Dear All,

An objectum is moving on straight line with changing speed and accelars what we can not measure. We can measure the position and time. Our measurement system is no correct, the measured values have noises. We know the initial values:
s = 0
v = 20 m / s
a = 5 m / s ^ 2
We do not know how velocity and acceleration will change in the future.
The task is to estimate the position of the objectum in all time with the Kalman Filter.

Best Regards,
Zoltan

input:
time;position
0;0,00
0,1;1,65
0,2;3,86
0,3;5,91
0,4;8,46
0,5;10,89
0,6;12,83
0,7;15,02
0,8;17,58
0,9;19,36
1;22,76
1,1;24,41
1,2;27,08
1,3;31,43
1,4;32,52
1,5;35,76
1,6;39,08
1,7;41,44
1,8;44,05
1,9;46,48
2;50,28
2,1;51,36
2,2;55,76
2,3;57,32
2,4;62,06
2,5;65,56
2,6;67,66
2,7;71,98
2,8;74,51
2,9;76,61
3;80,02

Sorry, but this is an economics forum. People will typically not be able to help you with general questions like this one. You need to bring your problem into state-space form. That is, you need to identify the states (I guess velocity and acceleration) and then describe how those two are linked over time (state transition equation). Once you know that, you need to map these state into the observed location (observation/measurement equation)