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flor1an42

opened on Oct 31, 2025

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In the documentation of lqe and dlqe, it states:

produces a state estimate x_e that minimizes the expected squared error using the sensor measurements y.

From my understanding of theory, this is quite inaccurate/imprecise.
A better wording would be:

produces a state estimate x_e that minimizes the generalized variance of x - x_e using the sensor measurements y.

Source:
https://en.wikipedia.org/wiki/Generalized_variance
https://arxiv.org/pdf/2103.07275

Another wording would be that it minimizes the trace of the covariance matrix x - x_e,
but thinking in a generalized variance is more catchy.

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1. murrayrm commented on Nov 9, 2025

   

   murrayrm

   on Nov 9, 2025

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   My sense is that using the term "generalized variance" is a bit more technical detail than we need here. The standard estimation setup is to minimize the mean squared error (= trace of the covariance matrix), so I think using that wording is fine for the summary. We could add something in the notes section about the fact that this is equivalent to minimizing the trace of the covariance matrix.

   Two examples of the "minimize the mean squared error" wording:

   • Wikipedia entry for the Kalman filter
   • FBS 2e, Theorems 8.4 (discrete) and 8.5 (continuous)

   Having said that, I find the wording "expected squared error" to be a bit odd and would support just saying "mean squared error".
2. murrayrm

   self-assigned this

   on Nov 9, 2025
3. murrayrm

   added

   quickfix

   documentation

   on Nov 9, 2025
4. murrayrm

   closed this as completedin #1219on Aug 14, 2026

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