Description

Acoustic Positioning System 1
Where Are We Now?
Imaging Touchscreen APS
Module Module Module

Today’s lab: Acoustic Positioning System
● Global Positioning System (GPS)
○ Uses radio waves instead of sound waves
● Understand mathematical tools used for shifting and detecting signals
○ Think about cross correlation!

Set-up
General Lab Specific receiver microphone
Satellites repeatedly transmitting Speakers repeatedly playing specific beacon signals specific tones (beacon signals)
● Known: Location of each satellite and what beacon signal each satellite is playing
● Unknown: Location of receiver ← what we want to figure out!
Set-up
● Satellite:
○ Known, periodic waveforms
○ Know satellite location ● Receiver:
○ Will record the waveform
■ Sum of all shifted beacons
○ Waveform will be shifted from known satellite waveform based on how far it is from satellite (sound takes time to travel)

Let’s go backwards

Assume we know the distance between the receiver and every satellite
● Use lateration and the satellites’ locations to locate the receiver!
● How many satellites do we need in a 2D world?
How do we get those distances?

Assume we know the time-delay (in secs) of every beacon
● Use the speed of sound through air to get exactly how far our receiver is from every satellite
○ d = vs⋅ t
○ vs ≈ 343 m/s
How do we get those time-delays?

Assume we know how many samples it takes for each beacon to arrive at the receiver
● Use the sampling frequency of receiver to get the time-delay
○ Sampling frequency [samples/sec] – rate at which microphone records samples
How do we get sample delays?

● Receiver’s recorded signal is the sum of all the beacon signals
● Need to separate the recorded signal into the individual beacons to see how many samples each is delayed by

Overview
Recall: Inner (Dot) product

● Computes how similar two vectors are

Recall: Inner (Dot) product

An alternate form of the dot product
● Given this expression, with ||x|| = ||y||, when is this expression maximized?
● 𝜃 = 0
● vectors point in the SAME DIRECTION, so they are the SAME SIGNAL
The bigger the dot product, the more
“similar” the two vectors are
Tool: Cross-correlation
In Python:
cross_correlation(r, BA)[k]
● Mathematical tool for finding similarities between signals
● Idea: Computes dot product between r and signal BA shifted by k samples
● From the previous slide, the peak of the cross-correlation vector tells us which shift amount makes BA “most similar” to r

Relative Measurements

● Now, we are able compute relative sample delays, then relative time delays
● How do we get from relative time delays to absolute distances?
○ With the current set-up, we can’t 🙁
Additional assumption for APS1

● What if we knew the absolute sample delay of beacon 0?
○ Now we can adjust all our relative measurements to absolute ones!
○ Assume delay0 is given, then
● Then we can use absolute time-delays to get distances then location!
Notes + next lab:

● If we know the absolute sample delay of beacon 0, we can locate the receiver
○ Note that this the same as telling you exactly how far the receiver is from satellite 0
● This week, this value will be given to you
● Find out how to get around this assumption in APS 2!