The project title goes by Improving the Performance of Online Predictive Modeling of the Thermal Effect of Bio-implants.

This is a research project taken by a 4-people team and my role in the project is to implement Kernel Recursive Least Squares (KRLS) algorithm for multi-input multi-output system identification. My teammates focused on the task of

  1. Redesigning Spatial Weight Matrix as there are 6 sensor inputs as they are spatially not at the same location
  2. Recorded data batch preprocessign.
  3. Investigating Fast Transversal Recursive Least Square algorithm

My task can be described via the following:

For a system described by equation

++\mathbf{x}_{t+1} = \mathbf{A} \mathbf{f}(\mathbf{x}_t) + \mathbf{B}\mathbf{q}(\mathbf{u}_t)++

That $\mathbf{x}$ and $\mathbf{u}$ represent a system state and its input, I aimed to find (approximate) the kernel function $\mathbf{\bar{f}}$ and system matrix $\mathbf{\bar{A}}$ with gaussian and bang-bang input that minimizes the following

++\sum_{t=0}^{T} || \mathbf{\bar{x}_{t} - x_{t}} || ++

where

++\mathbf{\bar{x}}_{t+1} = \mathbf{\bar{A}} \mathbf{\bar{f}}(\mathbf{x}_t)++

Note that the input term is gone as we are investigating the naturally evolving process under here.

My work primarily referenced [1]. I further attempted to fit multiple kernel functions for the particular use of this project.

Implementing a kernel function in the vector distance and gaussian distributed space successfully reduced MSE of prediction error from $2.6675\times 10^{-3}$ to $1.3904\times 10^{-4}$ and $4.59\times 10^{-5}$

Our research project can be found summarized in the following poster

[1] Y. Engel, S. Mannor and R. Meir, “The kernel recursive least-squares algorithm,” in IEEE Transactions on Signal Processing, vol. 52, no. 8, pp. 2275-2285, Aug. 2004, doi: 10.1109/TSP.2004.830985.