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Adaptive Filters are called "Adaptive" when they can adapt to changes in data. In the filters you mentioned above, which are part of the Linear Filters family the property means their coefficients are changing over time. Linear Filters are basically weighing and summing the data. For instance, given no prior information on data you may want to have exact ...

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[20180801: Stats update at the end] Units matter, when they differ (I love the rhyme) If they are commensurable, all values can be ranked, ordered, pairwise operated. While products of data with different units can make sense, their sum of difference is meaningless. Kilometers per second make sense, but what is "2 kilometers minus one second"? Homogeneity ...

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Most certainly yes. The units of the states are reflected in the state covariance, and state error covariance. The units of the measurements propagate throughout the filtering and prediction steps. Should units be appropriately scaled? Numerical accuracy typically benefits from appropriate scaling

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actually a covariance matrix can have negative values off the diagonal. variables can be negatively correlated, but the diagonal terms are variances which must be positive. The update you show can be a problem which is why updates of $P^{-1}$ are preferred.

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from the generality of your question then yes you can design a Kalman filter which would accept the target position as the only measurement possibly corrupted with noise. Then the Kalman filter will try to estimate the true position of the target based on the noisy position measurement and the assumed motion model. Hence in effect the Kalman filter would ...

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Absolutely! Every (extended / unscented) Kalman filter starts with a signal model. The state update equation in the second image is a very different beast from the little you show of the first model in the first image. Without seeing the complete model, it's hard to say whether it's all correct, but if the signal models are different, then certainly the ...

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Your mistake is that $\mathcal Z$ does depend on process noise. It's just a bit more obscure than the linear filter. $\mathcal Z$ is the projection of the sigma points through the observation function. The sigma points are a $\mathcal f(P)$. Therefore $\mathcal Z$ is a $\mathbf f(P)$, and therefore related to $\mathbf Q$.

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In order to derive equation (20) you can use the following steps: From substitution of equation (16) into equation (18) $$P_n = P_{n|n-1} - K_nP^t_{x_ny_n}$$ Now plugging right side equation of (19) into the last equation $$P_n = P_{n|n-1} - K_n(P_{y_ny_n} - R_n)=$$ $$=P_{n|n-1} - K_nP_{y_ny_n} + K_nR_n$$ Now Pluging (16) again we know that  ...

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The model they have used is general and you can apply it to QAM as well. In wireless communication systems, channel and noise are two different impairments affecting the overall transmission. Here as everywhere else, the noise is AWGN (additive white Gaussian; if you want to know what these terms mean, see this article). And the channel is a linear filter ...

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