# ps3 - UCSB Fall 2009 ECE 235 Problem Set 3 Assigned Friday...

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Unformatted text preview: UCSB Fall 2009 ECE 235: Problem Set 3 Assigned: Friday October 16 Due: Monday October 26 Reading: Hajek, Chapter 3 Topics: MMSE Estimation; Joint Gaussianity Practice problems (not to be turned in): The even numbered problems in Chapter 3, up to Problem 3.30. Compare your solutions with the solutions provided to make sure you understand the concepts. Problems 1-5: Problems 3.3, 3.5, 3.7, 3.9, 3.19 Problem 6: Consider a scalar Kalman filitering problem: State equation: x k +1 = 2 3 x k + w k , where w k ∼ N (0 , 1) are i.i.d., and x ∼ N (0 , 1). Measurement equation: y k = x k + v k , where v k ∼ N (0 ,σ 2 ) are i.i.d. Assume that x , { w k } and { v k } are independent. (a) Write down the Kalman filtering updates for ˆ x k | k in terms of ˆ x k- 1 | k- 1 and y k , expressing the gains involved in the updates in terms of the error variance sequence { Σ i | i } . (b) Write down the recursion for Σ k | k in terms of Σ k- 1 | k- 1 ....
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