From: 3D hand tracking using Kalman filter in depth space
Kalman filter
Control
Measurement
Update
x t = A t x t − 1 + B t u t + ε t
z t = C t x t + δ t
Mean
μ ̄ t = A t μ t - 1 + B t u t
μ t = μ ̄ t + K t ( z t - C t μ ̄ t )
Covariance
Σ ̄ t = A t Σ t - 1 A t T + R t
Σ t = ( I - K t C t ) Σ ̄ t
Kalman gain
-
K t = Σ ̄ t C t T ( C t Σ ̄ t C t T + Q t ) - 1