I agree that the Gaussian (white noise) representation of error or uncertainty is not specific to any one source of error, with a component of white noise present to varying degrees across different sources of error. I did not agree with Todorov's assertion that the Gaussian probabilistic description of uncertainty could handle multiple sources of error in 3DMA particularly STA and marker misplacement. Axes misalignment between the axes reconstructed from skin markers or sensors and the underlying anatomical axes cannot be considered random noise and do not fit into the Gaussian model. Axes misalignment errors (static offset or dynamic STA) are a major limiting factor to validity and reliability of 3DMA, but can be identified and described and therefore corrected to derive anatomical axes from external markers. The success of identifying and correcting axes alignment is up to debate but is a challenge that needs to be met.

Todorov: “The problem is formulated in a probabilistic framework so as to handle multiple and unavoidable sources of uncertainty: sensor noise, soft tissue deformation and marker slip, inaccurate marker placement and limb measurement, and missing data due to occlusions”

I think axes misalignment could be built into the Todorov model but not by the current limited Gaussian view of error in 3DMA. As suggested by Ton, by introducing additional unknowns into the predictive model (represented in the Kalman filter by matrix A). These may be constant unknowns (axes offsets) and variables (STA) representing the displacement the marker based axes from the anatomical. In this Kalman filter model the state variables of position, velocity and acceleration now represent the anatomical segment axes and the additional constants and variables describe the transformation to the marker based axes to then track measured 3D skin marker data with the addition of white noise.

Todorov: “We expect our methods to outperform alternative, which ignore uncertainties.”

The assertion that alternative methods ignore uncertainties is not correct, a marker cluster design with least squares approach accounts for random noise. Methods that attempt to measure axes misalignment (the most common approach being to minimize either knee add/abduction RoM or correlation with knee flex/ext in gait to adjust thigh medio-lateral axis) will outperform the Todorov method as currently presented. As the Todorov method does not include any assessment or correction for axes mis-alignment to the anatomical I would expect there to be little difference between an inverse dynamics least square approach that does not account for axes misalignment and the Todorov approach.

Cheers
Allan