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Definition of axes for linear and angular motion.
Schematic representation of spatial orientation process. “True state” vector, X, consisting of linear and angular positions and velocities, is produced by changes resulting from three sources: unforced behavior of body, Xprocessed by A, commanded body changes, commands U processed by B, and unmeasured disturbances, R. Various sensors are each responsive, especially to one or more components of measured state. Symbol “∧” indicates an estimate of the vector; ω, angular velocity; f, specific force, gravity minus linear accleration; θ, angle. Measured state signals are combined with “expected state,” , derived from a presumed internal model of the body, in optimum estimator to produce estimate of orientation, .
Subjective estimates of angular displacement (produced by triangular velocity wave form) are greater for retrospective than for concurrent estimates.
Subjective angular velocity decays and may reverse during prolonged constant‐velocity rotation. Sudden stop after prolonged rotation elicits transient, oppositely directed, postrotatory response.
Subjective velocity follows actual velocity only for 1st 10 s of constant angular acceleration, then plateaus and actually decays.
Normalized torsion‐pendulum response, X, for system with long time constant, TL = 15 s. A: rising response to acceleration step is detected when it reaches Xmin. B: decaying response following velocity step has duration tμ.
Time to detect, tdet, step of yaw angular acceleration of magnitude α increases sharply for acceleration levels less than 2–3 deg/s2.
Theoretical response of the torsion‐pendulum cupula model to threshold velocity step, Ut(t) = e−t/18, to threshold acceleration step, at(t) = 1 − e−t/18, and to a combined stimulus c(t) = K[Ut(t) + at(t)]. In theory, calculated cupula response for c(t) never exceeds threshold response to velocity or acceleration threshold steps alone and would be undetectable for K as large as unity. Measured thresholds for c(t) tended to values of K below 0.75, lending support to signal‐detection model rather than hard limit model for threshold.
Frequency response of adaptation model for subjective sensation during yaw angular motion: subjective angular velocity/input angular velocity equals 24.8e−0.3ss2/(s + 25)(s + 0.0625)(s + .033).
Exaggerated cupula displacement during A: angular acceleration; B: caloric stimulation; C: first phase of alcohol nystagmus (PAN I).
Measurement of relative inclination of luminous line that subjects set to apparent vertical when they are tilted laterally. Range and median shown for 13 subjects. Overestimation of tilt at small angles is the E or Müller effect shown by some subjects. The underestimation A or Aubert effect at large angles is more pronounced.
Measurements of angle of a line set to apparent vertical, plotted against lateral component of specific force for various body tilt angles (ϕ) and g levels. Apparent tilt varies according to shear force; it also increases with compressive force component.
Adapted from Correia et al.
Schematic representation of perceived pitch categories in various gravitational fields. The z‐axis component of specific force determines whether actual pitch is underestimated (category A) or overestimated (category E).
Alteration of z‐component of specific force to yield observed errors in perceived pitch. See text for explanation.
Model predictions for perceived lateral tilt angle as function of actual tilt (as in Fig. ) compared with data taken at 1 g and 2 g.
Comparison between settings of line to perceived horizontal by normals and labyrinthine defectives (LDs) in air and when tactile cues were reduced by submersion in water.
Latency to detection of step of horizontal linear acceleration for subjects upright. See text for equation of model.
Latency to detection of steps of vertical linear acceleration for subjects upright. Model is regression hyperbola for 8 subjects, yielding minimum response time of 0.37 s and velocity constant of 0.022 g‐s.
Phase angle frequency response for perceived velocity vs, input velocity. Vertical lines showing ±1 SD.
Illustration of perception of pitch during constant acceleration.
Shift of direction of specific force vector during constant velocity centrifuge rotation produces slow shift in direction of estimated vertical or horizontal.
Coordinated turn leading to error of spatial orientation.
Illustration of cross‐coupled stimulation. Rolling head movement, ωx, during sustained yaw rotation, ωz, leads to erroneous transient perception of yaw and pitch velocity.
Schematic representation of compensation principle for effect of head tilt on retinal image or proximal stimulus. ϕ, Interference function; ϕ−1, compensatory function; S, mapping function of sensory channel.
Flow‐chart representation of visual‐vestibular interaction.
Model of optic‐vestibular orientation to the vertical.
Sensory conflict model for resolution of visual‐vestibular interaction. A: dual input conflict model; B: conflict measure and weighting function.
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