How to compute equation (38)?

Question

How to compute equation (38)?

LeisureLei opened this issue 3 years ago · 6 comments

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.

Answer 1 · 2021-08-18T07:45:16.000Z

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

Answer 2 · 2021-09-20T10:52:11.000Z

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.

Answer 3 · 2021-11-16T09:47:15.000Z

how to compute Delta x_j? thanks

Answer 4 · 2021-12-12T05:03:20.000Z

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.

Answer 5 · 2022-01-05T06:01:40.000Z

Sorry for the late reply,

Answer 6 · 2022-01-05T06:03:37.000Z

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.