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3

So, you have a bunch of datapoints of the form (x,y), and considering all of those datapoints together, you have the vectors $x$ and $y$. To do a curve fit, you would like to solve the equation $Aw=y$ for the column vector $w$, which holds the coefficients of your curve fit polynomial. These coefficients are also the weights of the basis vectors in the ...


2

Check out this paper. I would have made a comment but not high enough rep. http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=1211087&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F81%2F27258%2F01211087 Looks like you need multiple in to get subharmonics in Volterra series The abstract states "Subharmonic generation is a complex nonlinear ...


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Consider one-dimensional function $f(x)$. The first order taylor expansion is $f(x_0+h) \approx f(x_0) + f'(x_0)h$ The second order taylor exapnsion is $f(x_0+h) \approx f(x_0) + f'(x_0)h + \frac 1 2 f''(x_0)h^2$ Now we expand three-dimensional function. $$ D(\mathbf{x_0}+\mathbf h) \approx D(\mathbf{X_0}) + \bigg(\frac{ \partial D}{\partial \mathbf x}\...


2

For $y\approx y_0$ you have $$\begin{align}\sqrt{p_m(y)q_m}&\approx\sqrt{p_m(y_0)q_m}+\frac{p_m(y)-p_m(y_0)}{2\sqrt{p_m(y_0)}}\sqrt{q_m}\\&=\frac12\sqrt{p_m(y_0)q_m}+\frac12 p_m(y)\sqrt{\frac{q_m}{p_m(y_0)}}\tag{1}\end{align}$$ So the function you're approximating is $f(x)=\sqrt{x}$, with $x=p_m(y)$, and you do this in the vicinity of the value $a=...


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They should improve the convergence properties of the state estimate, i.e. if you have an initial value far from the trajectory, they could improve the region of attraction. They should also reduce the bias in the estimate. In the EKF and UKF, there are no direct ways of including higher order moments of distributions, in both cases the state distributions ...


1

Many years later I was asked to write some of what I've learned on this. The short answer is that it depends on what the term "subharmonics" means - things are very different if we're looking at bilateral signals or unilateral ones. So this is a partial answer In a very strict sense it's not possible to generate subharmonics using any time-...


1

The quantity $\frac{\partial D}{\partial \textbf{x}}$ is a vector, since it is the derivative of the scalar function $D(\textbf{x})$ w.r.t. all the elements of $\textbf{x}$. In the formula it is assumed that all vectors are column vectors, so in order to compute the dot product of the derivative $\frac{\partial D}{\partial \textbf{x}}$ and the vector $\...


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