MCAR (multiple carrier ambiguity resolution)

Multiple Carrier Ambiguity Resolution (MCAR) is a technique used in Global Navigation Satellite System (GNSS) positioning, particularly in Real-Time Kinematic (RTK) applications. RTK is a satellite-based positioning technique that provides centimeter-level accuracy and is used in surveying, precision agriculture, and autonomous vehicles.

GNSS positioning works by measuring the time it takes for a signal to travel from a satellite to a receiver on the ground. The receiver uses this time and the known location of the satellite to calculate the distance between the two. By receiving signals from multiple satellites, the receiver can determine its own location through a process called trilateration. However, the accuracy of GNSS positioning can be affected by various factors such as atmospheric delays, multipath, and satellite clock errors.

One way to improve the accuracy of GNSS positioning is to use carrier phase measurements instead of pseudorange measurements. Carrier phase is the actual phase of the satellite signal, whereas pseudorange is the measured distance between the satellite and the receiver. Carrier phase measurements have a much higher resolution than pseudorange measurements and can provide centimeter-level accuracy. However, carrier phase measurements are ambiguous because the phase of the signal can wrap around multiple times as it travels from the satellite to the receiver. This wrapping effect is called cycle slip, and it introduces an unknown integer number of cycles to the carrier phase measurement.

MCAR is a technique used to resolve the carrier phase ambiguities and obtain the correct integer number of cycles. This is done by using multiple carrier frequencies from different GNSS constellations. Currently, there are four GNSS constellations: GPS (USA), GLONASS (Russia), Galileo (EU), and BeiDou (China). Each constellation broadcasts multiple carrier frequencies, and the carrier phases of these frequencies have different wraparound periods. By using carrier frequencies with different wraparound periods, MCAR can eliminate the ambiguity and obtain the correct integer number of cycles.

The MCAR process starts with initializing the carrier phase ambiguities to zero. The receiver then measures the carrier phases of multiple frequencies from different constellations and estimates the unknown integer number of cycles. This is done by comparing the measured carrier phase to the predicted carrier phase based on the receiver's position and the known position of the satellites. The difference between the measured and predicted carrier phase is called the residual. The goal of MCAR is to minimize the residuals by adjusting the carrier phase ambiguities.

The MCAR process involves two steps: integer estimation and integer fixing. In the integer estimation step, the receiver estimates the integer number of cycles for each carrier frequency. This is done by rounding the carrier phase measurement to the nearest integer and adding or subtracting a fixed integer number called the integer ambiguity. The integer ambiguity is the unknown integer number of cycles that needs to be resolved. The integer ambiguity is usually initialized to zero and updated during the integer fixing step.

In the integer fixing step, the receiver adjusts the integer ambiguity to minimize the residuals. This is done by comparing the residuals of the carrier phase measurements from different constellations. The carrier phase measurements from different constellations are combined using a process called carrier phase combination. The carrier phase combination is used to remove the ionospheric and tropospheric delays that affect the carrier phase measurements. The carrier phase combination is also used to reduce the noise in the carrier phase measurements.

The carrier phase combination involves weighting the carrier phase measurements based on their noise levels and combining them using a linear combination. The weights are calculated based on the signal-to-noise ratio (SNR) of each carrier frequency. The carrier phase combination can improve the accuracy of the carrier phase measurements by reducing the noise and removing the ionospheric and tropospheric delays.

Once the carrier phase measurements from different constellations are combined, the receiver can estimate the residuals for each carrier frequency. The residuals are the differences between the measured carrier phase and the predicted carrier phase based on the receiver's position and the known position of the satellites. The goal of MCAR is to minimize the residuals by adjusting the integer ambiguity. This is done by adjusting the integer ambiguity until the residuals are minimized for all carrier frequencies.

The integer fixing process can be done using different methods. One method is called the LAMBDA method, which stands for Least-squares AMBiguity Decorrelation Adjustment. The LAMBDA method is an iterative algorithm that adjusts the integer ambiguity by solving a set of linear equations. The linear equations are formed by combining the residuals of the carrier phase measurements from different constellations. The LAMBDA method can converge to the correct integer ambiguity in a few iterations.

Another method is called the Fixed Ambiguity method, which is a simpler method that fixes the integer ambiguity at a certain point in time. The Fixed Ambiguity method assumes that the integer ambiguity is constant over a certain period of time and fixes it at a certain epoch. The epoch can be chosen based on the quality of the carrier phase measurements or based on the availability of reference stations. The Fixed Ambiguity method can provide good results if the integer ambiguity is stable over time.

MCAR can provide centimeter-level accuracy in RTK applications. The accuracy of MCAR depends on various factors such as the quality of the carrier phase measurements, the number of satellites used, and the geometry of the satellite constellation. MCAR can also be affected by errors such as multipath, atmospheric delays, and satellite clock errors. To mitigate these errors, MCAR can be combined with other techniques such as carrier smoothing, ionosphere modeling, and troposphere modeling.

In conclusion, MCAR is a technique used in RTK applications to resolve the carrier phase ambiguities and obtain centimeter-level accuracy. MCAR uses multiple carrier frequencies from different constellations to eliminate the ambiguity and obtain the correct integer number of cycles. The MCAR process involves two steps: integer estimation and integer fixing. The integer fixing step adjusts the integer ambiguity to minimize the residuals of the carrier phase measurements from different constellations. MCAR can provide accurate results in RTK applications if combined with other techniques to mitigate errors.