Satellite Positioning and Trilateration Basics

Receiver and Trilateration

• Receivers identify visible satellites, estimate distances, and trilaterate their position.
• Additional features can enhance position estimation and provide services like route calculation or communication integration.

PVT Solution Basics

• A satellite transmits a signal at time TT X, received at TRX = TT X + τ, enabling distance estimation using R = c·τ, with c representing light speed.
• Precise satellite atomic clocks ensure synchronization; user clocks, however, have a bias (δtu), affecting distance measurement.
• Pseudorange is computed as ρ = c·τ + c·δtu due to user clock bias and potential satellite clock misalignment (δtS).

Positioning Calculations

• Measuring 4 pseudoranges from 4 satellites allows the determination of user coordinates (XYZ) and user clock bias.
• Position error covariance matrix includes variances of errors across dimensions and cross-correlation levels between them.
• Covariance matrix defined as cov(δx) = (HT H)−1HTcov(δρ)H(HT H)−1 indicates relationship between estimation errors and the measurement errors.

Dilution of Precision (DOP)

• Standard deviation of positioning error σx calculated as σx = GDOP·σU ERE, where GDOP is the Geometric Dilution of Precision.
• GDOP reflects satellite displacement; optimal at the barycenter of a tetrahedron.
• Other DOP factors include PDOP (Position DOP), TDOP (Time DOP), and HDOP (Horizontal DOP).

Error Sources in Position Estimation

• Two error types: Bias (deterministic) and Uncertainty (statistically derived).
• Key pseudorange errors include control segment errors, ionospheric delays, tropospheric influences, multipath effects, receiver noise, and relativistic impacts.

Ephemeris Error

• Ephemeris error stems from incorrect satellite positioning; user derives satellite position from broadcast orbital parameters.
• Significant contributors include satellite speed changes and gravitational field variations, with relativistic effects potentially causing a timing error of up to 70 ns.

Correction Methods

• Receivers must correct raw pseudoranges for satellite clock bias, atmospheric delays, and relativistic effects using broadcast corrections from satellites.
• Four-step process involves obtaining raw pseudoranges, applying corrections, refining measurements, and estimating user clock bias.

GLONASS Overview

• GLONASS, developed during the Cold War by the USSR, features 24 satellites across three orbital planes, primarily serving high-latitude areas.
• Utilizes Frequency Division Multiple Access (FDMA), transmitting signals at L band frequencies with a maximum accuracy of 25-45 meters.
• New GLONASS satellites also transmit codes using Code Division Multiple Access (CDMA).

Galileo and BOC Modulation

• Binary Offset Carrier (BOC) modulation introduced to mitigate mutual interference in signals through frequency shifting, enhancing signal resolution.
• Defined by BOC(n,m), where n represents the subcarrier frequency and m the chip rate, tailoring signal attributes for optimal performance.

Explore the fundamentals of satellite positioning, including how receivers identify satellites and estimate distances through trilateration. This quiz covers the principles of PVT solutions and the calculations involved in determining user coordinates and clock bias.