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I built EKF and UKF SLAM algorithms. The problem is that I expected to see a difference because of the more precise approximation of the system in the UKF.

Here's a screenshot from the estimated path from both filters [sorry about the German]:

enter image description here

As you can see, the differences are very minor and sum up to an equal performance of both filters within the mean errors for every estimated state. I thought increasing the system noise for a bigger uncertainty would make the advantages of the UKF clearer but it didn't make a difference.

UKF Parameters: $\alpha$: 0.01, $\kappa$: 0, $\beta$: 0.

My question is, what could be the reason for the similiar results of both filters and how can we enhence the UKF performance?

Thanks.

Nvm, the result improved with UKF parameters from a backup. The parameters where to low. New Parameters: $\alpha$: 0.5, $\kappa$: 25, $\beta$: 2.

New Result enter image description here

Mean error X-Position

EKF 0.7572

UKF 0.2501

mean error Y-Position

EKF 0.4535

UKF 0.1708

Mean error orientation

EKF 0.0112

UKF 0.0083

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The EKF is a first-order approximation, which is achieved by linearizing the system about the current state estimate (i.e., the mean). In some cases, the EKF is not stable due to nonlinearities. For example, if the system is highly nonlinear, then the EKF might not work well.

In contrast, the UKF uses the unscented transform , which is a function to estimate a nonlinear transformation applied to a probability distribution. Ideally, the exact nonlinear transformation would be used, but often is not possible or not practical.

The main benefit in using the UKF instead of the EKF is to handle nonlinearities, but the EKF is often less computationally expensive as the Jacobians can be computed analytically offline. If the system is linear, the UKF provides no benefit (as far as I know), and if the system is close to linear, the result of the EKF and UKF will be similar.

I suspect that the linearization is adequate, so the UKF just doesn't provide much benefit.

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  • $\begingroup$ Yeah, thank you for your answer. As i was able to fix my problem i think i know what caused the "missing" improvement from the ukf. The parameters of the UKF influence the sigma point spread and as i had very low values i think the sigma points where very close to each other and to the mean. This resulted in an approximation of the system which was very close to the one in the EKF. Atleast that´s my take on it. You probably knew this but i wanted to write it down for the people who maybe have the same problem. $\endgroup$
    – muller135
    Mar 23, 2021 at 10:30
  • $\begingroup$ Great. Glad you found the issue and shared. Yes, the spread of the sigma point affect the result. I’m not on expert on UKF, so I don’t have much suggestion on selecting UKF parameters, but seems you found a good choice. Best of luck! $\endgroup$
    – Ralff
    Mar 23, 2021 at 22:37

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