5. Motivation behind LDS 5/44
<latexit sha1_base64="nJ4PaDWcGLJqblnlpUarvV5Pz0Y=">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</latexit>
<latexit sha1_base64="x1tYp+agnmgdGSrqolLa6EjSZ4U=">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</latexit>
non-temporal
non-observable:
observable:
Ø non-temporal
<latexit sha1_base64="o67GmM33Y8vOaoVz6/OuD0aLr7Q=">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</latexit>
Ø given a single measurement :
Ø given lots of measurements : <latexit sha1_base64="mPdum5jrJmKamjAFbeyyOqIurhc=">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</latexit>
Ø Estimating z with observable x.
<latexit sha1_base64="u735SM6HSE/2/9viXs16Lj8V89c=">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</latexit>
<latexit sha1_base64="bc4fqIzLwBDwLHOOuyJjINoYgMw=">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</latexit>
<latexit sha1_base64="73hmnNxKpL26KoWdb+HSzGLRL7I=">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</latexit>
<latexit sha1_base64="LkiKuSyEp5KXehLk577ZpwiUM7I=">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</latexit>
<latexit sha1_base64="sKzmamoQ79/qGvrkx8cFxYFIpC8=">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</latexit>
…
<latexit sha1_base64="bc4fqIzLwBDwLHOOuyJjINoYgMw=">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</latexit>
<latexit sha1_base64="LkiKuSyEp5KXehLk577ZpwiUM7I=">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</latexit>
<latexit sha1_base64="sKzmamoQ79/qGvrkx8cFxYFIpC8=">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</latexit>
<latexit sha1_base64="uawi/Z8uf9VnF/qaBxEg4i+rEu8=">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</latexit>
<latexit sha1_base64="SUFUhv9oqsAAGsB6P8yo3McZtA4=">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</latexit>
…
<latexit sha1_base64="73hmnNxKpL26KoWdb+HSzGLRL7I=">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</latexit>
temporal
Ø temporal
Ø will be a new source of error.<latexit sha1_base64="qdCg6MJyW96rZUuCw/An8HcoR1w=">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</latexit>
6. Motivation behind LDS 6/44
Ø temporal
<latexit sha1_base64="YAIttKGk1GRBzVFGCHDJMwRFf/A=">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</latexit>
Ø change slowly, noise level is high.
Ø change quickly, noise level is low.
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long window
short window
Ø How to form a weighted
average?
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long window.
short window.
Ø More recent observations will contribute more.
weighted window
8. Requirements 8/44
Ø Efficient algorithm for inference.
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Ø distributions belonging to the exponential family.
same form
※cited from PRML13.2.1-
13.2.2_Enomoto #20
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14. Defining the Model 14/44
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Ø The transition distributions.
Ø The emission distributions.
Ø The initial latent variable.
Ø The parameters.
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21. The forward equations 21/44
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Ø Using (C.7)
: Kalman gain matrix
Ø Using (C.5)
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22. Kalman Filter equations 22/44
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<latexit sha1_base64="NwQ10MQr4OlBCTd6+hYfdIFKrGU=">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</latexit>
observed prediction for <latexit sha1_base64="OQm5cCOMww+hKCKMYwDmwfbiJvk=">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</latexit>
observable space
<latexit sha1_base64="CtAvwbIg2MZh5eamvfoE7oqQaDQ=">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</latexit>
<latexit sha1_base64="IWjwJfbl7EEpC7F8NM1GyFeu3LA=">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</latexit>
<latexit sha1_base64="L18TUq4awKn3Jt/yNA85LSojFSw=">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</latexit>
: unaffected by observations
make the variance small
make the variance large
23. Example for understanding Kalman gain 23/44
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<latexit sha1_base64="g8yjk7iRNpwCU/lDcCMTE1ulk7E=">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</latexit>
<latexit sha1_base64="TDzk7t+6AE5gtHI2naNc2BYxmiQ=">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</latexit>
<latexit sha1_base64="sxrQ0le2ykzFiU0+e54ud8Eab74=">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</latexit>
<latexit sha1_base64="xEDKDQNPjwnEIC4UFX091kumfgk=">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</latexit>
※cited from
PRML13.3_Taniyama #9