State-space with added noise?

Hi,

I'd like to simulate a state-space model where I add some process noise (to states) and measurement noise (to measurements). How do I do this in Simulink?

The system mathematically would be:

x_derivative = Ax+Bu+v (v is added noise to states)

y = Cx + w (w is added noise to measurements).

How do I add the noise vectors v and w to the basic state-space block found in Simulink library?

Or is the only way to calculate the state-space system inside a Matlab function block and add the noise there?

[Stefan Raab]

I think it is better to build up the state space model by yourself, then you can add arbitrary noise. The Gain block and the Integrator block will help you with this. Let me know if you need more information on how to do this.

[Joonas]

Hello Stefan,

let's say that I have used a state-space block now in Simulink and I want to add the process noise and measurement noise to this model.

Am I correct if I say that measurement noise can be simply added to the output of this State-space block (right after the block), but process noise is something that I cannot add to the state-space block?

What would be your solution for replacing my state-space block? A matlab function block, or just a state-space model built with basic block diagram algebra? Like here: https://en.wikipedia.org/wiki/State-space_representation

(See figure of state-space representation in "Linear systems" section.)

When using matlab-function block for state-space: I add the noise in the matlab script to the states and to the measurements.

When using state-space represented with basic blocks: I add the noise to the signal that carries the state information (x) and to the signal that carries the measurements (y).

Right?

[Stefan Raab]

Hello Joonas,

1) Yes, you could add the measurement noise simply to the output of the statespace block i suppose and I also think that there is no opportunity to add the process noise directly in the state-space block.

2) You found the right link. I would model the system like this. But if you have the equation x_derivative = Ax+Bu+v, you have to add the noise to x_derivative, not to x.

Kind regards, Stefan

[Joonas]

Hi Stefan,

thanks for reminding me for this. Exactly, the noise is added to the x_derivative as the state-space representation says. Good, I think now that I can handle this correctly. Thanks a lot for your help!