How to position and velocity predict for ekf using imu and gps

Hi, jimit here, I have IMU, GPS and magnatometer, I successfully build attitude estimations quaternion using ekf, now I want to build ekf for position estimations, but I have some questions, I am using ned reference frame,

Please correct me if I doing wrong to predict velocity and position.

I have Accel vector x = [ ax, ay, az], gravity vector g= [ 0,0, -9.807] , rotation matrix = R

Velocity = prevVelocity + (x * R + g ) * dt

Position= prevPosition + 0.5 * ( prevVelocity+ Velocity) * dt

My equation are right?

Note that when sensor at rest I get [0.0, 0.0, 9.81] approximately,

My equation are right or wrong.

One last question how to get measurement noise of GPS in ekf? Are they in datasheet ?

Please help me, I am stuck here last 5 days, I ask you because I build multirate ekf, my GPS has 10hz sample time where IMU has 500hz sample time.

This question comes up about once a week on the forum, and to my knowledge, no one has reported success in obtaining useful position and velocity measurements from a consumer grade IMU. They are simply too inaccurate.

This article explains one of the major problems.

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