# lab01 - 1 . 5 1 v Solve (analytically, using pencil and...

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Electronic Navigation Systems – Lab 1 Consider the following model: z = H x + v H = 2 . 43 - 0 . 56 - 0 . 56 - 0 . 83 - 1 . 12 0 . 31 0 . 65 - 0 . 28 - 1 . 45 - 0 . 19 - 1 . 60 - 0 . 71 0 . 43 0 . 09 - 0 . 90 - 0 . 97 - 1 . 54 - 0 . 77 - 0 . 53 - 0 . 52 - 0 . 58 - 2 . 32 2 . 20 - 0 . 49 E [ v ] = 0 E ± v v T ² = σ 2 I σ = 0 . 05 1. Simulate the model in Matlab using x = ± 1 2 3 ² T . Use the randn function to generate the noise vector, v . Solve for the least squares solu- tion, ˆx . 2. Use at least 1000 runs of your simulation to calculate an estimate of the error covariance matrix, estimate of E ± ˜x ˜x T ² = 1 K K X k =1 ˜x k ˜x T k . You must generate a new value of v for each run of the simulation. On the other hand, you will want to move the matrix inverse outside the simula- tion loop. Check that your estimate is reasonably close to the theoretical value. 3. Generate a correlated noise vector as follows: v 0 = 1 0 . 5 0 . 5 1 0 . 5 0 . 5 1 0 . 5 0 . 5 1 0 . 5 0 . 5 1 0 . 5 0 . 5 1 0 . 5 0 . 5

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Unformatted text preview: 1 . 5 1 v Solve (analytically, using pencil and paper) for the noise covariance matrix, E v v T . Simulate the model using v in place of v . Solve for x using 1 weighted least squares. What did you use for the weight matrix? Calculate an estimate of the error covariance matrix and compare it to the theoretical value, as in part 2 above. 4. How would you (numerically, using Matlab) conFrm that weighted least squares works better than unweighted least squares for the correlated noise vector of part 3? Explain your idea in your report and demonstrate it in Matlab code. 2...
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## This note was uploaded on 01/15/2012 for the course EEL 6935 taught by Professor Staff during the Fall '08 term at University of Florida.

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lab01 - 1 . 5 1 v Solve (analytically, using pencil and...

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