5.3 GPS localization

GPS localization is a crucial technology for autonomous robots operating outdoors. It uses satellite signals to determine a robot's position on Earth. Understanding GPS fundamentals, signals, and error sources is key to effective implementation in robotics.

Advanced techniques like differential GPS and real-time kinematic positioning can improve accuracy. Integrating GPS with other sensors, like inertial navigation systems, enhances robustness. This combination is vital for reliable robot localization in challenging environments.

Overview of GPS localization

• GPS (Global Positioning System) is a satellite-based navigation system that provides accurate position, velocity, and time information worldwide
• GPS localization plays a crucial role in autonomous robotics, enabling robots to determine their position and navigate in outdoor environments
• Understanding the principles, signals, error sources, and advanced techniques of GPS is essential for effectively utilizing GPS in robotic applications

Fundamentals of GPS

Satellites in GPS constellation

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• GPS consists of a constellation of 24 satellites orbiting the Earth at an altitude of approximately 20,200 km
• Satellites are arranged in six orbital planes, ensuring global coverage and availability
• Each satellite continuously transmits radio signals containing information about its position and the precise time the signal was sent

Trilateration for position estimation

• GPS uses the principle of trilateration to determine the position of a receiver on Earth
• Trilateration involves measuring the distances (pseudoranges) from the receiver to at least four satellites
• By solving a system of equations based on the pseudoranges and satellite positions, the receiver's 3D position can be estimated

Timing and synchronization

• Accurate timing is crucial for GPS positioning, as it directly affects the accuracy of pseudorange measurements
• GPS satellites carry highly stable atomic clocks that are synchronized with each other and a master control station on Earth
• GPS receivers use less expensive quartz clocks, which are synchronized with satellite clocks using the received GPS signals

GPS signals and measurements

GPS signal structure

• GPS satellites transmit signals on two main frequencies: L1 (1575.42 MHz) and L2 (1227.60 MHz)
• The signals consist of carrier waves modulated with binary codes and navigation data
• The coarse/acquisition (C/A) code on L1 is the primary signal used for civilian GPS applications

Pseudorange measurements

• Pseudorange is the apparent distance between a GPS satellite and a receiver, derived from the time difference between signal transmission and reception
• Pseudoranges are affected by various error sources, such as atmospheric delays, clock biases, and multipath interference
• Pseudoranges are the primary measurements used for GPS positioning, as they provide the necessary information for trilateration

Carrier phase measurements

• Carrier phase measurements are based on the phase of the GPS carrier wave, rather than the modulated codes
• Carrier phase measurements are more precise than pseudorange measurements, with potential accuracies in the millimeter range
• However, carrier phase measurements are ambiguous, requiring specialized techniques (e.g., integer ambiguity resolution) to determine the exact number of carrier cycles between the satellite and receiver

GPS error sources

Atmospheric effects on GPS

• The Earth's atmosphere, particularly the ionosphere and troposphere, can affect GPS signals as they travel from satellites to receivers
• The ionosphere is a layer of charged particles that can delay GPS signals and introduce errors in pseudorange measurements
• The troposphere, the lower part of the atmosphere, can also delay GPS signals due to variations in temperature, pressure, and humidity

Multipath interference

• Multipath interference occurs when GPS signals reach the receiver via multiple paths, such as direct line-of-sight and reflections from nearby surfaces (buildings, ground)
• Multipath interference can introduce errors in pseudorange measurements and degrade positioning accuracy
• Advanced receiver techniques, such as multipath mitigation algorithms and antenna design, can help reduce the impact of multipath interference

Clock errors and biases

• GPS positioning relies on precise timing, and any errors or biases in satellite or receiver clocks can affect the accuracy of pseudorange measurements
• Satellite clock errors are monitored and corrected by the GPS control segment, with corrections transmitted in the navigation message
• Receiver clock errors are estimated as part of the positioning solution, treating the receiver clock bias as an additional unknown parameter

GPS receiver architecture

Antenna and RF front-end

• The GPS antenna is responsible for receiving the weak GPS signals from satellites
• Antennas are designed to have a hemispherical coverage pattern, allowing reception from satellites at various elevations and azimuths
• The RF front-end amplifies, filters, and downconverts the received GPS signals to a lower frequency for further processing

Signal acquisition and tracking

• GPS receivers must acquire and track the signals from visible satellites to extract pseudorange and carrier phase measurements
• Acquisition involves searching for GPS signals in a two-dimensional search space (code delay and Doppler frequency)
• Tracking maintains a continuous lock on the acquired signals, adjusting the code and carrier tracking loops to follow signal variations

Navigation data decoding

• GPS signals contain navigation data that includes satellite ephemeris (precise orbital parameters), clock corrections, and almanac information
• Receivers decode the navigation data to obtain the necessary information for positioning calculations
• The navigation data is transmitted at a low rate (50 bps) and is organized into frames and subframes, with a complete data message lasting 12.5 minutes

GPS positioning techniques

Single-point positioning

• Single-point positioning is the most basic GPS positioning technique, using pseudorange measurements from four or more satellites to determine a receiver's position
• The positioning solution is obtained by solving a system of nonlinear equations, typically using least-squares estimation or Kalman filtering
• Single-point positioning can achieve accuracies in the range of a few meters, depending on the quality of the receiver and the error sources present

Differential GPS (DGPS)

• Differential GPS involves the use of a reference station at a known location to improve the positioning accuracy of nearby receivers (rovers)
• The reference station calculates corrections for the pseudorange measurements based on its known position and broadcasts these corrections to the rovers
• Rovers apply the corrections to their own pseudorange measurements, effectively canceling out common errors (e.g., atmospheric delays, satellite clock errors) and improving positioning accuracy to the sub-meter level

Real-time kinematic (RTK) positioning

• Real-time kinematic positioning is an advanced technique that uses carrier phase measurements to achieve centimeter-level accuracy in real-time
• RTK involves the use of a reference station that transmits its carrier phase measurements and position to the rover
• The rover combines its own carrier phase measurements with those from the reference station, solving for the integer ambiguities and estimating its precise position relative to the reference station

GPS/INS integration

Benefits of GPS/INS fusion

• GPS and inertial navigation systems (INS) have complementary characteristics that make their integration beneficial for many applications
• GPS provides absolute positioning information, but its accuracy can be affected by signal blockages and multipath interference
• INS provides high-rate relative positioning, orientation, and velocity information, but its errors accumulate over time due to sensor biases and drifts
• Integrating GPS and INS can provide a more robust, accurate, and continuous positioning solution than either system alone

Loosely vs tightly coupled integration

• GPS/INS integration can be implemented using either a loosely coupled or tightly coupled architecture
• In a loosely coupled integration, the GPS and INS solutions are computed independently and then combined using a Kalman filter
• In a tightly coupled integration, the raw GPS measurements (pseudoranges and/or carrier phases) are directly fused with the INS measurements in a single Kalman filter
• Tightly coupled integration can provide better performance in scenarios with limited satellite visibility or high dynamics, as it allows the INS to aid the GPS signal tracking

Kalman filtering for GPS/INS

• Kalman filtering is a widely used technique for GPS/INS integration, as it provides a statistically optimal way to combine the measurements from both systems
• The Kalman filter estimates the states of the integrated system (e.g., position, velocity, orientation, sensor biases) based on the GPS and INS measurements and a dynamic model of the vehicle
• The filter continuously updates the state estimates and their associated uncertainties, taking into account the relative accuracies of the GPS and INS measurements
• Kalman filtering can be implemented in real-time, making it suitable for autonomous robotics applications

GPS in robotics applications

GPS for outdoor robot localization

• GPS is a key sensor for outdoor robot localization, providing absolute position information in a global reference frame
• Robots can use GPS receivers to estimate their position and aid in navigation tasks, such as waypoint following or path planning
• GPS can be combined with other sensors (e.g., INS, odometry, lidar) to improve localization accuracy and robustness

Challenges of GPS in urban environments

• Urban environments pose challenges for GPS-based localization due to signal blockages, multipath interference, and reduced satellite visibility
• Tall buildings, narrow streets, and other obstacles can block or reflect GPS signals, degrading positioning accuracy or causing complete signal loss
• Robots operating in urban environments may need to rely on additional sensors or techniques (e.g., 3D mapping, SLAM) to maintain accurate localization during GPS outages

Combining GPS with other sensors

• Integrating GPS with other sensors can improve the overall localization performance of a robot
• GPS can be combined with inertial sensors (IMUs) to provide a more robust and continuous positioning solution, as discussed in the GPS/INS integration section
• Other sensors, such as lidar, cameras, or ultrasonic sensors, can provide additional information about the robot's surroundings and help in tasks like obstacle avoidance or landmark-based localization
• Sensor fusion techniques, such as Kalman filtering or particle filtering, can be used to optimally combine the measurements from multiple sensors and estimate the robot's state

Advanced GPS concepts

Multi-constellation GNSS

• In addition to GPS, other global navigation satellite systems (GNSS) exist, such as Russia's GLONASS, Europe's Galileo, and China's BeiDou
• Multi-constellation GNSS receivers can track and use signals from multiple satellite systems simultaneously
• Using multiple GNSS constellations can improve positioning accuracy, reliability, and availability, particularly in challenging environments with limited sky visibility

Precise Point Positioning (PPP)

• Precise Point Positioning is a technique that enables high-accuracy positioning using a single GNSS receiver, without the need for a nearby reference station
• PPP relies on precise satellite orbit and clock information, as well as advanced models for correcting atmospheric delays and other error sources
• PPP can achieve centimeter-level accuracy, but it typically requires a longer convergence time (e.g., 30 minutes or more) compared to RTK positioning

GPS spoofing and countermeasures

• GPS spoofing is a type of intentional interference where fake GPS signals are transmitted to deceive a receiver into calculating an incorrect position
• Spoofing attacks can pose serious risks to autonomous robots that rely on GPS for localization and navigation
• Countermeasures against GPS spoofing include using encrypted GPS signals (e.g., military GPS), signal authentication techniques, and cross-checking GPS with other sensors or positioning methods
• Advanced receiver architectures, such as multi-antenna or multi-frequency receivers, can also help detect and mitigate spoofing attacks