ECE313.Lecture15

ECE313.Lecture15 - ECE 313 Probability with Engineering...

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Decision-making under uncertainty I Professor Dilip V. Sarwate Department of Electrical and Computer Engineering © 2000 Dilip V. Sarwate, University of Illinois at Urbana-Champaign. All Rights Reserved ECE 313 Probability with Engineering Applications

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ECE 313 - Lecture 15 © 2000 Dilip V. Sarwate, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 2 of 42 Introduction Making decisions is one of the most fruitful enjoyable empowering aggravating enervating human activities Probabilists and statisticians study the methodology for making rational decisions
ECE 313 - Lecture 15 © 2000 Dilip V. Sarwate, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 3 of 42 An example from radar systems A radar transmitter emits electromagnetic pulses in the direction of a target that may (or may not) be “out there” The radar receiver listens for the echoes The length of time between transmission of the pulse and reception of the echo is used to estimate the range of the target Other information (e.g. Doppler shift in frequency, antenna orientation) is used to estimate velocity and compass bearing

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ECE 313 - Lecture 15 © 2000 Dilip V. Sarwate, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 4 of 42 I hate the inverse square law… The signal (if any) that is the input to the radar receiver is very weak, and is also contaminated by background noise The echo (if present at all) of a pulse is weak, and difFcult to distinguish from the background noise If n transmitted pulses are reﬂected from a target, it is not certain that all n echoes will be heard clearly by the radar receiver
ECE 313 - Lecture 15 © 2000 Dilip V. Sarwate, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 5 of 42 I shot an arrow into the air… A radar system does not know if a target is present or not The radar system transmits pulses and listens for echoes Based on the presence (or absence) of echoes, the radar system must decide whether a target is present or not This decision-making process is the subject of this lecture

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ECE 313 - Lecture 15 © 2000 Dilip V. Sarwate, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 6 of 42 It fell to the earth I know not where System decides if a target is present or not The decision may be correct or incorrect If the decision is that a target is present then this decision is correct if in fact , there is a target present but this decision is incorrect if in fact , there is no target present Such an incorrect decision is called a
ECE 313 - Lecture 15 © 2000 Dilip V. Sarwate, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 7 of 42 Being wrong the other way System decision as to whether a target is present or not may be correct or incorrect If the decision is that a target is absent then this decision is correct if in fact , the

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This note was uploaded on 09/29/2009 for the course ECE 123 taught by Professor Mr.pil during the Spring '09 term at University of Iowa.

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ECE313.Lecture15 - ECE 313 Probability with Engineering...

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