Dear Maximilian,

As in any problem, linearization gives you a first approximation and leads to simpler expressions and procedures. How far the approximation can go to give you sufficiently good results for the actual system, is anyone's guess.

Extended Kalman Filter uses the nonlinear model and so, it is more precise, of course. However, requires using more complex expressions.

It is always good to play a bit (or more) with some specific applications to get some feeling.

Best,

Itzhak

A lay answer:

From a theoretical point of view, I don't think that the error-state space gives you any advantage. I think people working in orientation problems use them for practical reason as they want to keep the meaning of their states. You may want to read this document:

http://www.iri.upc.edu/people/jsola/JoanSola/objectes/notes/kinematics.pdf

(This report provides this reference: Conference Paper Extended Kalman Filter vs. Error State Kalman Filter for Air...

which could provide the information that you are looking for!)

Note that noises are included to cope with issues in the model. For example, if you model a fusion KF for gyro and accelerometer, you can assume that the state representing the bias is constant, and then you are a noise to allow this state to change. So you can tune easily the filter because your Q matrix have a clear meaning with respect to the behaviour of the Kalman filter.

Regarding linearising the dynamics of the states, it seems silly to me, as evolving Ax_k+Bu_k will have very similar computational cost to evolving f(x_k,u_k). It may exist cases where it provides some practical advantage, but I have not found any so far.

Dear Maximilian,

In Linearized Kalman Filter nominal estimate of state is used to define Jacobian matrix of the dynamic model function f as F and Jacobian matrix of the measurement function h as H. But in EKF, corrected state estimate is used in each step for linearization.

With the time, error due to linearization will grow in LKF. Using updated state estimates in each step it is likely to obtain more accurate results.

I drew a simple representation of both.

Hope it helps,

Good Luck

I would add that Kalman Filter has initially been developed for LTI systems. When the system is nonlinear, this could imply many things and very complex. Extended Kalman Filter works with the actual nonlinear system and so, although for the tracking error the representation is linear, it ends with better estimations

Some people on RG have recently "discovered" and old paper of mine of 1978 (and I added it under my name on RG), where I have been using the Extended Kalman Filter with pretty good results for tracking and prediction systems.

However, even only for our general education, it is worth mentioning that the general nonlinear filter for nonlinear systems can be much more complex.

Thanks for the various answers, it helped me a lot!

Greetings,

Max

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