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In short, yes: the key phrase that you want to search on is optimal smoothing. You didn't ask how to do it, and the "how" is chapter-length, in a good book about Kalman filtering. So I'm not going to try to describe that. In general hand-wavy terms, though, optimal smoothing takes into account that if you know both past and future values of a ...

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If you want to filter signals with an IIR filter, it's best to use the "standard" filter function of the language. That would be filter() for Matlab, lfilter() for Python and for R I believe this is signal::filter(). All of these functions allow you to specify the initial state. The exact details of how this is done, depends on the specific ...

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First, typically when you're exerting a force on something and getting a position, the acceleration varies instantaneously with force. A more or less universal equation of motion for a single-axis linear system would be $m \ddot x = f_v(\dot x) + f_p(x)$. For a mass-spring-damper system, it'd be $m \ddot x = b \dot x + k x$. So you can easily express that ...

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As you pointed out, there are many state-space realizations of one particular transfer function. The reason is that a transfer function only represents the input-output behavior of a system (observable and controllable dynamics) and not the internal states. That being said, you can directly write state-space realizations from a transfer function with the so-...

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