There have been significant advances in range-based numerical methods for sensor network localizations over the past decade. However, there remain a few challenges to be resolved to satisfaction. Those issues include, for example, the flip ambiguity, high level of noises in distance measurements, and irregular topology of the concerning network. Each or a combination of them often severely degrades the otherwise good performance of existing methods. Integrating the connectivity constraints is an effective way to deal with those issues. However, there are too many of such constraints, especially in a large and sparse network. This presents a challenging computational problem to existing methods. In this paper, we propose a convex optimization model based on the Euclidean Distance Matrix (EDM). In our model, the connectivity constraints can be simply represented as lower and upper bounds on the elements of EDM, resulting in a standard 3-block quadratic conic programming, which can be efficiently solved by a recently proposed 3-block alternating direction method of multipliers. Numerical experiments show that the EDM model effectively eliminates the flip ambiguity and retains robustness in terms of being resistance to irregular wireless sensor network topology and high noise levels.
The presence of measurement bias and random noise significantly deteriorates the information quality of plant data. Data reconciliation techniques for steady‐state processes have been widely applied to processing industries to improve the accuracy and precision of the raw measurements. This paper develops an algorithm for simultaneous bias correction and data reconciliation for dynamic processes. The algorithm considers process model error as an important contributing factor in the estimation of the measurement bias and process state variables. It employs black‐box models for the process as would be done when phenomenological models are difficult or impractical to obtain. Simulation results of a distillation column demonstrated that this algorithm effectively compensates constant and non‐constant measurement biases yielding much improved reconciled values of process variables. It has computational advantages over previously proposed algorithms based on non‐linear dynamic data reconciliation because an analytical solution is available when using linear process models to approximate the process.
Abstract. The problem of data representation on a sphere of unknown radius arises from various disciplines such as Statistics (spatial data representation), Psychology (constrained multidimensional scaling), and Computer Science (machine learning and pattern recognition). The best representation often needs to minimize a distance function of the data on a sphere as well as to satisfy some Euclidean distance constraints. It is those spherical and Euclidean distance constraints that present an enormous challenge to the existing algorithms. In this paper, we reformulate the problem as an Euclidean distance matrix optimization problem with a low rank constraint. We then propose an iterative algorithm that uses a quadratically convergent Newton-CG method at its each step. We study fundamental issues including constraint nondegeneracy and the nonsingularity of generalized Jacobian that ensure the quadratic convergence of the Newton method. We use some classic examples from the spherical multidimensional scaling to demonstrate the flexibility of the algorithm in incorporating various constraints. We also present an interesting application to the circle fitting problem.Key words. Euclidean distance matrix, Matrix optimization, Lagrangian duality, Spherical multidimensional scaling, Semismooth Newton-CG method.AMS subject classifications. 49M45, 90C25, 90C331. Introduction. In this paper, we are mainly concerned with placing n points {x 1 , . . . , x n } in a best way on a sphere in IR r . The primary information that we use is an incomplete/complete set of pairwise Euclidean distances (often with noises) among the n points. In such a setting, IR r is often a low-dimensional space (e.g., r takes 2 or 3 for data visualization) and is known as the embedding space. The center of the sphere is unknown. For some applications, the center can be put at origin in IR r . Furthermore, the radius of the sphere is also unknown. In our matrix optimization formulation of the problem, we treat both the center and the radius as unknown variables. We develop a fast numerical method for this problem and present a few of interesting applications taken from existing literature.The problem described above has long appeared in the constrained Multi-Dimensional Scaling (MDS) when r ≤ 3, which is mainly for the purpose of data visualization, see [9, Sect. 4.6] and [4, Sect. 10.3] for more details. In particular, it is known as the spherical MDS when r = 3 and the circular MDS when r = 2. Most numerical methods in this part took advantages of r being 2 or 3. For example, two of the earliest circular MDS were by Borg and Lingoes [5] and Lee and Bentler [28], where they introduced a new point x 0 ∈ IR r as the center of the sphere (i.e., circles in their case) and further forced the following constraints to hold:
Measured values of process variables are subject to measurement noise. The presence of measurement noise can result in detuned controllers in order to prevent excessive adjustments of manipulated variables. Digital filters, such as exponentially weighted moving average (EWMA) and moving average (MA) filters, are commonly used to attenuate measurement noise before controllers. In this article, we present another approach, a dynamic data reconciliation (DDR) filter. This filter employs discrete dynamic models that can be phenomenological or empirical, as constraints in reconciling noisy measurements. Simulation results for a storage tank and a distillation column under PI control demonstrate that the DDR filter can significantly reduce propagation of measurement noise inside control loops. It has better performance than the EWMA and MA filters, so that the overall performance of the control system is enhanced.
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