I have two questions on the quaternion which I hope could be clarified.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Q1)

The multiplicative error quaternion has equation:

q_aposteriori = [δqτ √(1-δqτ * δq)]τ χ q_apriori

I have some data where δqτ * δq > 1 and thus √(1-δqτ * δq) give me an imaginary number, which is supposed to be the scalar fourth component of quaternion. Am I doing anything wrong here, and how can I solve it?

Q2) For numerical integration, can I just integrate quaternion like I will normally do with dynamic equations?

as per usual propagation:

x = x + w*dt

for quartenion:

q = q + qdot*dt

then normalize(q)

is this correct?

2. Relevant equations

The multiplicative error quaternion has equation:

q_aposteriori = [δqτ √(1-δqτ * δq)]τ χ q_apriori

where:

q_aposteriori = quartenion after update

q_aposteriori = quartenion before update

τ = transpose

χ = quaternion multiplication

3. The attempt at a solution

as above

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Quartenion and Kalman

**Physics Forums | Science Articles, Homework Help, Discussion**