# Stanford EE259 I GPS receiver architecture, acquisition & tracking, position est. I 2023 I Lecture 4 | Summary and Q&A

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January 19, 2024
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Stanford EE259 I GPS receiver architecture, acquisition & tracking, position est. I 2023 I Lecture 4

## TL;DR

The GPS receiver uses a system level architecture to acquire and track satellites, estimate the receiver's position and timing offset, and localize itself based on the measured pseudo ranges to multiple satellites.

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### Q: How does a GPS receiver determine satellite positions accurately?

GPS receivers determine satellite positions using information from navigation messages and ephemeris data. The receiver uses the parameters in the navigation messages, such as the orbital parameters, to estimate the position of the satellite at a given point in time.

### Q: How is time of flight estimation done in GPS?

Time of flight estimation in GPS is done using ranging codes. The receiver calculates correlations between the received signal and the locally generated replica of the code to find the point at which the correlation is maximized, which corresponds to the optimal time of flight estimate.

### Q: What are M sequences and why are they important in GPS?

M sequences, also known as maximal length sequences, are a class of codes used in GPS. These codes have good correlation properties, low side lobes, and are easy to generate. Multiple codes of the same length with different feedback taps can be used in GPS receivers for code division multiple access (CDMA), allowing each receiver to track a specific satellite.

### Q: How does a GPS receiver compensate for Doppler shifts?

GPS receivers use a numerically controlled oscillator (NCO) to compensate for Doppler shifts. The NCO generates a sine and cosine term with a frequency equal to the sum of the nominal carrier frequency and the estimated Doppler shift. This compensates for the Doppler shift in the received signal during the demodulation process.

### Q: How does a GPS receiver track timing offsets?

GPS receivers track timing offsets by continuously estimating and adjusting the time delay between the receiver's clock and the GPS system's clock. By monitoring the Doppler-shifted signals from multiple satellites, the receiver can refine its estimate of the timing offset, allowing for accurate localization.

### Q: How does a GPS receiver disambiguate range ambiguity?

GPS receivers disambiguate range ambiguity by using geometric constraints, satellite movement, or bit synchronization methods. By analyzing multiple range measurements and geometric relationships, receivers can find the correct physical time of flight and resolve any ambiguities caused by periodic correlations.

### Q: What is the difference between the acquisition and tracking phases in GPS?

The acquisition phase in GPS involves searching for and acquiring satellites by estimating their Doppler shifts and pseudo ranges. Once acquired, the receiver enters the tracking phase, where it continually adjusts its estimates of Doppler shift and pseudo ranges based on updated measurements from the satellites.

### Q: How does a GPS receiver estimate its position using pseudo ranges?

GPS receivers estimate their position by solving a system of nonlinear equations using pseudo ranges, which are the time equivalent of the measured range between the receiver and multiple satellites. The receiver uses the pseudo ranges and satellite positions to estimate its own position and timing offset through an optimization process.

## Summary & Key Takeaways

• GPS receivers determine satellite positions using information from navigation messages and ephemeris data, allowing them to estimate satellite positions accurately.

• Time of flight estimation is crucial for GPS, and it is done using ranging codes. The receiver calculates correlations to find the optimal time of flight estimate.

• GPS uses M sequences or maximal length sequences for ranging codes, which have good correlation properties and low cross correlations. This allows for code division multiple access (CDMA) in GPS receivers.

• GPS receivers compensate for Doppler shifts in satellite signals and track timing offsets to continuously estimate the receiver's position and timing relative to the GPS system.