20 GPS Location: Architecture and Error Control

20.1 Start With the Decision

This section: Start With the Decision — A receiver can see four satellites and still produce a poor fix.

A receiver can see four satellites and still produce a poor fix. Clock, atmosphere, geometry, and multipath each change the answer.

20.2 Route Overview

This section: Route Overview — This is part 2 of 2.

This is part 2 of 2. Review GPS Location: Ranging Methods for the preceding evidence.

20.3 Learning Objectives

This section: Learning Objectives

• Trace a GPS fix through receiver architecture.
• Estimate timing, geometry, and propagation error effects.

20.4 Chapter Roadmap

This section: Chapter Roadmap

• GPS Architecture
• Satellite Synchronization
• Relativity Effects in GPS
• Relativistic Time Dilation
• Checkpoint: Satellite Timekeeping
• GPS Position Calculation
• Position from Satellite Signals
• Uber GPS Accuracy in Manhattan
• GPS Error Sources
• Checkpoint: Operational Accuracy
• Knowledge Check
• Quiz: GPS Fundamentals
• Interactive Quiz: Match Concepts
• Interactive Quiz: Sequence the Steps
• Key Takeaway
• For Kids: Meet the Sensor Squad!
• Concept Relationships
• See Also
• Try It Yourself
• Common Pitfalls
• Overbuilt Initial Prototypes
• Security During Development
• Failure Modes and Recovery
• Label the Diagram
• What’s Next
• Code Challenge

20.5 GPS Architecture

This section: GPS Architecture — Use Figure 20.1 to separate the satellite, ground control, and receiver parts of positioning.

Use Figure 20.1 to separate the satellite, ground control, and receiver parts of positioning.

+

Satellites transmit their time and orbit information, while ground stations monitor the orbits and upload corrections. The receiver measures when signals arrive using its own clock, then solves for position and a clock offset together. The figure’s four satellite condition follows from those four unknowns: three coordinates and one clock term. This is why a time error cannot be treated as a small display issue. Review the received signals, correction data, and geometry before claiming that a position estimate is reliable.

GPS is TDoA (Inverted):

Satellites play the part of static devices (but are transmitters). Mobile device measures reception time using its clock. Uses satellite’s transmitted time for the time difference. For each satellite: measures (ToF + c × clockOffset). These are pseudoranges (erroneous distances).

20.6 Satellite Synchronization

This section: Satellite Synchronization — The clocks in Figure 20.2 show why GPS timing and receiver timing must be treated separately.

The clocks in Figure 20.2 show why GPS timing and receiver timing must be treated separately.

+

Each satellite carries an atomic clock so transmitted times share a precise reference. A phone does not carry that clock; it uses incoming satellite signals while estimating its own clock offset. The precision note in the figure shows how quickly a small timing error becomes distance error. For the positioning decision, check the time carried by the signal and the offset solved at the receiver. Treating the phone clock as already synchronized would hide a core unknown in the range calculation.

How Satellites Stay Synchronized:

Atomic Clocks On Board (Caesium or Rubidium). Cost: ~$100,000 per clock. Accuracy: ~1 nanosecond per day. All satellites share time reference.

But They Aren’t Static?. True! But we know their orbits precisely. Can predict positions quite accurately. Small errors do creep in…

Ground Control Segment:. Dedicated ground stations monitor satellite orbits. Track actual positions vs predicted. Upload corrections to satellites. Must model relativistic effects!

Use Figure 20.3 to see why a satellite’s position must be known when its signal is received.

+

The satellites in the figure are moving around Earth, not fixed points above the receiver. A range measurement therefore needs orbit information for the signal’s transmission time as well as the measured arrival time. Ground control tracks actual paths against predicted paths and supplies corrections that help the receiver place each satellite. If that location is wrong, the same travel time points to the wrong geometry. Check the orbit data and its age before assigning all position error to the receiver.

Relativistic Effects:

Special Relativity: Satellite clocks run slower due to velocity (~7 μs/day slower). General Relativity: Satellite clocks run faster due to weaker gravity (~45 μs/day faster). Net Effect: ~38 μs/day faster → must be corrected! (NIST)

+Checkpoint: Satellite Timekeeping

You now know:

• Satellite atomic clocks and ground control keep the shared time reference usable.
• Relativity matters at GPS orbit: about 7 us/day slower from velocity, 45 us/day faster from gravity, and 38.7 us/day net.
• Without correction, the timing drift would accumulate about 10 km of position error per day.

20.7 GPS Position Calculation

This section: GPS Position Calculation — The equations in Figure 20.4 connect four measured ranges to position and receiver clock offset.

The equations in Figure 20.4 connect four measured ranges to position and receiver clock offset.

+

For each satellite, the receiver knows a position from orbit data and measures a range that includes clock error. The model adds true distance, receiver clock offset, and any error left over. Four separate satellite equations can solve three position values and one clock offset. Yet a solution can still be poor. The record asks for the error left by each satellite, signal geometry, and correction data. Check those items before using the point for a product action. A coordinate alone does not show how much trust it deserves.

Position Equations:

For each satellite $i$:

Where: $\rho_i$ = pseudorange to satellite $i$ (measured). $(x_i, y_i, z_i)$ = satellite $i$ position (known from ephemeris). $(x_r, y_r, z_r)$ = receiver position (unknown). $c$ = speed of light. $\Delta t$ = receiver clock offset (unknown). $E_i$ = error term (atmospheric delays, etc.).

Four Unknowns:

$x_r$ (receiver X position). $y_r$ (receiver Y position). $z_r$ (receiver Z position). $\Delta t$ (clock offset).

Need at least 4 satellites to solve for 4 unknowns!

20.8 Position from Satellite Signals

This section: Position from Satellite Signals — Scenario: Your GPS receiver picks up signals from 4 satellites.

Scenario: Your GPS receiver picks up signals from 4 satellites. You need to understand how position is derived from raw timing measurements.

Given data (simplified to 2D for clarity):

Step 1: Convert time to distance

Each pseudorange = speed of light x travel time:

• Sat A: 299,792 km/s x 0.06733 s = 20,185.0 km

Step 2: Notice the clock offset

All pseudoranges include the same unknown clock error. If the receiver clock is 50 nanoseconds fast, every pseudorange is 15 meters too long. The fourth satellite lets us solve for this offset.

Step 3: Solve the system of equations

With 4 equations and 4 unknowns (x, y, z, clock offset), the receiver’s least-squares solver finds the position. In practice, modern receivers process signals from 10-12 satellites simultaneously; additional usable satellites can improve geometry and redundancy, depending on measurement quality, and help detect anomalies.

Key insight: Additional usable satellites can improve geometry and redundancy, but the accuracy gain depends on geometry and measurement quality; no fixed 20-30% reduction applies per satellite.

20.9 Hypothetical Manhattan Pickup Exercise

This section: Hypothetical Manhattan Pickup Exercise — Assume reflected GPS signals displace some pickup pins by 20–50 m; model how wrong-side-of-street placements affect calls, delay and driver idle cost.

Assume reflected GPS signals displace some pickup pins by 20–50 m; model how wrong-side-of-street placements affect calls, delay and driver idle cost. Do not attribute the scenario figures to Uber.

Hypothetical mechanism: Manhattan’s dense skyscraper grid can create multipath interference. For this exercise, assume reflected signals add 50–200 ns of delay, corresponding to illustrative 15–60 m range-bias values.

The technical challenge in numbers:

Possible multi-technology mitigations for the hypothetical urban scenario:

1. Sensor fusion: Combine GPS with phone accelerometer and gyroscope data; dead reckoning between fixes may help during multipath events.
2. Map matching: Snap estimated positions to the road network using a suitable model, while retaining uncertainty about the match.
3. 3D building models: Use building-height data to estimate satellite visibility and potential multipath interference.
4. Wi-Fi fingerprinting: Add access-point signal strengths as supplementary positioning data where coverage supports it.

Modeled outcomes:

• Manhattan pickup accuracy improved from 25-50m median error to 8-12m
• Assumed phone calls for pickup coordination drop 62%
• Assumed average pickup time decreases by 2.8 minutes
• Assumed annual savings are $32 million in reduced driver idle time

Lesson for IoT designers: Any IoT application that depends on GPS positioning in urban environments must budget for multipath mitigation. Raw GPS alone is insufficient — sensor fusion, map matching, and supplementary positioning technologies are essential for sub-10-meter accuracy in built-up areas.

20.10 GPS Error Sources

This section: GPS Error Sources — Use Figure 20.5 to see how independent timing, atmosphere, geometry, and reflection errors combine in a position estimate.

Use Figure 20.5 to see how independent timing, atmosphere, geometry, and reflection errors combine in a position estimate.

+

Read the satellite and receiver clock terms first. A small time error becomes a range error because the radio wave moves so fast. The upper air and lower air add more delay. Orbit error and satellite shape then affect how all those range errors turn into a point on the map. Near a building, a bounced path is longer than the direct path. The metre values are parts of the error, not a promise of final accuracy. Save fix quality and facts about the site with each point; latitude and longitude are not exact truth by themselves.

Signal Strength Challenge:

GPS signal transmitted at 20 watts. Travels 20,200 km (GPS orbit altitude). Received power: ~10^-16 watts (incredibly weak!). Various atmospheric effects introduce errors.

+Checkpoint: Operational Accuracy

You now know:

• Four satellites solve the minimum four unknowns; 10-12 satellites let receivers improve and cross-check the solution.
• Dense streets can add 50-200 ns of delay and 15-60 m of position error.
• A weak 20 W satellite signal arriving from 20,200 km needs correction, filtering, and honest quality metadata.

20.11 Knowledge Check

This section: Knowledge Check

20.12 What’s Next

This section: What’s Next — Continue to GPS Accuracy and Enhancement to learn about the GPS error budget, differential GPS corrections, and RTK techniques that achieve centimeter-level accuracy for precision applications.

Continue to GPS Accuracy and Enhancement to learn about the GPS error budget, differential GPS corrections, and RTK techniques that achieve centimeter-level accuracy for precision applications.

20.13 Continue Your Route

This section: Continue Your Route — This is the last part of this chapter.

This is the last part of this chapter. Return to GPS Location: Ranging Methods. See ux-design module index.