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Imagine you are solving this recursive least squares problem $(x-x_0)^T \Pi_0^{-1}(x-x_0) + || H_{i} x - Y_i ||^2$ at each step $i-1$, you already have a solution $\hat{x}_{i-1}$ to $(x-x_0)^T \Pi_0^{... • 116 0 votes ### Kalman Filter and Generalized Least Squares It is not an apples to apples comparison. The Kalman Filter is a Bayesian estimator, minimizing the MMSE Risk Function, while the Least Squares is a Parametric estimator. Indeed, one can show that the ... • 20.2k 2 votes ### Initial Rest Condition in Linear Systems This is a matter of viewpoint. Both views are correct if one clearly defines what constitutes the system and what constitutes the input. If we say that we have an input signal$x(t)$, and we consider ... • 91.3k 0 votes ### Why$y[n] = x[-n]\$ is not time-invariant?

The point is even if the result is the same in both when the input is x[n-k] and when the output is y[n-k], the output x[-n+k] is shifted to the left, whilst the input is shifted to the right. So if ...
Accepted

### Kalman Filter to enforce constraints or norm penalization on kalman gain

What you're after is called Non Negative Least Squares. In general, it doesn't have a closed form solution. Since you have a good starting point, I'd use few iterations of Projected Gradient Descent. ...
• 20.2k
Accepted

### Show that a sinusoidal is an eigenfunction of an LTI system

Everything you did is correct. The problem is that you can't prove that sinusoids are eigenfunctions of LTI system because they aren't. What you mean is that if the input signal to a real-valued LTI ...
• 91.3k