# GPS/INS integration using kalman filter

Started by July 20, 2007
```Hi

I like to integrate GPS and INS using kalman filter to predict the
position of a vehicle.

first of all i like to use GPS sensor readings with kalman filter .
I have read lot of research papers for that purpose but I donot know how
to use real time data of GPS sensor in the kalman filter measurement
equation.

My question is that where i have to put the readings from the gps sensor
in measurement equation i.e where to put numerical values from the sensor
in the measurement equation.how these values make sense.
zk=Hxk+wk
also i like to ask as how can i determine the state transition matrix F
and observation matrix H for a particular application.

also how can i determine the measrement noise matrix from the gps sensor.

thanks and regards

```
```On Fri, 20 Jul 2007 09:31:37 -0500, mjukhan wrote:

> Hi
>
> I like to integrate GPS and INS using kalman filter to predict the
>
> position of a vehicle.
>
> first of all i like to use GPS sensor readings with kalman filter .
> I have read lot of research papers for that purpose but I donot know how
>
> to use real time data of GPS sensor in the kalman filter measurement
>
> equation.
>
> My question is that where i have to put the readings from the gps sensor
>
> in measurement equation i.e where to put numerical values from the sensor
>
> in the measurement equation.how these values make sense.
> zk=Hxk+wk
> also i like to ask as how can i determine the state transition matrix F
>
> and observation matrix H for a particular application.
>
> also how can i determine the measrement noise matrix from the gps sensor.
>
> thanks and regards

Have you studied up on Kalman filters at all?  "Optimal State Estimation:
Kalman, H-infinity, and Nonlinear Approaches" by Dan Simon is a good place
to start.  He's got a web site at http://academic.csuohio.edu/simond/.

Do you mean that you want to take the output of a non-GPS aided INS
(inertial nav system) and correct it with the GPS signals, or are you going
to combine an IMU (inertial measurement unit) with GPS to form an INS?
The latter case will be far easier, because while an INS does have an
embedded IMU, it obscures the IMU data pretty thoroughly.

No matter what, you will be getting IMU data at a much higher rate than
GPS data.  This means that your Kalman filter will need to be time
varying; you'll have one set of transition, input and output matrices to
use when the data comes from the IMU only, and another one to use when you
have IMU data and GPS data.  If your IMU data isn't synchronized with the
GPS data you may also have to do some interpolation on the fly.

The AIAA (www.aiaa.org) has a book out on this subject.  It'll probably
have the closest thing you can get to a recipe on the subject.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html
```
```>Hi
>
>I like to integrate GPS and INS using kalman filter to predict the
>position of a vehicle.
>
>first of all i like to use GPS sensor readings with kalman filter .
>I have read lot of research papers for that purpose but I donot know how
>to use real time data of GPS sensor in the kalman filter measurement
>equation.
>
First question is what kind of GPS/INS integration are u using. Loosely
coupled, tightly coupled or ultra tightly coupled integration. The later
two integrations gives better results but your INS should be able to accept
GPS measurments (carrier and beat pahse, or I and Q in the ultra coupled
case).

>My question is that where i have to put the readings from the gps sensor
>in measurement equation i.e where to put numerical values from the sensor
>in the measurement equation.how these values make sense.
>zk=Hxk+wk

This also follow the ingeration part, talking about loosely coupled. Your
measurement is basically:
Z = GPS postion - INS measurment
this occurs at a 1PPS rate ( the rate the gps position is measured).
To say this in a very simple way, your INS kalman predicts the position of
the rover at a rate f_s from 50Hz up to 2500Hz, and the gps postion is
received at f_GPS = 1 Hz. When the gps signal is there you feedback the
error corrections so ur INS kalman compensates the bias and other errors
that results from long term predicitions.

As Tim said, Synchronization in this case is something u have to worry
about when u need high precision and u have high dynamics in ur system.

>also i like to ask as how can i determine the state transition matrix F
>and observation matrix H for a particular application.
>
>also how can i determine the measrement noise matrix from the gps sensor.
>
>thanks and regards
>
>
>
>
>
>
```