Register to reply

Sampling from transition equation (state space model)

by kasraa
Tags: non linear, sampling, state space
Share this thread:
kasraa
#1
Nov13-10, 02:42 AM
P: 16
Hi.

Consider the following state space equation
[tex]x_k = f(x_{k-1},v_k)[/tex]
where f(.) is a nonlinear function and v_k is a white Gaussian noise (independent of state).

I want to generate samples according to [tex] p(x_k | x_{k-1} = x_{k-1}^i) [/tex] for a particular [tex]x_{k-1}^i[/tex]. I've seen people generate samples [tex] v_k^j [/tex] from [tex] p(v) [/tex] (which is a Gaussian) and consider [tex] x_k^{(i,j)} = f(x_{k-1}^i,v_k^j) [/tex] as samples generated according to [tex] p(x_k | x_{k-1} = x_{k-1}^i) [/tex].
I can understand the intuition behind this approach, but can you suggest any mathematical proof?

Thanks,
K.
Phys.Org News Partner Science news on Phys.org
'Smart material' chin strap harvests energy from chewing
King Richard III died painfully on battlefield
Capturing ancient Maya sites from both a rat's and a 'bat's eye view'

Register to reply

Related Discussions
Convert transfer function model to state space model Engineering, Comp Sci, & Technology Homework 0
Help constructing state-space model of a system Engineering, Comp Sci, & Technology Homework 1
Kalman, state-space model Engineering, Comp Sci, & Technology Homework 1
State Space Model HW Engineering, Comp Sci, & Technology Homework 0
Genral state space model - runge kutte Differential Equations 6