Symbol	Definition	SI Unit/Type
Kinematics
x	Kalman state vector [r, v]ᵀ	Vector
r, v	Position vector; resultant velocity	m, m/s
ṙ	Time derivative of position (=velocity in state-space)	m/s
a, a_peak	Resultant acceleration; peak resultant deceleration	m/s2
θ	Resultant impact/trajectory angle	° (degrees)
ω	Angular velocity (general)	rad/s
d	Pedestrian post-impact throw distance	m
Biomechanics
m	Pedestrian mass	kg
v	Resultant impact velocity	m/s or km/h
E_k	Kinetic energy	J
F, F_lateral	Impact force; lateral force component	N or kN
HIC	Head Injury Criterion (15 ms or 36 ms window)	Dimensionless
BrIC	Brain Rotational Injury Criterion	Dimensionless
ω_xc, ω_yc, ω_zc	Critical angular velocity thresholds: 66.3, 56.5, 42.87 rad/s	rad/s
σ_liver	Hepatic tissue stress	kPa
V_organ	Total organ volume (hepatic: 1560 ± 280 cm3)	cm3
Φ	Standard normal cumulative distribution function (probit)	Probability
β0, β1	Mertz–Prasad lognormal probit model intercept and slope coefficients (β0 = −ln(HIC50)/σ_ln, β1 = 1/σ_ln; HIC50 ≈ 900, σ_ln ≈ 0.37)	Dimensionless
k (vehicle)	Vehicle-class throw distance coefficient—v expressed in km/h, k in m·(km/h)−1·5	m·(km/h)−1·5
State Estimation
P(t|t)	Kalman posterior covariance matrix at time t	Matrix (m2)
σ2_total	Total propagated variance (Monte Carlo output)	Units2
σ2_i	Variance of the i-th uncertainty source	Units2
Cov(x_i, x_j)	Covariance between uncertainty sources i and j	Units2
Acoustics/MFCC
MFCC_k	Mel-Frequency Cepstral Coefficient of index k	Dimensionless
S_m	Mel-filterbank energy for channel m	Energy (arbitrary)
M	Total number of mel-filterbank channels	Integer
k (MFCC)	Cepstral coefficient index (distinct from vehicle k above)	Integer
m (MFCC)	Mel-filterbank channel index (distinct from mass m above)	Integer