How to compute equation (38)?

[LeisureLei]

I am confusing how to compute equation (38) in "Kalman Filters on Differentiable Manifolds" even though I figure out the method in "The iterated kalman filter update as a gauss-newton method". They have different loss functions.

[LeisureLei]

Delta x_j is ok. But how to compute covariance P?

[Joanna-HE]

Using the one-order Taylor expansion to represent x_{k+1|k+1}^j through the value of x_{k+1|k}, then the covariance projection could be obtained.

[zuowei1998]

how to compute Delta x_j? thanks

[youzhenxing]

x_{k+1|k

Using the one-order Taylor expansion to represent x_{k+1|k+1}^j through the value of x_{k+1|k}, then the covariance projection could be obtained.

Hi,Joanna, I read the paper, and also have questions about the computations of J^j_{k+1}, just as you said, use the Taylor expansion, in that way, I found J^j_{k+1} = A(x_{k+1|k}) instead of J^j_{k+1} = A(\delta x^j_{k+1|k+1}), is there any misunderstanding? thanks.

[Joanna-HE]

Sorry for the late reply,

[Joanna-HE]

how to compute Delta x_j? thanks

Delta x_j = x_{k+1|k+1}^j \boxminus x_{k+1|k} as shown in the equation of calculating J_{k+1}^j.