Satellite Positioning and Trilateration Basics

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Questions and Answers

What does the receiver do to determine its position?

Uses GPS coordinates stored in a database to find its location.

Estimates the distance to the satellites and calculates the average distance.

Identifies the satellites in view, estimates distance, and trilaterates its position. (correct)

Measures the signal strength and triangulates based on satellite positions.

What is the primary challenge in aligning user clocks with satellite time?

User devices do not have the necessary hardware for synchronization.

User clocks cannot be relied upon for accurate time measurement.

The cost and complexity of achieving synchronization is prohibitive. (correct)

User clocks are often much slower than satellite clocks.

What is the term used for the calculated distance that includes user clock bias?

Measured distance

Corrected range

Pseudorange (correct)

Geometric range

What does PDOP stand for in position estimation?

Position Dilution of Precision Signup and view all the answers

How many pseudoranges does a user need to measure to determine its coordinates and clock bias?

4 pseudoranges Signup and view all the answers

Which factor contributes solely to TDOP?

g44 Signup and view all the answers

What happens when a satellite clock deviates from nominal operation?

The satellite must be changed. Signup and view all the answers

What are the main characteristics of uncertainty in error sources?

Residual and uncompensated Signup and view all the answers

Which factor is not corrected during the positioning measurement?

User clock bias (δtu) Signup and view all the answers

What contributes to the maximum relativistic effect experienced by a satellite?

The satellite's speed and gravitational field change Signup and view all the answers

What is the primary reason the satellite clock runs slower at perigee?

Higher velocity and lower gravitational potential Signup and view all the answers

Which error type affects the pseudorange in a deterministic way?

Bias Signup and view all the answers

What corrections are typically applied to the satellite clocks?

Satellite clock bias corrections Signup and view all the answers

What additional functionalities can improve position estimation?

Route calculation and enhanced user interfaces Signup and view all the answers

What is a consequence of multipath in signal reception?

Signal reflections due to obstacles Signup and view all the answers

How is the error budget for corrected pseudoranges characterized?

Statistically independent and Gaussian distributed Signup and view all the answers

Which of the following factors does NOT contribute to pseudorange errors?

Signal processing delay Signup and view all the answers

Which of these factors does NOT require bias correction in satellite measurements?

Frequency response Signup and view all the answers

What is the main purpose of smoothing range measurements?

To reduce the variance of estimations Signup and view all the answers

What does the standard deviation of total pseudorange error represent?

Random variables of independent errors Signup and view all the answers

Which error arises from incorrect satellite position information?

Ephemeris error Signup and view all the answers

What is the Sagnac Effect primarily attributed to during signal transmission?

Rotational movement of the Earth Signup and view all the answers

What process occurs first in the correction of raw pseudorange measurements?

Obtaining raw pseudorange measurements Signup and view all the answers

What might contribute to the residual errors in GNSS measurements?

Statistically independent external factors Signup and view all the answers

What does the diagonal of the covariance matrix represent?

The variances of the error in different dimensions Signup and view all the answers

Which statement about the GDOP is true?

GDOP is dependent on the configuration of the satellites. Signup and view all the answers

How is the standard deviation of the positioning error computed?

By taking the square root of the sum of each dimension's variance. Signup and view all the answers

What does the symbol σU ERE represent?

The standard deviation of the error on pseudorange estimation. Signup and view all the answers

What does the trace of the matrix (HT H)−1 signify in relation to GDOP?

It gives a measure of satellite dispersement and its influence. Signup and view all the answers

What outcomes are produced by the off-diagonal elements of the covariance matrix?

They indicate the level of cross-correlation between the variables. Signup and view all the answers

What happens to GDOP when the position is at the barycenter of a tetrahedron?

GDOP value is minimized. Signup and view all the answers

In the formula for covariance, which component uses the term cov(δρ)?

It relates to the uncertainties in pseudorange measurements. Signup and view all the answers

What is the main reason GLONASS is considered to have worse performance compared to GPS?

It employs FDMA and is affected by ionospheric impact. Signup and view all the answers

What is the orbital inclination of the GLONASS satellites with respect to the equatorial plane?

64.8° Signup and view all the answers

What modulation technique is used to reduce mutual interference between signals in BOC?

Split Spectrum Modulation Signup and view all the answers

How many satellites are there in total in the GLONASS constellation?

24 Signup and view all the answers

What does the 'n' represent in the terminology for BOC(n,m)?

Subcarrier frequency in multiples of 1.023 MHz Signup and view all the answers

What is the orbit period of the GLONASS satellites?

11 hours and 15 minutes Signup and view all the answers

What is the accuracy range of the C/A code used by GLONASS?

25-45 meters Signup and view all the answers

How is the power spectrum affected in BOC modulation?

It is allocated around a subcarrier frequency. Signup and view all the answers

Study Notes

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.

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Description

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.