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 | \(|\boldsymbol {\mu }^{2}| + \eta ^{2} e^{-{\Delta t \over \tau }} \cos (\omega \Delta t)\) | |