add some comments

    const vec4_t dq = getF(q)*((0.5f*dT)*we);

    x0 = normalize_quat(q + dq);

    // P(k+1) = F*P(k)*Ft + G*Q*Gt

    // P(k+1) = Phi(k)*P(k)*Phi(k)' + G*Q(k)*G'

    //

    // G = | -I33    0 |

    //     |    0  I33 |

    //

    //  Phi = | Phi00 Phi10 |

    //        |   0     1   |

    //

    //  Phi00 =   I33

    //          - [w]x   * sin(||w||*dt)/||w||

    //          + [w]x^2 * (1-cos(||w||*dT))/||w||^2

    //

    //  Phi10 =   [w]x   * (1        - cos(||w||*dt))/||w||^2

    //          - [w]x^2 * (||w||*dT - sin(||w||*dt))/||w||^3

    //          - I33*dT

    const mat33_t I33(1);

    const mat33_t I33dT(dT);

    const mat33_t wx(crossMatrix(we, 0));