Optimal State Estimation

  • Simon D
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Abstract

We propose a model for human postural balance, combining state feedback control with optimal state estimation. State estimation uses an internal model of body and sensor dynamics to process sensor information and determine body orientation. Three sensory modalities are modeled: joint proprioception, vestibular organs in the inner ear, and vision. These are mated with a two degree-of-freedom model of body dynamics in the sagittal plane. Linear quadratic optimal control is used to design state feedback and estimation gains. Nine free parameters define the control objective and the signal-to-noise ratios of the sensors. The model predicts statistical properties of human sway in terms of covariance of ankle and hip motion. These predictions are compared with normal human responses to alterations in sensory conditions. With a single parameter set, the model successfully reproduces the general nature of postural motion as a function of sensory environment. Parameter variations reveal that the model is highly robust under normal sensory conditions, but not when two or more sensors are inaccurate. This behavior is similar to that of normal human subjects. We propose that age-related sensory changes may be modeled with decreased signal-to-noise ratios, and compare the model's behavior with degraded sensors against experimental measurements from older adults. We also examine removal of the model's vestibular sense, which leads to instability similar to that observed in bilateral vestibular loss subjects. The model may be useful for predicting which sensors are most critical for balance, and how much they can deteriorate before posture becomes unstable.

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Authors

  • Dan Simon

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