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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. [ABSTRACT FROM AUTHOR]

This paper addresses the optimal linear estimation problem for a class of networked descriptor systems with multiple packet dropouts, measurement multiplicative noises and finite-step correlated process and measurement noises. Based on a fast–slow subsystem decomposition approach (FSD), the descriptor system is transformed into two reduced-order linear nonsingular subsystems with finite-step correlated noises. Optimal linear estimators including filter, predictor and smoother with corresponding estimation error covariance matrices for the states and noises of new systems are developed via the innovation analysis approach. Then, the optimal linear estimators are obtained for the original descriptor system. An example shows the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of persistently covering an environment with a group of mobile robots. In contrast to traditional coverage, in our scenario the coverage level of the environment is always changing. For this reason, the robots have to continually move to maintain a desired coverage level. In this context, our contribution is a complete approach to the problem, including distributed estimation of the coverage and control of the motion of the robots. First, we present an algorithm that allows every robot to estimate the global coverage function only with local information. We pay special attention to the characterization of the algorithm, establishing bounds on the estimation error, and we demonstrate that the algorithm guarantees a perfect estimation in particular areas. Second, we introduce a new function to determine the possible improvement of the coverage at each point of the environment. Upon this metric, we build a motion control strategy that drives the robots to the points of the highest improvement while following the direction of the gradient of the function. Finally, we simulate the proposal to test its correctness and performance. [ABSTRACT FROM AUTHOR]

Covariance-based DoA estimation (CB-DoA) algorithms represent lower computational complexity alternatives to the traditional ESPRIT approach. This paper investigates CB-DoA using Krylov-subspace techniques (including Arnoldi's and Lanczos' updates) with respect to the resulting computational cost and estimation error performance. The proposed modifications also allow an automatic estimation of the number of sources. Computational analyses performed for the resulting CB-DoA algorithm indicate cost savings above $$60\,\%$$ in comparison with the standard CB-DoA implementation, which already represents a $$20\,\%$$ improvement upon its ESPRIT counterpart, at an equivalent mean squared error level, as verified in numerical simulations. [ABSTRACT FROM AUTHOR]

The unscented Kalman filter (UKF) became very attractive for the navigation sensors data fusion, because of algorithm significant accuracy and implementation advantages. The unscented Kalman filter is based on the unscented transform (UT) to perform the estimation of the system states. The main idea of the unscented transformation is following. It's more effective to approximate probability distribution function than arbitrary transformation or nonlinear function. The developed sensors data fusion algorithm using the UKF is considered in this work. This algorithm was applied for the state estimation of the loosely coupled GPS/INS integrated navigation system. GPS/INS integrated navigation system contains low cost inertial sensors and low cost GPS receiver. To demonstrate the estimation performance, the processing of sensors data was done using linear Kalman filter (KF), extended Kalman filter (EKF) and UKF. As a result, UKF has lower velocity estimation error than EKF during simulated GPS signal outage. [ABSTRACT FROM AUTHOR]

This work proposes an improved unscented Kalman filter (UKF)-based simultaneous localization andmapping (SLAM) algorithm based on an adaptive unscented Kalman filter (AUKF) with a noise statistic estimator. The algorithm solves the issue that conventional UKF-SLAMalgorithms have declining accuracy, with divergence occurring when the prior noise statistic is unknown and time-varying. The new SLAM algorithm performs an online estimation of the statistical parameters of unknown system noise by introducing a modified Sage-Husa noise statistic estimator. The algorithm also judges whether the filter is divergent and restrains potential filtering divergence using a covariance matchingmethod. This approach reduces state estimation error, effectively improving navigation accuracy of the SLAM system. A line feature extraction is implemented through a Hough transform based on the ranging sonar model. Test results based on unmanned underwater vehicle (UUV) sea trial data indicate that the proposed AUKF-SLAM algorithm is valid and feasible and provides better accuracy than the standard UKF-SLAM system. [ABSTRACT FROM AUTHOR]

The most critical component of any adaptive numerical quadrature routine is the estimation of the integration error. Since the publication of the first algorithms in the 1960s, many error estimation schemes have been presented, evaluated, and discussed. This article presents a review of existing error estimation techniques and discusses their differences and their common features. Some common shortcomings of these algorithms are discussed, and a new general error estimation technique is presented. [ABSTRACT FROM AUTHOR]

We explore the theoretical framework as well as the associated algorithms for the problem of optimally placing mobile observation platforms to maximise the improvement of estimation accuracy. The approach in this study is based on the concept of observability, which is a quantitative measure of the information provided by sensor data and user-knowledge. To find the optimal sensor locations, the observability is maximised using a gradient projection method. The Burgers equation is used to verify this approach. To prove the optimality of the sensor locations, Monte Carlo experimentations are carried out using standard 4D-Var algorithms based on two sets of data, one from equally spaced sensors and the other from the optimal sensor locations. The results show that, relative to equally spaced sensors, the 4D-Var data assimilation achieves significantly improved estimation accuracy if the sensors are placed at the optimal locations. A robustness study is also carried out in which the error covariance matrix is varied by 50% and the sensor noise covariance is varied by 100%. In addition, both Gaussian and uniform probability distributions are used for the sensor noise and initial estimation errors. In all cases, the optimal sensor locations result in significantly improved estimation accuracy. [ABSTRACT FROM AUTHOR]