The function should be called as x iter cgsolveH b tol maxiter where the inputs

# The function should be called as x iter cgsolveh b

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The function should be called as [x, iter] = cgsolve(H, b, tol, maxiter); where the inputs and outputs have the same interpretation as in the previous problem. Use your code to solve the same image deconvolution problem, and comment on the number of iterations required relative to steepest descent. Turn in your code, your recovered image, and the number of iterations it took you to reduce the relative residual error to less than 10 - 4 from a starting guess of 0 . You will want to explicitly calculate the residual every 50 iterations here as well. 5. Recall the simple “pulse tracking” example we looked at in the Kalman filter notes. (a) Write down the Kalman update equations for this special case. Make them as simple as possible ... (Do you really need to compute ˆ x k +1 | k and P k +1 | k as intermediate steps?) (b) As k gets large, the solution for ˆ x k | k becomes a fixed weighted sum of the previous measurements, i.e. it (approximately) obeys the convolution equation ˆ x k | k L X =0 w [ ] y [ k - ] . This equation is extremely accurate for very moderate values of k and L . What is an appropriate value of L and what are the weights w [ ]? (Hint: For a k = 2 , 3 , 4 , 5 , 6 , . . . , create A T k A k , invert it, and extract the appropriate row. One “easy” way to create A T k A k is to use the toeplitz command and then modify the far upper left and far lower right entries.) 6. We are using a radar to track a truck moving in a 2D plane with coordinates ( p x , p y ). At a series of times t k indexed by k , we are interesting in estimating its position ( p x ( t k ) , p y ( t k ) in the plane, and its velocity ( v x ( t k ) , v y ( t k )) along each coordinate. We stack these into a single vector x k = p x ( t k ) p y ( t k ) v x ( t k ) v y ( t k ) . Although the velocity of the truck will drift, we expect it to remain close to a constant — that is, our best guess for ( v x ( t k +1 ) , v y ( t k +1 )) is simply ( v x ( t k ) , v y ( t k )). Our best guess for the position at time t k +1 is determined by the previous position ( p x ( t k ) , p y ( t k )), previous velocity 3 Last updated 11:14, November 26, 2019

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( v x ( t k ) , v y ( t k )), and the time t k +1 - t k that has elapsed between the samples. The evolution of the parameters can be modeled by x k +1 = F k x k + k . At time t = 0, we make a direct observation that ( p x (0) , p y (0)) = (0 , 0) , and ( v x (0) , v y (0)) = (1 , π/ 2) . You might write this as y 0 = A 0 x 0 , where A 0 = I . At subsequent times t k > 0, we make a single measurement of the position and velocity of the truck. This measurement is of the form y [ k ] = cos(1150 πt k ) p x ( t k ) + sin(1150 πt k ) p y ( t k ) + cos(1250 πt k ) v x ( t k ) + sin(1250 πt k ) v y ( t
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