T3

### robust estimator of the direction cosine matrix

#### Replies

• new diagram

IMG_20160422_125659.jpg

https://storage.ning.com/topology/rest/1.0/file/get/3702813223?profile=original
• new draft

• Dear

I can understand it now.

Thanks

for example. the x-axis has the whole Centrigual acceleration(Vector C). the Gravity works in z-axis (Vector G)

under this condition. the Accelerometer will output the result  Vetor  A = C + G

so if we want to get the G, we need A-C,but the Eqn.26 shows G= A+C

may I know the reason?

• sorry for the stupid question .

I have known it .

the sign is negative if exchange the cross product of them

• Dear  Bill

quote:

the bottom row of the direction cosine matrix should be aligned with the vector produced by the accelerometers

May I know the reason why these two vectors should be aligned ?under what condition?

because,from the earth frame. the plane also can own an acceleration other than the Z-axis(earch reference). it is a normal case i think.

so i am confused why we know it is a gyro drift when there two vectors are not aligned

maybe gyro has no drift ,and currently the plane is accelerating in some direction .therefore

the accelerateometer's output is also not aligned to earth Z-axis

Thanks

• Dear Bill

in the paper, we got "a convenient matrix form" in Eqn 17

we know the new "DCM“ is not a definite  DCM for its magnitude is not 1 ,and each vector member is not orthogonality.so the next step is "Renormalization"

In my understand ,although we get a new definite DCM after renormalization,but it is still an approximate one  to the  true accurate dcm. anyway this renormalized DCM is acceptable in such a little time slice(eg: 0.02s)

However, I wonder  that there will be an apparent error(or deviation) after a long time 's calculation.

(we assume that the gyro output is very accurate)

I mean every renormalization process will create deviation,and these deviation will accumulate into a "big" DCM error.

Is it possible?

sorry for my poor english.

Thanks.

• Hi Bill

I have been trying to write a matlab code using the dcm imu theory. i had one question though. Is yaw angle and heading of the aircraft same? As in isnt it possible for and aircraft to point in one direction and have an overall heading in another... if so is there anyway to find the heading from the pitch, roll and yaw?

Regards

Naomi

• Hi,

In the DCM, the accelerometers used for the pitch-roll compensator, and the GPS used for the roll compensator. Does anyone know why the GPS did not use for the pitch-roll compensator?

Best regards,

Don

• I’m confused with the effectiveness and accuracy of the proposed direction cosine matrix method.

Without doubt, if the UAV is not aclinic(level), the forward acceleration is measured by accelerometer, together with the gravity component. Unless the UAV is stationary, The horizontal attitude angle determined by the output of accelerometer is not believable. Of course, the azimuth angle obtained by GPS is also not believable. You known, the frequency of GPS signal is low, the azimuth will be vibrated, and the accuracy is too low to use.

I guess the core of this method is using the attitude reference to compute the gyro errors. So, I think it is better to equip a magnetometer.

The IMU computed attitude is limited by IMU errors(Gyro errors bias and Accelerometer bias errors). During motion, these errors can be estimated and compensated by EKF. I’d like to know the accuracy of the proposed method with attitude reference obtained by GPS and accelerometer. Of course, the accuracy equipped a magnetometer.

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