Differential Loran

Ben Peterson, Ken Dykstra & Peter Swaszek

Peterson Integrated Geopositioning &

Kevin Carroll,

USCG Loran Support Unit

Funded by Federal Aviation Administration, Mitch Narins, Program Manager International Loran Association, November 4, 2003

Outline

• Background & Basic approach • Proposed Modulation • Message Formats • Reed Solomon forward error correction – Integrity from FEC – Synchronization & coset vector • Modulator & receiver status • Data collection example – E field vs H field

Background/Basic Approach

• LORIPP determined in 9/02 that some form of LDC would be necessary to enable all-in-view master independent navigation (station ID & cross chain lane ambiguity) – Mitch Narins pushed 9 th pulse concept – Absolute time msg is one way to resolve lane ambiguity – In 4/03, Gordon Weeks, Kevin Carroll & I proposed 9 th pulse for dLoran • Receiver calculates ASF’s as sum of two terms: – Temporal terms measured at a local base station – A spatial grid based on survey of ASF’s compared to those observed simultaneously at the local base station – Differential corrections will be offsets from published nominal values vice absolute to conserve bits/maintain dynamic range • Effort is to demonstrate that Loran can meet HEA requirements and to determine base station density

Proposed Modulation Scheme

• 9 th pulse Pulse Position Modulation (PPM) • 32 state PPM, 5 bits/GRI – 3 bits phase, 2 bits envelope & phase • Averages to zero in legacy receivers, CRI increases 0.5dB

• Message length is 24 GRI or max of 2.38 seconds • PPM vice IFM means no transmitter modifications, modulation done in software in TFE • Do not have to demodulate more than the strongest signal to get absolute time, positively ID all signals, and to get all corrections for your area • 9 th pulse in cross rate would be blanked, other 8 could be cancelled if desired.

Determination of minimum envelope delay between groups of 8 symbols Distance between PPM symbols as function of envelope and phase difference 2 1.8

1.6

1.4

1.2

1 0.8

0.6

1.25 usec = 0.766

1 usec (Eurofix) = 0.618

0.4

0.2

Same Phase Code Opposite samples at 0.625 usec Used in proposed format 0 0 10 20 30 40 Difference in time between pulses in usec 50 60 To get same distance as 1.25 usec phase shift need to delay envelope 50 usec (Earlier version had negative phase codes and 45.625 usec between groups, changed to make SSX modulator easier)

symbol 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Symbol delays in usec

d(i) = 1.25 mod(i,8) + 50.625 floor(i/8) present delay 0 1.25

2.5

3.75

5 6.25

7.5

8.75

50.625

51.875

53.125

54.375

55.625

56.875

58.125

59.375

delay w/5MHz clock 0 1.2

2.6

3.8

5 6.2

7.6

8.8

50.6

51.8

53.2

54.4

55.6

56.8

58.2

59.4

symbol 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 present delay 101.25

102.5

103.75

105 106.25

107.5

108.75

110 151.875

153.125

154.375

155.625

156.875

158.125

159.375

160.625

delay w/5MHz clock 101.2

102.6

103.8

105 106.2

107.6

108.8

110 151.8

153.2

154.4

155.6

156.8

158.2

159.4

160.6

Symbols in the time domain Blue: xxx00, Red: xxx01, Green: xxx10, Magenta: xxx11 1 0.8

0.6

0.4

0.2

0 -0.2

-0.4

-0.6

-0.8

-1 0 50 100 150 Time in usec 200 250 300 350

180 26 Polar plot of symbol space 90 25 24 Phase in deg re symbol 0 17 135 45 18 10 2 9 16 Delay in usec 31 re symbol 0 3 11 1 0 0 8 50 19 4 100 23 150 0 12 15 5 7 27 6 30 13 20 14 22 225 315 21 28 29 270

Update Rate/Time to 1

• Time to alarm: 24 GRI format, max 2.38 sec message length st • Time to first fix: By the time dLoran becomes operational, system will be TOT control, 1 vice 2 corrections per LORSTA, 6 vice 12 per monitor site

Fix/Alarm Limit

– 3 messages/site @ 2 corrections/message – Assume maximum of 20-40 sites/LORSTA, 60-120 dLoran messages • For dual rated station, update rate/time to 1 st fix of 2 to 4 minutes • For single rated station, these times double.

– Jupiter and Middletown are only single rated LORSTA’s with significant potential for maritime base stations

Bit Assignments for Time and dLoran messages Time MSG type Time Leap Secs Next leap Sec (Format for aviation integrity msg TBD) # bits Resolution 4 31 1 msg epoch 6 1 Range 16 97-163 yrs 64 sta ID Total 3 45 8 dLoran MSG type Time Base Quality Ref ID Sig ID Corr # 1 Corr # 2 Age/Quality Total # bits 4 3 10 3 10 10 5 45 Resolution 2 2ns 2ns Range 16 1024 16 +/- 1.022 usec +/- 1.022 usec

dLoran for Precise Time Transfer

• Format includes base station time base quality term so that timing users can use corrections from high quality sites (NIST, USNO, LORSTA) but would not use maritime sites – Since maritime sites may have GPS for time, if GPS is lost, ASF of nominal strongest signal could be set to zero and all other ASF’s are relative • Performance details in next paper

Aviation Early Skywave Warning

• Warning not to use signal – When geomagnetic latitude of midpoint of propagation path exceeds XX degrees, and – Either predicted groundwave signal strength < YY dB, or path > ZZ NM • Message content much less than the available # of bits leaving room for CRC – This enables recovering Reed Solomon error correction performance lost by using RS for integrity • More details on problem in paper tomorrow AM

Synchronization/HMI

• An unsynchronized transmitter and receiver pair will not yield accurate data – In early tests w/CRC, erroneous messages were “corrected” by RS, and then accepted by 24 bit CRC • Could use decoder failure as a way to test synchronization: – Issue of cyclic-like nature of RS code – Issue of the effect of error correction

Coset vector

• Solution: use a constant coset vector

c

* – Add to codeword before transmission – Subtract from channel observation before decoding • Effects of

c

*: – Cancelled if synchronized – Usually cause decoding failure if unsynchronized (high probability)

45 data bits 45 data bits

Encoding & Decoding

c

* RS (24,9) encoder RS (24,9,X) bounded distance decoder + modulo 32 adder modulator channel

c

* + modulo 32 subtraction demodulator

Bounded Distance Decoding

• Release codeword if HD(

r,c

)  threshold for some codeword

c

; otherwise, decoder failure HD = Hamming distance * * * * * * Yellow = correct Orange = undetected error Gray = failure

Probability of HMI

• Random observations: – 24 random symbols – Error if they fall in an incorrect decodable region

P UE

 (

q k

 1 )

j t

  0  

n j

  (

q

 1 )

j q n

10 -4 10 -5 10 -6 10 -1 10 -2 10 -3 10 -7 10 -8 10 -9 0 1 Number of erasures 2 3 4 Number of corrections (t) 5 6 7 Aviation Threshold w/16 bit CRC Maritime Threshold Aviation Threshold

Integrity performance of the (24,9) RS code when > 6 errors results in rejection P UE undetected error P F decoder failure Error count

u

0,1,2,3,4,5,6 7,8,9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 P UE (

u)

0 0 1.1 × 10 -10 5.5 × 10 -10 1.4 × 10 -9 2.3 × 10 -9 3.0 × 10 -9 3.2 × 10 -9 3.2 × 10 -9 3.2 × 10 -9 3.2 × 10 -9 3.2 × 10 -9 3.2 × 10 -9 3.2 × 10 -9 3.2 × 10 -9 3.2 × 10 -9 3.2 × 10 -9 P F (

u)

0 1 1 – P UE (10) 1 – P UE (11) 1 – P UE (12) 1 – P UE (13) 1 – P UE (14) 1 – P UE (15) 1 – P UE (16) 1 – P UE (17) 1 – P UE (18) 1 – P UE (19) 1 – P UE (20) 1 – P UE (21) 1 – P UE (22) 1 – P UE (23) 1 – P UE (24)

dLoran Status

• TTX – Modulator & receiver finished (too many times due to numerous changes in msg format) – Two versions of prototype user equipment • Comms only receiver that gets Loran data from Locus receiver, calculates dLoran fix & send NMEA message • Combined comms/navigation receiver (both E and H field) – Base stations write messages to hard drive of modulator PC • SSX – Prototype – TSC under contract as of early September – Will modify TFE to send msg via serial port requesting next msg, & modulate signal.

– PIG will modify software to generate msg & send via RS232 – Expect prototype by 1 DEC • Starting data collection effort to evalute dLoran accuracy

Transmission test: 30 SEPT LSU TTX to Waterford, E field, no CRI canceling, errors only decoding Note: Smallest cross rate pulse that can cause error is -7dB (Fraction of last 10 msgs) Transmitter off

Data Collection Example

• 65’ US Army Corps of Engineers Survey Vessel Shuman in Cheaspeake Bay 29-30 October • Locus TM LRSIIID with E field antenna • Locus TM SatMate with H field antenna • DGPS for ground truth • Receivers in TOA mode; TOA’s relative to common, but free running oscillator • Software automatically starts at 0700 & quits at 1600 every weekday

Path of Shuman during depth survey 17.9

17.85

15:02 17.8

17.75

17.7

17.65

17.6

17.55

15:05 15:44 15:04 15:06 15:11 15:43 15:07 15:14 15:16 15:09 15:15 15:42 15:38 15:39 15:37 15:33 15:40 15:36 15:34 15:35 15:41 15:41 15:03 17.5

-13.7

-13.65

-13.6

-13.55

-13.5

-13.45

-13.4

Longitude, minutes re 76W -13.35

-13.3

-13.25

6 4 2 0 -2 -4 -6 -8 -10

Scatter plot of fix errors

-10 -5 0 East Error - m 5 10

0.5

0.4

0.3

0.2

0.1

0 0 LRSIIID Accuracy vs Estimated Delay 1 0.9

0.8

15 16 17 18 0.7

0.6

2 4 6 8 10 12 Radial error - m 14 16 18 20

Test of directional dependence of H field antenna 18.3

16:38 18.28

18.26

16:39 18.24

18.22

16:33 16:37 18.2

16:34 16:40 18.18

16:32 16:41 16:36 18.16

16:35 18.14

18.12

16:32 18.1

-12.92 -12.9 -12.88 -12.86 -12.84 -12.82

-12.8 -12.78 -12.76 -12.74 -12.72

Longitude, minutes re 76W

9960Z TD re 59100 usec 24.5

24 23.5

23 Predicted from GPS LRSIIID (E field) SatMate (H field) 22.5

16.52 16.54 16.56

16.58

16.6

16.62 16.64 16.66

Relative to predicted 16.68

0.4

16.7

16.72

0.2

0 -0.2

-0.4

LRSIIID SatMate -0.6

16.52 16.54 16.56

16.58

16.6

16.62 16.64 16.66

Hours - GMT 16.68

16.7

16.72

Comparison of E & H field accuracy during turns 1 0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 0 2 4 6 8 10 Radial error - m 12 LRSIIID (E field) SatMate (H field) 14 16 18 20

Summary

• Modulation & message format is hopefully frozen at least for the proof of concept phase • TTX modulator & LDC receiver succesfuuly demo’ed, SSX modulator under development • Very early in the ASF data collection and accuracy analysis effort, early data promising – E field better than H field at this point, calibration and/or antennas with less bias may solve problem

Acknowledgements, etc.

Funded by Federal Aviation Administration – Mitch Narins – Program Manager For additional info:

[email protected]

Or [email protected]

-Note- The views expressed herein are those of the authors and are not to be construed as official or reflecting the views of the U.S. Coast Guard, the U. S. Federal Aviation Administration, or the U.S. Departments of Transportation and Homeland Security.

9

th

Very good Question

! pulse PPM vs EUROFIX

• Both have comparable data rates & message lengths, EUROFIX could easily transmit the same data we are proposing. Why a new format??

• Main reason is ability to cancel 8/9 of cross rate pulses – For maritime & timing users can merely blank cross rate: Only issue for aviation where short time constants preclude cross rate blanking – It is possible to cancel cross rate with Eurofix • After demodulation & data wipeoff – if demodulation errors, canceling not effective • After demodulation and decoding (& data wipeoff) – need delays of up to 3 seconds for completion of message • Formats are completely compatible, same transmitter can transmit both, same receiver can receive both.