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(OP)
Hello,
I am trying to create a filter that can integrate inertial measurements with GPS measurements. My inertial sensors are a yaw axis gyro, an odometer, and possibly a 3axis accelerometer.
Could you please help me with some guidance? I have read papers, articles and books on the subject but I am still a little confused.
I consider the acceleration constant, so I have a state vector x=[E N v_E v_N a_E a_N], E and N are the positions in NED coordinate system, v_E and v_N are the speed on each axis, and a is the acceleration on each axis
The measurement vector z is [E_GPS N_GPS E_DR N_DR a_E a_N] where E_GPS and N_GPS are the coordinates obtained from the GPS receiver and E_DR and N_DR are the coordinates obtained from the inertial sensors through dead reckoning, and a is the acceleration obtained from the accelerometer.
F, the transformation matrix is: [1 0 dt 0 (dt^2)/2 0; 0 1 0 dt 0 (dt^2)/2; 0 0 1 0 dt 0; 0 0 0 1 0 dt; 0 0 0 0 0 1];
H, the measurement matrix is: [1 0 0 0 0 0; 0 1 0 0 0 0 ; 1 0 0 0 0 0; 0 1 0 0 0 0; 0 0 0 0 1 0; 0 0 0 0 0 1],
Does it make any sense so far? Should I chose a different state vector?
My problem is that I don't know, for this system how can I determine the process noise covariance and measurement noise covariance.
Can you give me some indications in that direction?
Thank you very much.

The noise is not a function of the solution method; it's a function of the process and the sensors.  Your Kalman filter does not predict nor alter the actual process noise; you need to know what it is ahead of time.

(OP)
So I should introduce an estimate in the equations the measurement and process noise? Like z=Hx+w (where w is the measurement noise) and x(+)=Fx(-)+v (where v is the process noise)?

Is this for school?

(OP)
It's not for school. It's a project i'm trying to do im my spare time. So I'm far from the topic? Can you give me some guidance please, so I can clear some of the confusion?
Im trying to integrate the output from an IMU(3 axis gyro, yaw axis accelerometer and odometer if needed) with GPS.
Where do I go wrong in the system described before?

The noise estimates are what you put in the covariance matrix.  I don't recall, offhand, how the process noises are added.

(OP)
The process noise is added to the state update equation:
x(+)=x(-)F+w (w process noise)
and the measurement noise is added to the measurement equation:
z=Hx+v (v measurement noise)
My question is how to determine the values of v and w?
You determine the values experimentally, analytically or you just assume some value by trial and error?

Either of the first two.  You usually need to "tune" the filter after fabrication to get the "right" values.

(OP)
Thx for the help. :)
For a Inertial system with a gyro and an odometer, should I introduce more states then [position velocity acceleration]?
Should I introduce in the state vector also the heading, gyro and odometer bias? and i get a state vector like [position velocity acc heading gyro_bias odo_bias] ?
Or in case I don't introduce the bias from the odometer and gyro, they will be part of the measurement noise, and they only downside is that I cannot correct the sensors?

Probably, it's a trade between computational throughput and accuracy of the model.

(OP)
Should also the heading be part of the state vector? How can I determine what is vital to be in the state vector and what can be skipped?
Thank you

Well, do you need to know the heading?  How does one navigate without heading?

Is this for school?

(OP)
No, it's not for school. I graduated 2 years ago from university.
Why is everybody asking me if it is for school? It shouldn't be?

Sorry, I forgot I already asked.  The fact that you don't know what to do with heading raised a red flag.

Student postings are not allowed on this site.  This site is supposed to be for engineering professionals asking work related questions.  Some leeway is allowed for cross-discipline work.

(OP)
I'm asking if the heading needs to be part of the state vector as I saw different approaches that did not use it.
And my experience with Kalman filters doesn't go too far. I have read about it but it's the first time I'm trying to implement sth like this.
So then a better state vector would be: [position speed acceleration heading gyro_bias odometer_byas]
or should i leave out the acceleration?

If you have no other attitude information, then why do you have heading and gyro_bias?  Seems like you picked a bigger problem that necessary for a first project.

A relatively complete set might be:
3 positions
3 velocities
3 accelerations
3 angle
3 angle rates
3 angle accelerations
same with biases

36 states is not unheard-of

Quote (IRstuff):

36 states is not unheard-of
And how...!

If you're adding in GPS, you'll want:
position
velocity
clock bias
clock drift
wheel speed scale factor (I'm assuming this is vehicle-based)
compass offset

Add all of that into what IRstuff listed and you have a pretty significant-sized matrix.  Luckily, a large percentage of the coefficients are zero (with the majority of non-zero coefficients along the diagonal), so the calculations are faster than one would expect from a typical 30-coefficient+ matrix.

Dan - Owner
http://www.Hi-TecDesigns.com

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