simm.mba {adehabitatLT}  R Documentation 
This function simulates an Arithmetic Brownian Motion.
simm.mba(date = 1:100, x0 = c(0, 0), mu = c(0, 0), sigma = diag(2), id = "A1", burst = id, proj4string=CRS())
date 
a vector indicating the date (in seconds) at which
relocations should be simulated. This vector can be of class

x0 
a vector of length 2 containing the coordinates of the startpoint of the trajectory 
mu 
a vector of length 2 describing the drift of the movement 
sigma 
a 2*2 positive definite matrix 
id 
a character string indicating the identity of the simulated
animal (see 
burst 
a character string indicating the identity of the simulated
burst (see 
proj4string 
a valid CRS object containing the projection
information (see 
The arithmetic Brownian motion (Brillinger et al. 2002) can be described by the stochastic differential equation:
dz = mu * dt + Sigma dB2(t)
Coordinates of the animal at time t are contained in the vector
z(t)
. dz = c(dx, dy)
is the increment of the
movement during dt. dB2(t)
is a bivariate brownian Motion (see
?simm.brown
). The vector mu
measures the drift of the
motion. The matrix Sigma
controls for perturbations due to the
random noise modeled by the Brownian motion. It can also be used to
take into account a potential correlation between the components dx
and dy of the animal moves during dt (see Examples).
An object of class ltraj
Clement Calenge clement.calenge@ofb.gouv.fr
Stephane Dray dray@biomserv.univlyon1.fr
Manuela Royer royer@biomserv.univlyon1.fr
Daniel Chessel chessel@biomserv.univlyon1.fr
Brillinger, D.R., Preisler, H.K., Ager, A.A. Kie, J.G. & Stewart, B.S. (2002) Employing stochastic differential equations to model wildlife motion. Bulletin of the Brazilian Mathematical Society 33: 385–408.
simm.brown
, ltraj
,
simm.crw
, simm.mou
suppressWarnings(RNGversion("3.5.0")) set.seed(253) u < simm.mba(1:1000, sigma = diag(c(4,4)), burst = "Brownian motion") v < simm.mba(1:1000, sigma = matrix(c(2,0.8,0.8,2), ncol = 2), burst = "cov(x,y) > 0") w < simm.mba(1:1000, mu = c(0.1,0), burst = "drift > 0") x < simm.mba(1:1000, mu = c(0.1,0), sigma = matrix(c(2, 0.8, 0.8, 2), ncol=2), burst = "Drift and cov(x,y) > 0") z < c(u, v, w, x) plot(z, addpoints = FALSE, perani = FALSE)