## Inertial Navigation Integration FIlter

## Inertial Navigation Integration FIlter

(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.

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.

## RE: Inertial Navigation Integration FIlter

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## RE: Inertial Navigation Integration FIlter

## RE: Inertial Navigation Integration FIlter

Is this for school?

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## RE: Inertial Navigation Integration FIlter

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?

## RE: Inertial Navigation Integration FIlter

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## RE: Inertial Navigation Integration FIlter

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?

## RE: Inertial Navigation Integration FIlter

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## RE: Inertial Navigation Integration FIlter

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?

## RE: Inertial Navigation Integration FIlter

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## RE: Inertial Navigation Integration FIlter

Thank you

## RE: Inertial Navigation Integration FIlter

TTFN

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Chinese prisoner wins Nobel Peace Prize

## RE: Inertial Navigation Integration FIlter

TTFN

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Chinese prisoner wins Nobel Peace Prize

## RE: Inertial Navigation Integration FIlter

Why is everybody asking me if it is for school? It shouldn't be?

## RE: Inertial Navigation Integration FIlter

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.

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## RE: Inertial Navigation Integration FIlter

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?

## RE: Inertial Navigation Integration FIlter

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

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## RE: Inertial Navigation Integration FIlter

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