Groves, Chapter 8

Advanced Satellite Navigation

Differential GNSS, carrier-phase positioning, integer ambiguity, poor SNR environments, and multipath mitigation.

Prerequisites: Chapter 7 (range errors, tracking, nav processor).
9
Chapters
1
Simulation
9
Quizzes

Chapter 0: The DGNSS Concept

Many GNSS error sources are spatially correlated: two receivers close to each other see nearly the same satellite clock error, ephemeris error, ionospheric delay, and tropospheric delay.

Differential GNSS exploits this. A reference station at a precisely known position computes corrections (the difference between its measured and true ranges) and transmits them to the user. The user applies these corrections, canceling the correlated errors.

˜ρcorrectedj = ˜ρuserj − δρrefj

The accuracy improvement depends on the separation distance between user and reference station (spatial decorrelation) and the age of correction (temporal decorrelation).

DGNSS accuracy: Local-area DGNSS (<100 km baseline) typically achieves sub-meter accuracy. Wide-area systems like WAAS/EGNOS model the errors over large regions and achieve 1–2 meter accuracy across continents.
Check: What principle makes differential GNSS work?

Chapter 1: Types of DGNSS

Three main architectures for delivering corrections:

TypeCoverageHow It WorksAccuracy
Local-area DGNSS<100 kmSingle reference station, direct corrections0.5–3 m
Wide-area DGNSS (SBAS)ContinentalNetwork of stations; separate corrections for clock, ephemeris, ionosphere1–2 m
Precise Point Positioning (PPP)GlobalPrecise orbit/clock products from global network; no local reference needed5–20 cm (converged)

SBAS systems: WAAS (USA), EGNOS (Europe), MSAS (Japan), GAGAN (India). They broadcast corrections via geostationary satellites on the GPS L1 frequency.

PPP uses carrier-phase measurements and precise satellite products (orbits accurate to ~2 cm, clocks to ~0.1 ns). Convergence takes 20–30 minutes as the ionosphere and ambiguities are estimated. PPP-RTK adds atmospheric corrections for faster convergence.

Relative GNSS: When only the position of one user relative to another matters (not absolute position), many common errors cancel. This enables centimeter-level relative positioning over short baselines.

Check: Why does PPP take 20-30 minutes to converge?

Chapter 2: Carrier-Phase Positioning

Code-based pseudo-ranges have meter-level noise. The carrier phase can be tracked with millimeter-level noise — 100× better. But there is a fundamental complication.

The carrier-phase measurement counts the fractional phase plus all whole cycles since tracking began. But the initial number of whole cycles (the integer ambiguity N) is unknown:

φj = ρj/λ + Nj + δφatm + ε

where λ is the carrier wavelength (~19 cm for L1). Until N is determined, the carrier phase gives only relative range changes, not absolute range.

GNSS attitude: By mounting multiple antennas on a rigid structure with known baselines, the carrier-phase differences between antennas give the vehicle attitude (heading, pitch, roll) to ~0.1° accuracy.

The precision hierarchy: Code pseudo-range ≈ 1 m noise. Carrier-smoothed code ≈ 0.3 m. Carrier-phase with resolved ambiguity ≈ 1–2 cm. Each level requires more sophisticated processing.
Check: What prevents carrier-phase measurements from immediately giving centimeter positioning?

Chapter 3: Integer Ambiguity Resolution

Resolving the integer ambiguities is the key challenge in carrier-phase positioning. The main approaches:

Double differencing: Form differences between two satellites and two receivers. This cancels satellite and receiver clock errors and most atmospheric delays, reducing the problem to estimating the integer ambiguities.

Float solution: Estimate the ambiguities as real numbers using least squares or a Kalman filter. As data accumulates, the estimates converge toward integers.

Integer fixing: Use algorithms like LAMBDA (Least-squares AMBiguity Decorrelation Adjustment) to find the most likely set of integers given the float solution and its covariance. LAMBDA decorrelates the ambiguity space before searching, dramatically reducing computation.

Validation: Check that the best integer set is significantly better than the second-best (ratio test). If not, keep the float solution until more data is available.

Multi-frequency helps: With three carrier frequencies, wider "virtual wavelengths" can be formed by differencing, making the ambiguities easier to resolve. This is a major benefit of modernized GNSS signals.

RTK (Real-Time Kinematic): A local reference station streams its carrier-phase observations to the user in real-time. With short baselines (<20 km) and good geometry, ambiguities can be resolved in seconds, giving centimeter-level positioning. This is the standard for surveying and precision agriculture.
Check: What does the LAMBDA algorithm do?

Chapter 4: Weak Signal Environments

GNSS signals arrive at the Earth's surface at roughly −130 dBm — well below the thermal noise floor. In difficult environments (indoors, urban canyons, under foliage), signal power drops further by 10–30+ dB.

Strategies for weak signals:

TechniqueGainTrade-off
High-gain antenna3–10 dBLarger, directional, costlier
Front-end filteringReduces out-of-band interferenceHardware complexity
Assisted GNSSReduces search space dramaticallyRequires cellular/network connection
Extended integration3 dB per doubling of timeMust wipe off navigation data bits; limited by dynamics
Collective detectionUses all visible signals jointlyHigh computational cost

Extended coherent integration: Integrating beyond one data bit (20 ms for GPS C/A) requires data-bit aiding. Data-free pilot signals (GPS L5Q, Galileo E1-c) can be integrated for much longer without this problem.

Check: Why are data-free pilot signals beneficial for weak-signal environments?

Chapter 5: Multipath Mitigation

Multipath occurs when GNSS signals reflect off nearby surfaces and arrive at the antenna alongside the direct signal. The reflected signals are delayed and attenuated, distorting the correlation peak and biasing the range measurement.

Antenna-based mitigation:

Choke-ring antennas use concentric rings to suppress ground-reflected signals

Ground planes block signals arriving from below the antenna

Receiver-based mitigation:

Narrow correlator: reduces the effect of long-delay multipath by using closer early-late spacing

Strobe/edge correlator: samples only the leading edge of the correlation peak, which is less affected by reflections

Multipath estimating delay lock loop (MEDLL): models and subtracts the multipath signals

Multipath mapping: In static or repeating environments, multipath errors repeat with satellite geometry. Mapping these errors over time enables prediction and correction.

Navigation processor filtering: Carrier-smoothing of code measurements averages out rapidly varying multipath.

Multipath is the dominant residual error in many environments after atmospheric and clock corrections are applied. It can cause errors from tens of centimeters (open sky) to tens of meters (severe urban canyons). No single technique eliminates it; defense in depth is essential.
Check: Why does a narrow correlator help with multipath?

Chapter 6: Signal Monitoring

GNSS signals can be intentionally or unintentionally degraded. Signal monitoring detects problems before they corrupt the navigation solution.

Spoofing: Fake GNSS signals that mimic real ones to misdirect the receiver. Defenses include monitoring for sudden jumps, checking signal consistency across frequencies, and using INS consistency checks.

Jamming: Intentional interference that overwhelms the GNSS signals. Defenses include adaptive antenna arrays (controlled reception pattern antennas, CRPAs) that null the interference direction.

Anomalous signals: Satellite failures can cause gradually degrading signals. The control segment monitors for these and broadcasts integrity alerts, but there is a time lag. Receiver-level monitoring (RAIM) provides faster detection.

Semi-codeless tracking: Before military GPS signals were openly documented, civilian receivers used semi-codeless techniques to track the encrypted P(Y) code on L2, enabling dual-frequency ionosphere correction. This required squaring the signal, losing ~30 dB of signal power.

Check: What is GPS spoofing?

Chapter 7: Carrier Phase Simulation

This simulation shows how carrier-phase measurements (green) are far more precise than code measurements (orange) but require integer ambiguity resolution.

Code vs Carrier-Phase Measurements
Check: How much more precise are carrier-phase measurements compared to code?

Chapter 8: Summary

Key takeaways:
• DGNSS exploits spatial correlation of errors; reference station corrections cancel common errors
• Local DGNSS: sub-meter; Wide-area (SBAS): 1–2 m; PPP: 5–20 cm (after convergence)
• Carrier-phase measurements: mm-level noise but integer ambiguity must be resolved
• Double differencing cancels clock and most atmospheric errors
• LAMBDA algorithm efficiently searches for correct integer ambiguities
• RTK: real-time centimeter positioning using carrier-phase with local reference
• Weak-signal techniques: assisted GNSS, extended integration, pilot signals
• Multipath: dominant residual error; mitigated by antenna design, narrow correlator, mapping
• Multi-frequency aids ambiguity resolution via wider virtual wavelengths
• Signal monitoring detects spoofing, jamming, and anomalous signals
Check: What accuracy does RTK carrier-phase positioning typically achieve?