Application of trilateration and Kalman filtering algorithms to track dynamic brain deformation using sonomicrometry

Abstract

Trilateration and Kalman filtering algorithms have been used in many tracking applications ranging from Global Positioning Systems to biomechanics experiments to track rigid body motion and position. Recently, a technique called sonomicrometry was used to measure the deformation of human brain tissue during an injurious impact by measuring distances between sensor pairs embedded in the parenchyma and skull. The array of measured distances were used to calculate the position of each sensor at high sampling rates to quantify brain dynamic deformation. However, non-linear trilateration and Kalman filtering algorithms, which are traditionally used to track object positions, have not been investigated for the unique application of high-rate, small displacement, and dynamic deformation data collected using sonomicrometry. The objective of this study was to compare eight trilateration and Kalman filtering algorithms to determine the most suitable method for sonomicrometry trilateration. The algorithms were tested using experimental brain deformation sonomicrometry data in which random measurement errors were intentionally introduced to evaluate the effect and robustness on tracking dynamic position. The results showed that linear least squares trilateration methods performed poorly compared to the non-linear methods. Maximum Likelihood Estimate and Kalman filtering were the best performing algorithms. The Kalman filtering method was the most suitable for tracking dynamic brain deformation using sonomicrometry because it provided an accurate estimation of dynamic position and the estimated position was insensitive to the chosen initial parameters. The algorithms and error analysis can be extended to a variety of positioning applications using sonomicrometry or similar high-rate dynamic deformation tracking.