently and were mainly presented in conferences. Some, such as the use of sensitivity functions to reduce more quickly the size of outer approximations of the sets of interest, are new. Challenges for future research in the context of guaranteed nonlinear estimation are mentioned. Copyright © 2010 John Wiley & Sons, Ltd.

Probabilistic Set-Membership Approach for Robust Regression

Interval constraint propagation methods have been shown to be efficient and reliable to solve difficult nonlinear bounded-error estimation problems. However they are considered as unsuitable in a probabilistic context, where the approximation of a probability density function by a set cannot be accepted as reliable. This paper shows how probabilistic estimation problems can be transformed into a set estimation problem by assuming that some rare events will never happen. Since the probability of occurrence of those rare events can be computed, we can give some prior lower bounds for the probability associated to solution set of the corresponding set estimation problem. The approach will be illustrated on a parameter estimation problem.

Robot Localization Algorithm using Odometry and RFID Technology

This paper presents a localization algorithm based on the particle filter using odometry and RFID sensor readings. The integration of both measurements permits to localize a mobile robot with a bounded error estimation, while dead reckoning approaches using only odometry let the error diverge. RFID tags are integrated in the environment; it is supposed their positions have been learnt during a learning step not considered here. The localization algorithm is based on the observation model for the RFID measurements; this model is determined experimentally. The algorithm and the RFID reader are embedded and evaluated on a mobile robot; experimental results show that our localization algorithm gives the robot position with a bounded error when using RFID measurements, additionally in order to correct odometry drifts.

Image Shape Extraction using Interval Methods

This paper proposes a new method for recognition of geometrical shapes (such as lines, circles or ellipsoids) in an image. The main idea is to transform the problem into a bounded error estimation problem and then to use an interval-based method which is robust with respect to outliers. The approach is illustrated on an image taken by an underwater robot where a spheric buoy has to be detected. The results will then be compared to those obtained by the more classical generalized Hough transform.

Dynamic structured routing in mobile networks

This paper describes dynamic structured routing schema for mobile users in a hostile, noisy environment. It is difficult to maintain a structured routing especially for large ad hoc networks due to dynamically changing configuration of the Mobile Ad Hoc Network (MANET). This paper describes a new approach to the cluster head election. The proposed method is based on the election of a head node for a cluster depending on the status of nodes and the cluster itself. The goal is to predict a location of the cluster head based on a guaranteed estimation of mobile users' current locations. Guaranteed estimation, also known as a bounded-error estimation, allows construction of the information set of state or parameter vectors that are compatible with the measured data for dynamic systems with unknown, but bounded errors and system inputs. The new approach is based on polygonal approximations of systems' information sets.