EE16A Lab: APS 2 -- LAST LAB!ee16a/sp19/lab/APS 2.pdf3 Beacon example Let beacon centers be: (x 0, y...
Transcript of EE16A Lab: APS 2 -- LAST LAB!ee16a/sp19/lab/APS 2.pdf3 Beacon example Let beacon centers be: (x 0, y...
![Page 1: EE16A Lab: APS 2 -- LAST LAB!ee16a/sp19/lab/APS 2.pdf3 Beacon example Let beacon centers be: (x 0, y 0), (x 1, y 1) and (x 2, y 2) Time of arrivals: t 0, t 1, t 2 Distance of beacon](https://reader033.fdocuments.in/reader033/viewer/2022052105/604117a25423517df64805fe/html5/thumbnails/1.jpg)
EE16A Lab: APS 2 -- LAST LAB! :(
![Page 2: EE16A Lab: APS 2 -- LAST LAB!ee16a/sp19/lab/APS 2.pdf3 Beacon example Let beacon centers be: (x 0, y 0), (x 1, y 1) and (x 2, y 2) Time of arrivals: t 0, t 1, t 2 Distance of beacon](https://reader033.fdocuments.in/reader033/viewer/2022052105/604117a25423517df64805fe/html5/thumbnails/2.jpg)
Announcements!
● This is the last lab!!!● Get APS1 checked off at the
beginning of the lab ● Buffer week next week
○ (ONLY Touch 3b, APS 1, APS 2)● Course evaluations:
○ course-evaluations.berkeley.edu● Good luck on Finals !! :))
![Page 3: EE16A Lab: APS 2 -- LAST LAB!ee16a/sp19/lab/APS 2.pdf3 Beacon example Let beacon centers be: (x 0, y 0), (x 1, y 1) and (x 2, y 2) Time of arrivals: t 0, t 1, t 2 Distance of beacon](https://reader033.fdocuments.in/reader033/viewer/2022052105/604117a25423517df64805fe/html5/thumbnails/3.jpg)
Last lab: APS 1
● Cross correlated beacons with received signal
● Found the offsets (in samples) between peaks, converted to TDOAs, and calculated distances from each beacon
● What was the missing piece that we needed to calculate distance?○ Hint: we don’t have absolute
times of arrival for all the beacons, only offsets.
Calculate distances and location
![Page 4: EE16A Lab: APS 2 -- LAST LAB!ee16a/sp19/lab/APS 2.pdf3 Beacon example Let beacon centers be: (x 0, y 0), (x 1, y 1) and (x 2, y 2) Time of arrivals: t 0, t 1, t 2 Distance of beacon](https://reader033.fdocuments.in/reader033/viewer/2022052105/604117a25423517df64805fe/html5/thumbnails/4.jpg)
3 Beacon example
● Let beacon centers be: (x0, y0), (x1, y1) and (x2, y2)● Time of arrivals: t0, t1, t2● Distance of beacon m (m = 0, 1, 2) is dm = vtm = Rm
(circle radii)Circle equations: (x - xm)2 + (y - ym)2 = d2
m
![Page 5: EE16A Lab: APS 2 -- LAST LAB!ee16a/sp19/lab/APS 2.pdf3 Beacon example Let beacon centers be: (x 0, y 0), (x 1, y 1) and (x 2, y 2) Time of arrivals: t 0, t 1, t 2 Distance of beacon](https://reader033.fdocuments.in/reader033/viewer/2022052105/604117a25423517df64805fe/html5/thumbnails/5.jpg)
● Only know time offsets: τm= tm–t0● Rm=
● R0=
● Rm - R0 = vs (tm - t0) = vsτm
Problem: We do not know t0
t0 t1t2τ2
τ3
![Page 6: EE16A Lab: APS 2 -- LAST LAB!ee16a/sp19/lab/APS 2.pdf3 Beacon example Let beacon centers be: (x 0, y 0), (x 1, y 1) and (x 2, y 2) Time of arrivals: t 0, t 1, t 2 Distance of beacon](https://reader033.fdocuments.in/reader033/viewer/2022052105/604117a25423517df64805fe/html5/thumbnails/6.jpg)
Setting up n-1 hyperbolic equations
● m ≠ 0 (as τ0 = 0)● This is the equation for a
hyperbola● :( This is hard to solve tho
simplify!
![Page 7: EE16A Lab: APS 2 -- LAST LAB!ee16a/sp19/lab/APS 2.pdf3 Beacon example Let beacon centers be: (x 0, y 0), (x 1, y 1) and (x 2, y 2) Time of arrivals: t 0, t 1, t 2 Distance of beacon](https://reader033.fdocuments.in/reader033/viewer/2022052105/604117a25423517df64805fe/html5/thumbnails/7.jpg)
Making it linear:
● Same trick: subtract first equation from others
simplify!Linear!
Not linear :(
![Page 8: EE16A Lab: APS 2 -- LAST LAB!ee16a/sp19/lab/APS 2.pdf3 Beacon example Let beacon centers be: (x 0, y 0), (x 1, y 1) and (x 2, y 2) Time of arrivals: t 0, t 1, t 2 Distance of beacon](https://reader033.fdocuments.in/reader033/viewer/2022052105/604117a25423517df64805fe/html5/thumbnails/8.jpg)
Making it linear:
● After simplifying, we have n-2 linear equations● Can do least-squares regardless of number of
beacons○ Best estimate of location if measurements are
inconsistent○ If there is no exact point of intersection bc of error or
noise
![Page 9: EE16A Lab: APS 2 -- LAST LAB!ee16a/sp19/lab/APS 2.pdf3 Beacon example Let beacon centers be: (x 0, y 0), (x 1, y 1) and (x 2, y 2) Time of arrivals: t 0, t 1, t 2 Distance of beacon](https://reader033.fdocuments.in/reader033/viewer/2022052105/604117a25423517df64805fe/html5/thumbnails/9.jpg)
Important Notes
● Read over the math carefully, We’ll be asking you about it!
● Task 3c: Let us know when you’re ready to take your own recording.
● Your recordings will be uploaded to tinyurl.com/aps-sp19