Wednesday AM: (Doug) 2. PS and Long Period Signals
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1 Wednesday AM: (Doug) 2 PS and Long Period Signals
2 What is Colorado famous for?
3 32 satellites 12
4 Early on in the world of science synchronization of clocks was found to be important. consider Paris: puffs of air pneumatic time synchronization service master clock
5 Seismology needs synchronized clocks too GPS antenna Quite simply: GPS gives an accurate time to what the seismometer measures.
6 This is done with GNSS (GPS). But to most glaciologists and seismologists, GPS is a black box Goal here is to look inside the black box just a tiny bit
7 Lesson Goals: Understand the satellite to earth range problem Understand least-squares inverse for all types of problems Get a sense of why GPS is not a substitute for long-period seismometer data. GPS seems to be good enough for some co-seismic motion purposes, but not for co-witnessing what seismometers see (in my humble opinion) at least not yet
8 The range problem: processor, power supply, solar panel, charge controller, receiver hardware, processing software, data storage phase center MHz, 19 cm wavelength L1 and L2 C/A code P code ephemeris antenna Figure out: X,Y,Z,T GPS receiver on McMurdo Ice Shelf in January, 2017 (note bad field technique)
9 GPS was created for and is operated by the U.S. Military
10 But scientists have always been at the heart of it.
11 GPS is open to civilian uses. GLONAS, GALILEO, BEIDOU, and more coming
12
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16 Clearing, Illinois
17
18 Seismology uses Coarse Acquisition technique to determine time (to milliseconds) and position (to meters) This lesson tries to explain how Glaciology and Geodesy use phase tracking technique to determine time (to nanoseconds) and position (to mm) Usually a full week summer school would only scratch the surface of this technique
19 Data: t travel time (for radio signal from satellite to receiver) c x s = 19,650 km Game plan Unknowns: X, Y, Z in earth centered, earth fixed coordinates (ECEF), ττ of clock running the seismometer satellite orbit in ECEF coordinates (twice a day) Your GPS receiver says: Hey, this signal arrived at 3: UTC! O satellite sends you a signal saying: I sent this signal at exactly 3:00 UTC and my position is here. you guess you are here. but you are really here!
20 Digression: How is travel time observed? meet Bob Gold
21 Bob Gold invented Gold Codes for GPS: each satellite owns a coarse acquisition Gold code: binary sequence, 1024 digits long
22 Gold codes never cross correlate and Gold codes autocorrelate only once with zero time lag
23 Every seconds, each GPS satellite broadcasts its Gold code toward the receiver antenna: Each GPS receiver internally broadcasts replicas of the GPS Gold codes
24 a hand held GPS can sense the digit to 1% or about 3 meters
25 The GPS receiver has a replica Gold code for each satellite by lining up the receiver code with the code arriving from the satellite t can be determined very precisely
26 Something you might not want to know Gold codes Gold codes are also in the nuclear football
27 Data: t travel time (for radio signal from satellite to receiver) c x s = 19,650 km Game plan Unknowns: X, Y, Z in earth centered, earth fixed coordinates (ECEF), ττ of clock running the seismometer satellite orbit in ECEF coordinates (twice a day) Your GPS receiver says: Hey, this signal arrived at 3: UTC! O satellite sends you a signal saying: I sent this signal at exactly 3:00 UTC and my position is here. you guess you are here. but you are really here!
28 Data: t travel time (for radio signal from satellite to receiver) c x s = 19,650 km Unknowns: X, Y, Z in earth centered, earth fixed coordinates (ECEF), ττ of clock running the seismometer data unknowns speed of light known satellite position - c x satellite clock error known clock error
29 Unknowns: X, Y, Z in earth centered, earth fixed coordinates (ECEF) 4 ττ of clock running the seismometer (clock error) Data: t travel time (for radio signal from satellite to receiver) only 1??! satellite orbit in ECEF coordinates (twice a day) t precisely known satellite position you are here!
30 4 satellites sufficient to solve the problem: N=4 is just enough Typically 12 satellites used to give least-squares solution.
31 Not so fast! This problem isn t linear
32 provisional solution: correct solution: Taylor series expressing delta-terms:
33 unknowns data partial derivatives of the pseudorange expression: use your Grandmother s house coordinates, good enough
34 a linear algebra problem:
35 How do you solve an over-determined inverse problem? if you already knew what m was, you could predict what the perfect data D should be but, the real d doesn t D lies in the range of A,
36 How do you solve an over-determined inverse problem? choose an m that gives a D that is as close as possible to d. D lies in the range of A,
37 How do you solve an over-determined inverse problem? choose an m that gives a D that is as close as possible to d. perpendicularity vector: (d - D) vector: Am
38 How do you solve an over-determined inverse problem? for all D, defining the range of A columns of A must span the range of A basis vectors: columns of A, rows of A T
39 How do you solve an over-determined inverse problem? vector: (d - D) must be perpendicular to columns of A
40 How do you solve an over-determined inverse problem? but,
41 How do you solve an over-determined inverse problem? but, least-squares inverse: in MatLab-ese:
42 Workflow: 1. each time epoch (~15 s to 5 min.) gather pseudo range data 2. compute satellite positions for each time epoch 3. solve the least-squares inverse problem for ECEF coordinates and time 4. post-process either ECEF, ENU or LLH data to estimate kinematics of ice flow
43 Geodetic GPS C/A gives: accuracy in space: meters accuracy in time: microseconds carrier phase tracking can give: accuracy in space: milimeters? always reliable, not that accurate accuracy in time: nanoseconds? accurate, but subject to ambiguity X X X X X
44 Tricks of the trade differencing, differencing and more differencing Two receivers that see the same satellite eliminate the satellite s clock error and, if one receiver is on a fixed benchmark (land), ionosphere and troposphere error.
45 Tricks of the trade differencing, differencing and more differencing add a second satellite and you can eliminate clock errors on both receivers and some ambiguity
46 Tricks of the trade differencing, differencing and more differencing add a second transmitted carrier wave and you can eliminate ionosphere effects and some ambiguity
47 Tricks of the trade and the Kalman filter Rudolf Kalman Apollo 8 board computer containing the Kalman filter software
48 GPS will get better and glacial seismology will likely use it more closely
49 But don t try it by yourself! Phase ambiguity + ionosphere troposphere satellite orbit uncertainty use a GPS processing package from MIT or elsewhere
50 What does geodetic GPS data look like? yup! missing!???
51 ???
52 10 min 30 cm many hours 5 cm mostly noise 1 day s motion
53 What does GPS data look like? Rinex file SP3 file alternatively: you can use the broadcast ephemeris
54 Rinex file What does GPS data look like? X X X military only hand-helds and seismometers geodetic quality phase tracking
55 Rinex file What does GPS data look like? date and time which satellites are in view
56 Rinex file What does GPS data look like? range as number of wavelengths (integer) pseudorange from Gold code autocorrelation (m)
57 What does GPS data look like? SP3 file clock error of satellite date and time X Y Z dt satellite number date and time ECEF coordinates of satellites
58 Exercise(s) with GPS data: Part A: process 1-day of 15-min sample rate C/A data for position and clock error Part B: examine phase-tracking GPS data for 60 days of McMurdo Ice Shelf (deduce tidal constituents, correct for IBE) attempt to co-witness a seismic signal on the McMurdo Ice Shelf introduced in previous exercise (Monday s seismology basics )
59 you will compare C/A result you create with your own hands with JPL s PPP phase tracking solution
60 Part B: 60 days of GPS data from an ice shelf November 2016 to late January 2017
61 ocean tide > 100 cm We want to look beyond the tide: what is the long term vertical motion?
62 problem: estimate these 12 coefficients.
63
64
65 inverse barometer effect -1 cm per 1 mb rise in pressure
66 Why is the ice going up?
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