Transcript
GPS receivers for spinning rockets Ken Harima
Saito Lab. - University. of Tokyo
Introduction
Simulation Results
- Current rocket navigation systems are based on INU (Inertial Navigation Unit) or Radar. - GPS receivers are an attractive alternative
S-310
H-IIA
Epsilon
- Errors don’t accumulate as in INU - Don’t have range limitations nor requires ground support - Low power and weight
- High dynamics are a technical challenge for rocket-born GPS - High translational dynamics - High dynamics causes large frequency tracking errors due to Doppler effect
- High rotational dynamics - Multiple antennas must be used - Receiving antennas changes rapidly making signal combining difficult - High dynamics causes large frequency tracking errors
GPS receiver design Antennas and RF
Medium-scale solid fuel rocket - 15 G/s Jerk - 2 m diameter - 2 Hz Spin
Carrier & code Tracking errors
- Multi-antenna GPS receivers
GPS Signal
S-310
Rocket
H-IIA
Epsilon
L1(1.575MHz) carrier.
- Change in rocket orientation - Antenna gain must be ensured for all directions
- 1.024MHz C/A code. - 50bps Nav. message
- RF frontend for each antenna - Same clock for each RF chip
Carrier & Code Tracking
Error due to Jerk
- Carrier: 13 Hz - Code: 2.7m
- Carrier:10 Hz - Code: 2.5m
- Carrier: 12 Hz - Code: 2.6m
Error due to Noise (3σ, 37dBHz)
- Carrier:52 Hz - Code: 5.4m
- Carrier:39 Hz - Code: 4.9m
- Carrier:47 Hz - Code: 5.2m
Error due to Spin - Carrier:8 Hz - Code: 0.08m
- Carrier:10 Hz - Code: 1m
- Carrier: 30 Hz - Code: 0.4m
Total Tracking error
- Carrier:59 Hz - Code: 7.4m
- Carrier: 89 Hz - Code: 8.2m
- Carrier:73 Hz - Code: 8.18m
Position /velocity - Velocity: 35m/s errors (DOP=2.5)
- Signal combining at
-Velocity: 28m/s - Velocity: 42m/s
- Position: 20.5m -Position:18.5m - Position: 20.5m
phase level difficult -Carrier Discriminator:
Navigation Symbol demodulation
- Calculate carrier frequency at each antenna Di (k ) X i (k ) X i* (k 1) - Combine using equal gain combining D (k ) D (k ) car
Large liquid fuel rocket - 6 G/s Jerk - 5 m diameter - 0.03 Hz Spin
Small Solid fuel rocket - 25 G/s Jerk - 30 cm diameter - 3 Hz Spin
i
- Demodulation error rate - With Maximum likelihood frequency estimator
i
- Code Discriminator:
Pdem=10-5 for C/N0=34dBHz
- Select antenna with highest power - Calculate code phase discriminator for the antenna
- With Kay and Quinn-Fernandes frequency estimator Pdem=10-5 for C/N0=37dBHz
- Expected minimum C/N0: C/N0>37dBHz
Navigation Symbol demodulation
Demodulation error rate for DPSK demodulators with various frequency estimators
Navigation message decoding
- -Demodulate DemodulatePSK PSKmodulated modulatednavigation navigationmessage messageas asDPSK DPSK - - Carrier Carrierphase phaseunavailable unavailabledue duetotohigh highdynamics dynamics
Decoding Philosophy
- - DPSK DPSKdemodulator demodulatorwhich whichincludes includesaafrequency frequencyestimator estimatorisisused used - - Large Largecarrier carrierfrequency frequencytracking trackingerrors errorsdue duetotohigh highdynamics dynamics - - Normal NormalDPSK DPSKdemodulator demodulatorcannot cannotbe beused used - - Frequency Frequencyestimation estimationalgorithm algorithmmust mustbe beincluded includedinindemodulator demodulator DPSK with Freq. est. Normal DPSK
Decoding error rate
RAIM Availability
Error Detection Only
< 2.04 x 10-10
>1 - 1.34 x 10-4
Parity based error correction Parity & Periodogram based error correction
< 1.67 x 10-8
>1 – 2.41 x 10-6
< 1.79 x 10-8
>1 – 2.84 x 10-12
Decoding performance for demodulation error rate 10-5
Conclusions Proposed DPSK demodulation algorithm which includes a frequency estimator
Demodulation with normal and proposed algorithms
Navigation message decoding
- Multi-antenna receiver that doesn’t use a combined signal - Replicas calculated from antenna signals - Demodulation with frequency estimation for each antenna
- Decoder must be adapted to correct burst errors - PSK modulated navigation message is demodulated as DPSK - One demodulation error generates a string of bit errors
- GPS receiver for use onboard spinning rockets and other high dynamic spacecraft was designed
Error patterns after DPSK demodulation
- Periodogram based partially-soft decision decoding is used - Use of Receiver Autonomous Integrity Monitoring (RAIM) is assumed - Continuous communication with 6 satellites must be ensured - Discarding data is not desirable→Error correction must be made - Soft information is needed to correct all error patterns produced by one incorrect demodulation
- Navigation errors are below 21m for position and below 43m/s for speed - Navigation messages can be demodulated with an error rate of less than 10 -5 for the expected C/N0>37dBHz. - Decoding error rates are below 1.80 x 10-8 - RAIM unavailability is less than 2.84 x 10-12 if Parity & Periodogram based error correction in decoding
