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Inaccurate wording in documentation of lqe and dlqe #1183
Description
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.
Activity
murrayrm commentedon Nov 9, 2025
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:
Having said that, I find the wording "expected squared error" to be a bit odd and would support just saying "mean squared error".