Optimization for temperature estimation using magnetic nanoparticle: A set of equations solving solution investigation

This paper investigates a set of equations solving solution for magnetic nanoparticle temperature estimation. To achieve the temperature estimation using magnetic nanoparticles, a solution should be employed to solve the set of equations. And the solution to solve the set of equations is a key factor that affects the accuracy of temperature probing. To determine the dependence of the solution on the temperature probing accuracy, the matrix solution and least square solution were presented to solve the set of equations by simulation. The simulation results shows that, the matrix solution allows a maximum temperature probing error of 2 K with a standard deviation of 0.79 K, whereas the least square solution allows a maximum temperature error of 0.08 K with a standard deviation of 0.034 K. It indicates that the temperature probing accuracy was improved by a factor of 20 using the optimized solution of least square solution to solve the set of equations.