cs401r_w2016:lab7
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cs401r_w2016:lab7 [2016/02/17 16:34] admin |
cs401r_w2016:lab7 [2021/06/30 23:42] |
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| - | ====Objective:==== | ||
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| - | To understand state space models, and in particular, the Kalman filter. | ||
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| - | ---- | ||
| - | ====Deliverable:==== | ||
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| - | For this lab, you will implement the Kalman filter algorithm on two datasets. Your notebook should produce two visualizations of the observations, the true state, the estimated state, and your estimate of the variance of your state estimates. | ||
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| - | For the first dataset, you will implement a simple random accelerations model and use it to track a simple target. Your final visualization should look something like the following: | ||
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| - | {{ :cs401r_w2016:lab7_kf.png?direct |}} | ||
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| - | ---- | ||
| - | ====Grading:==== | ||
| - | Your notebook will be graded on the following elements: | ||
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| - | * 20% Kalman gain is correctly computed | ||
| - | * 20% State is correctly updated | ||
| - | * 20% Covariance is correctly computed | ||
| - | * 20% State and covariance are correctly recorded | ||
| - | * 20% Final plot is tidy and legible | ||
| - | |||
| - | ---- | ||
| - | ====Description:==== | ||
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| - | For the first dataset, you will perform simple target tracking using the random accelerations model. You should use the equations given in Lecture 17. The data can be found here: | ||
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| - | [[http://hatch.cs.byu.edu/courses/stat_ml/kfdata.mat|Simple target tracking data]] | ||
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| - | There are two arrays in this .mat file: ''data'' contains the actual (noisy) observations at each timestep, while ''true_data'' contains the true x,y coordinates at each timestep. Note that your kalman filter should only use the noisy observations; the true x,y coordinates are only given for visualization purposes. | ||
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| - | To visualize the uncertainty at each timestep, the code for plotting the 95% confidence interval of a Gaussian, from lab 6, can be used. | ||
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| - | The model is given by | ||
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| - | <code python> | ||
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| - | # our dynamics are described by random accelerations | ||
| - | A = np.asarray([ | ||
| - | [ 1, 0, 1, 0, 0.5, 0 ], | ||
| - | [ 0, 1, 0, 1, 0, 0.5 ], | ||
| - | [ 0, 0, 1, 0, 1, 0 ], | ||
| - | [ 0, 0, 0, 1, 0, 1 ], | ||
| - | [ 0, 0, 0, 0, 1, 0 ], | ||
| - | [ 0, 0, 0, 0, 0, 1 ] ]) | ||
| - | |||
| - | # our observations are only the position components | ||
| - | C = np.asarray([ | ||
| - | [1, 0, 0, 0, 0, 0], | ||
| - | [0, 1, 0, 0, 0, 0]]) | ||
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| - | # our dynamics noise tries to force random accelerations to account | ||
| - | # for most of the dynamics uncertainty | ||
| - | Q = 1e-2 * np.eye( 6 ) | ||
| - | Q[4,4] = 0.5 # variance of accelerations is higher | ||
| - | Q[5,5] = 0.5 | ||
| - | |||
| - | # our observation noise | ||
| - | R = 20 * np.eye( 2 ) | ||
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| - | # initial state | ||
| - | mu_t = np.zeros(( 6, 1 )) | ||
| - | sigma_t = np.eye( 6 ) | ||
| - | |||
| - | </code> | ||
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cs401r_w2016/lab7.txt ยท Last modified: 2021/06/30 23:42 (external edit)
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