A Power Growth State-Space Model as an Extended Kalman Filter Example

Summary

The document presents a learner’s request for a scalar example of the extended Kalman filter, motivated by difficulty implementing a nonlinear power growth state-space model. It first gives a local-level observation equation, then asks how to estimate a model in which the latent level evolves through a power transformation involving another state. This makes the central learning topic the application of nonlinear state estimation to a simple scalar model.

The document provides the proposed equations and describes the author’s limited programming experience, but it does not include an answer, derivation, implementation, or evidence that the model can be estimated as written. In particular, the displayed evolution equation for the auxiliary state appears to use the current state on both sides, so its intended transition may need clarification before constructing an EKF. The material is therefore useful for identifying a modeling question, but it does not teach an EKF solution or establish that the proposed equations are valid.

Key ideas

• The document asks how to use an extended Kalman filter for a scalar nonlinear state-space model.
• Its proposed power growth model makes the latent level transition nonlinear in an auxiliary state.
• The author contrasts this request with a local-level model that they had already implemented.
• No EKF derivation, worked example, or implementation guidance is supplied.
• The auxiliary-state transition as written may need clarification before estimation.

Tags

# Example Scalar Model Extended Kalman Filter


# Example Scalar Model Extended Kalman Filter












I have a simple question. I think not a question is, is a request. This month I have been studying how to understand and implement the Kalman filter algorithm for simple models such as the local level.

$ Y_t = \mu_t + \epsilon_t$

$\mu_t = u_{t-1} + \gamma_t$

I managed to implement this model (i don't have ability in programming).

Now I'm studying the part of Extended Kalman Filter.

And I'm having trouble implementing the model below using the EKF:

- Power Growth Model:

$ Y_t = \mu_t + \epsilon_t$

$\mu_t = \mu_{t-1}^{(v_{t-1}+1)} + \gamma_t$

$v_{t} = \phi v_{t} + \eta_t$

It was then that I thought there would be a scalar model example to estimate using the EKF, with only $\mu_{t}$ and some nonlinear form?

I have not found Scalar models as an example of use for EKF.

Is there any alternative for the local level model that i could use the EKF to estimating?

Any suggestion?

Thanks, Laorie.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.