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This article presents a new platform independent approach to the real-time solution of inverse problems on embedded systems. The class of problems addressed corresponds to ordinary differential equations (ODEs) with generalized linear constraints, whereby the data from an array of sensors forms the forcing function. The algebraic discretization of the problem enables an one-to-one mapping of the ODE to its discrete equivalent linear differential operator, together with an additional matrix equation representing the constraints. The solution of the equation is formulated as a least squares (LS) problem with linear constraints. The LS approach makes the method suitable for the explicit solution of inverse problems where the forcing function is perturbed by noise. The algebraic computation is partitioned into an initial preparatory step, which precomputes the matrices required for the run-time computation, and the cyclic run-time computation, which is repeated with each acquisition of sensor data. The cyclic computation consists of a single matrix-vector multiplication, in this manner computation complexity is known a-priori, fulfilling the definition of a real-time computation. The solution is implemented with model based design and uses only fundamental linear algebra, consequently, this approach supports automatic code generation for deployment on embedded systems. The targeting concept was tested via software-and processor-in-the-loop verification. The method was tested on a laboratory prototype with real measurement data for the monitoring of flexible structures. The measurement arrangement consists of an embedded system with a chain of 14 inclinometer sensors connected to it, two additional nodes implement a total of four constraints. The problem solved is: the real-time overconstrained reconstruction of a curve from measured gradients. Such systems are commonly encountered in the monitoring of structures and/or ground subsidence.

2015 ieee 17th international conference on high performance computing and communications, 2015 ieee 7th international symposium on cyberspace safety and security, and 2015 ieee 12th international conference on embedded software and systems

An Algebraic Framework for the Real-Time Solution of Inverse Problems on Embedded Systems