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Scilab help >> Signal Processing > filters > system

# system

observation update

### Calling Sequence

`[x1,y]=system(x0,f,g,h,q,r)`

### Arguments

x0

input state vector

f

system matrix

g

input matrix

h

Output matrix

q

input noise covariance matrix

r

output noise covariance matrix

x1

output state vector

y

output observation

### Description

define system function which generates the next observation given the old state. System recursively calculated

```x1=f*x0+g*u
y=h*x0+v```

where `u` is distributed `N(0,q)` and `v` is distribute `N(0,r)`.

### Examples

```// initialize state statistics
// (mean and err. variance)
m0=[10 10]';
p0=[2 0;0 2];
// create system
f=[1.1 0.1;0 0.8];
g=[1 0;0 1];
h=[1 0;0 1];
// noise statistics
q=[.03 0.01;.01 0.03];
r=2*eye(2);
// initialize system process
rand("seed",2);
rand("normal");
p0c=chol(p0);
x0=m0+p0c'*rand(ones(m0));
yt=[];
//initialize kalman filter
xke0=m0;pk0=p0;
// initialize err. variance
ecv=[pk0(1,1) pk0(2,2)]';
[x1,y]=system(x0,f,g,h,q,r)```
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