The main cause of dynamic errors is the sensor's frequency response limitation. One way of solving this problem is designing an effective inverse filter. Since the problem is ill-conditioned, a small uncertainty in the measurement will cause large deviation in reconstructed signals. The amplified noise has to be suppressed at the sacrifice of biasing in estimation. Based on stabilized solutions of Fredholm integral equations of the first kind, the paper presents a group of inverse filters from which correcting dynamic characteristics of measurement systems can be selected or optimized to reduce dynamic errors. Compared with previous work, the method has advantage of generalization. So, it is more flexible in designing inverse filters.

A Group of Inverse Filters Based on Stabilized Solutions of Fredholm Integral Equations of the First Kind

This paper presents the theoretical background for a new measurement system for the monitoring of possible road subsidence and its verification with experimental results. A combination of theodolite measurements and inclinometers are used to perform the monitoring of possible land subsidence. The aim is to detect ground motion near critical infrastructure during excavation is the vicinity. The required computation corresponds to an inverse boundary value problem with uncertain boundary values. The solution is formulated as a covariance weighted Hermite approximation problem. Additionally, a method of taking advantage of the properties of the over-constrained system to identify a defective sensor is presented. The correct functionality of the proposed method and its performance in terms of uncertainty is demonstrated with a Monte Carlo simulation. Additionally, tests were performed with a real monitoring system with reference measurements. The correct functionality of the measurement system was verified.

Inverse boundary value problems with uncertain boundary values and their relevance to inclinometer measurements

A generalized method for correcting dynamic characteristics of measurement systems is presented to reduce dynamic errors. The cause of dynamic errors is the sensor's frequency response limitation. ...

Correction of Signal Distortion Resulting from Measurement Systems Limitation

This paper presents a mathematical model and partitioning for a software system for the solution of inverse problems involving arrays of sensors. Handling the data from the array of sensors as vectors and matrices, while defining the inverse problem as a least squares computation with linear constraints, leads naturally to the use of matrix algebra for the solution of the system of equations. The matrix algebra is also well suited for the use of automatic code generation to support the rapid development of embedded code. The full functionality of the proposed methods was demonstrated with an inclinometer based system for the monitoring of structural deformation.

http://ieeexplore.ieee.org/iel7/6971895/6984913/06985066.pdf

Mathematical model and software architecture for the solution of inverse problems involving sensor arrays

The paper investigates deconvolution of transient signals The problem is ill-conditioned, which means that a small uncertainty in the measurement causes large deviation in the reconstructed signal This amplified noise has to be suppressed at the price of bias in the estimation A goal of this paper is to search for a generalized approach to the deconvolution technique We take the problem of deconvolution as solving stabilized solutions of Fredholm integral equations According to the principium of solving inverse problems in mathematics, we structure a stabilized method for obtaining deconvolution, and study a kind of multiparameter model The superiority of the presented method is verified by simulation

G.N. Solopchenko

Papers

Inverse problems in measurement