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Table 2 Notation, parameters, units and derived properties of correlated velocity movement models

From: Correlated velocity models as a fundamental unit of animal movement: synthesis and applications

Model Parameter (units) Mean speed Mean squared speed Velocity auto-covariance function
  τ - characteristic time scale (time)
Unbiased CVM
UCVM(τ,ν) ν - mean speed (dist/time) ν \({2 \over \pi } \nu ^{2} \) \({2 \nu ^{2} \over \pi } e^{-{\Delta t \over \tau }}\)
UCVM(τ,η) η - random rms speed (dist/time) \(\sqrt {\pi \over 2} \eta \) η 2 \({\eta ^{2}} e^{-{\Delta t \over \tau }}\)
Advective CVM
ACVM(τ,η,μ) μ - advective velocity (2D - dist/time) eq. A6 η 2+|μ|2 \(|\boldsymbol {\mu }|^{2} + \eta ^{2} e^{-{\Delta t \over \tau }} \)
Rotational CVM
RCVM(τ,η,ω) ω - angular speed (radians/time) - η 2 \(\eta ^{2} e^{-{\Delta t \over \tau }} \cos (\omega \Delta t)\)
Rotational-advective CVM
RACVM(τ,η,ω,μ)   - η 2+|μ|2 \(|\boldsymbol {\mu }^{2}| + \eta ^{2} e^{-{\Delta t \over \tau }} \cos (\omega \Delta t)\)