Double-differenced Carrier Phase Measurements Research Articles

Risk overbounding for ionospheric gradient monitor using geometry-free double differenced carrier phase measurements

Ionosphere anomaly can cause large spatial gradients in the double-differenced carrier phase (DDCP) measurements. Taking advantage of this characteristic, the ionospheric gradient monitor (IGM) is designed with multiple ground reference stations to detect threatening ionospheric gradients for safety of life applications. An optimal IGM should be most sensitive to ionospheric gradients and least sensitive to other errors. However, current IGM suffers from the influence of tropospheric error, which can degrade monitor performance under extreme weather conditions by causing risks of false alarms and missed detections. To address this issue, an alternative IGM is proposed using the geometry-free combination of DDCP as the test statistic. Ambiguity resolution procedure is designed for estimating the ambiguity term in the test statistic. The risk induced by the wrong ambiguity fix and tropospheric error are analyzed and bounded with required averaging period and minimum baseline length. The results show that the proposed theoretical IGM is capable of achieving probability of false alarm of 10–8 and probability of missed detection of 10–6 with a filtering period of 612 s and baseline length of 371.7 m or a filtering period of 544 s and baseline length of 384.4 m. The experimental results using data collected from Hong Kong Satellite Positioning Reference Station Network demonstrate that the performance of the proposed theoretical IGM is comparable to that of the existing detection algorithm.

Global Navigation Satellite System Real-Time Kinematic Positioning Framework for Precise Operation of a Swarm of Moving Vehicles.

The global navigation satellite system (GNSS) real-time kinematic (RTK) technique is used to achieve relative positioning centimeter levels among multiple agents on the move. A typical GNSS RTK estimates the relative positions of multiple rover receivers with respect to a single-base receiver. In a fleet of rover GNSS receivers, this approach is inefficient because each rover receiver only uses GNSS measurements of its own and those sent from a single-base receiver. In this study, we propose a novel GNSS RTK framework that facilitates the precise positioning of a swarm of moving vehicles through the GNSS measurements of multiple receivers and broadcasts fixed-integer ambiguities of GNSS carrier phases. The proposed framework not only provides efficient RTK positioning but also reliable performance with a limited number of GNSS satellites in view. Our experimental flight tests with six GNSS receivers showed that the systematic procedure of the proposed framework could maintain lower than 6 cm of 3D RMS positioning errors, whereas the conventional RTK failed to resolve the correct integer ambiguities of double difference carrier phase measurements more than 13% in five out of nine total baselines.

Impact of medium-scale traveling ionospheric disturbances on network real-time kinematic services: CATNET study case

Medium-scale traveling ionospheric disturbances (MSTIDs) are fluctuations in the plasma density that propagate through the upper layer of the atmosphere at velocities of approximately 100 m/s and periods reaching some tens of minutes. Due to their wavelengths, MSTIDs can degrade the performance of differential positioning techniques, such as real-time kinematics (RTK) or network-RTK (NRTK). This paper defines a novel methodology as a tool for relating the errors in NRTK positioning based on an MSTIDs indicator using the second difference in time of the slant total electron content (STEC). The proposed methodology performs integer ambiguity resolution (IAR) on the undifferenced measurements instead of using double-differenced carrier-phase measurements, as it is usual in RTK and NRTK. Statistical tests are applied to evaluate the degradation in the position errors caused by the impacts of MSTIDs on RTK and NRTK positioning over a data set spanning one year gathered from the CATNET network; a dual-frequency network of fixed permanent GNSS receivers located at the mid-latitudes of northeastern Spain. With the development of the proposed methodology for measuring the position degradation, another results of the present research are the establishment of thresholds for the proposed MSTIDs index, which can be used to monitor the positioning solution and to warn users when the measurements are affected by MSTIDs events, relating the position error to MSTIDs that affect not only the user receivers but also of the reference receivers within the network.

Integration and Simulations of INS/GNSS System using the Approach of Carrier Phase Measurements

<p class="MsoNormal" style="margin-top: 12.0pt; margin-right: 0in; margin-bottom: 6.0pt; margin-left: 0in; text-align: justify;"><em><span style="font-size: 9.0pt; font-family: "Arial",sans-serif; mso-ascii-theme-font: minor-bidi; mso-hansi-theme-font: minor-bidi; mso-bidi-theme-font: minor-bidi;" lang="EN-GB">This paper discusses the techniques of attitude, velocity ad position estimation from GNSS carrier phase measurements, and investigates the performance of the lower precision MEMS-based INS/GNSS system based on carrier phase measurements. Double differenced carrier phase measurements provide more accurate velocity and position estimation compared to code and Doppler measurements. However, integer ambiguity is required to be removed for precise positioning. Multiples<span style="color: red;"> </span>antennae approach is used to derive the attitude information from carrier phase measurements in order to control the large initial misalignment angles for initialization of the integration process or to utilize during benign dynamics. Lever arm effect is considered to compensate for the separation of GNSS antenna and IMU location. The derived three GNSS observables are used to correct the INS through optimal Kalman filtering in a closed loop. Simulation results indicates the effectiveness of the integrated system for airborne as well as for land navigation vehicles</span></em><span lang="EN-GB">. </span></p><div id="_mcePaste" class="mcePaste" style="position: absolute; left: -10000px; top: 0px; width: 1px; height: 1px; overflow: hidden;"><p class="MsoNormal" style="margin-top: 12.0pt; margin-right: 0in; margin-bottom: 6.0pt; margin-left: 0in; text-align: justify;"><em><span style="font-size: 9.0pt; font-family: "Arial",sans-serif; mso-ascii-theme-font: minor-bidi; mso-hansi-theme-font: minor-bidi; mso-bidi-theme-font: minor-bidi;" lang="EN-GB">This paper discusses the techniques of attitude, velocity ad position estimation from GNSS carrier phase measurements, and investigates the performance of the lower precision MEMS based INS/GNSS system based on carrier phase measurements. Double differenced carrier phase measurements provide more accurate velocity and position estimation compared to code and Doppler measurements. However, integer ambiguity is required to be removed for precise positioning. Multiples<span style="color: red;"> </span>antennae approach is used to derive the attitude information from carrier phase measurements in order to control the large initial misalignment angles for initialization of the integration process or to utilize during benign dynamics. Lever arm effect is considered to compensate for the separation of GNSS antenna and IMU location. The derived three GNSS observables are used to correct the INS through optimal Kalman filtering in a closed loop. Simulation results indicates the effectiveness of the integrated system for airborne as well as for land navigation vehicles</span></em><span lang="EN-GB">. </span></p></div>

Improving the Performance of INS/GNSS System Using the Approach of Carrier Phase Measurements

This paper discusses the techniques of attitude, velocity ad position estimation from GNSS carrier phase measurements, and investigates the performance of the lower precision MEMS based INS/GNSS system based on carrier phase measurements. Generally, a GPS receiver estimates the position and velocity from code phase and Doppler measurements. Double differenced carrier phase measurements provide more accurate velocity and position estimation compared to code and Doppler measurements. However, for position measurement, the integer ambiguity is required to be removed. Multiples antennae approach is used to derive the attitude information from carrier phase measurements in order to control the large initial misalignment angles for initialization of the integration process or to utilize during benign dynamics. Lever arm effect is considered to compensate for the separation of GNSS antenna and IMU location. The derived three GNSS observables are used to correct the INS through optimal Kalman filtering in a closed loop. Simulation results indicates the effectiveness of the integrated system for airborne as well as for land navigation vehicles.

High-Accuracy GPS-Based Aircraft Navigation for Landing using Pseudolites and Double-Difference Carrier Phase Measurements

The GPS code phase measurements provide accuracy about 5-20 m. This accuracy level is not sufficient for some applications such as aircraft landing. Precise positioning can be achieved by using differential carrier phase measurements. But these measurements contain unknown integers. The Carrier phase integer ambiguity can be resolved with the aid of ranging information from two integrity beacons, placed one on each side of the approach path to a runway. The clock bias present in the single difference carrier phase measurements is cancelled by the double-differencing. However, the double-difference measurements are correlated. The decorrelation is achieved by using LAMBDA method. This paper presents the integer ambiguity resolution algorithm and position estimation with single-difference and double-difference carrier phase measurements.

A Direct Attitude Determination Approach Based on GPS Double-Difference Carrier Phase Measurements

The principle of the traditional attitude solution approach based on GPS (Global Position System) is to get the attitude matrix according to the relationship of coordinates. During the progress, the error of baseline position assumed in ECEF (Earth-Centered Earth-Fixed) and the error of coordinate transform between body frame and reference frame (ENU, East-North-Up) have been included in the result, and finally the precision of attitude determination is reduced. This contribution presents a new approach of attitude determination, in which the attitude angles are calculated by the double-difference carrier phase equation of GPS according to the relationship of attitude matrix and attitude angles through least-squares estimate method. The new approach predigests the procedure of attitude determination which reduces the error assumed. According to the analysis the precision of attitude determination is higher than that of traditional method. It is shown it gets a precise attitude result with the direct attitude determination method in the simulation. A novel algorithm is proposed to solve some problems. Simulation results show the effectiveness of the proposed algorithm.

Noise analysis and suppression method in attitude determination using the global positioning system (GPS)

A noise suppression method is developed for attitude determination using the global positioning system. The influence of noise on attitude determination application is analyzed to determine the relationship of errors. In order to suppress the noise, the total least squares method is utilized for double difference carrier phase measurements and unit vectors between satellites and antennas. Experimental results indicate that compared to the traditional least squares method without noise suppression, the accuracy of the measurement of attitude angles is increased by about 30–50%. The increased computation time of this method does not significantly influence the real time performance for land vehicle application.

Smoothing GPS carrier phase double differences using inertial measurements for high performance applications

This paper will describe an enhancement to the GPS double difference carrier phase measurements on a single airborne platform by smoothing them with inertial measurements while preserving the dynamic bandwidth. This enhancement will reduce the impact of carrier phase multipath and carrier phase noise on baseline determination between multiple antennas on an aircraft when in flight. This type of measurement system has numerous applications where platform pointing and relative body motion must be determined at the mm-level for applications such as sensor stabilization, Synthetic Aperture Radar, long range RADAR (i.e. angle-of-arrival measurements). Lower noise levels (mm-level and below) enable more performance to the stabilized system such as increased aperture for longer range, operation at higher frequencies, and more image resolution. The focus of this paper will be on a technique to provide this enhanced performance for these various applications using the available navigation systems. Additionally, this type of smoothing can effectively remove the additional noise induced by carrier phase measurement differencing. The noise level of a double or triple difference can be reduced below that of the raw measurement. A complimentary synthesized double difference quantity with ultra-low-noise characteristics will be used to smooth the GPS carrier phase double difference measurements without losing dynamic bandwidth since it follows the airborne dynamics. Flight test data will be presented to demonstrate the performance improvement in the midst of aircraft dynamics. Results will show that the noise reduction follows the theoretical prediction.

10 Hz or 10 s?

Data sampling frequencies in many kinematic GNSS applications are often in the range of 2–10 Hz or even higher. In contrast, the sampling frequency of standard reference stations is usually not higher than 1 Hz, and many stations even deliver data at sampling intervals as large as 30 s. An easily implemented algorithm for data interpolation will be presented and it will be demonstrated that interpolation of pseudorange and carrier phase reference station data is possible at a high level of accuracy. This technique—which has not received proper attention so far—is helpful to reduce data storage capacity for postprocessing applications, but and can also be beneficial for real-time applications suffering from slow data links. Results of test trials indicate that a standard deviation better than 2 mm can be reached for interpolated carrier phases collected at reference sites sampling data with 5-s intervals in double difference mode. These interpolated double difference data obviously still follow a Gaussian distribution. A trend function for the expected standard deviation of interpolated double difference carrier phase measurements will be presented. From this function, a recommendation for an optimal sampling rate of reference station data can be derived which is close to 10 s.

GPS를 이용한 저궤도 위성 자세 결정의 미지정수 결정 성공확률 향상

GPS 반송파 측정값을 이용하게 되면 수 cm 이하의 정밀도로 위치 결정을 수행 할 수 있으며, 두 개 이상의 안테나를 움직이는 물체에 장착할 경우 정밀한 자세 결정을 수행할 수 있다. GPS 반송파 측정값을 사용하는 경우 항상 미지정수 결정의 어려움이 발생하게 되며, 미지정수 결정 과정에서 올바른 결정을 할 수 있는 척도로 성공확률을 확인할 필요가 있다. 본 논문에서 저궤도 위성의 자세 결정을 위하여 이중차분된 측정값을 사용하게 되며, 이때 만들어진 측정행렬과 측정값의 공분산을 이용하여 성공확률을 계산하게 된다. 성공확률을 향상시키기 위하여 저궤도 위성의 위치벡터와 자세벡터가 수직이라는 제한 조건을 사용하여 측정값을 증가시키는 방법을 제안하였다. 적용된 저궤도 위성의 궤도는 우리별 3호의 궤도 정보를 이용하여 만들었으며 시뮬레이션을 통하여 그 결과를 확인 하였다. To determine precise position GPS carrier phase measurements are used. In addition, the multi-antenna system consisting of 2 or more GPS antennas can make attitude determination effectively. When GPS carrier phase measurements are used the integer ambiguity must be fixed. The success rate is used to validate the integer ambiguity. For LEO satellite attitude determination the double difference carrier phase measurements are used, the success rate is calculated using the covariance matrix and the measurement matrix. The constraint that LEO satellite position vector and attitude vector is orthogonal is suggested for improving the success rate. The LEO satellite orbit model is KITSAT3. The results of the simulation are shown and analyzed.

On-the-fly GPS-based attitude determination using single- and double-differenced carrier phase measurements

Carrier phase measurements are primary observations for GPS attitude determination. Although the satellite-related errors can be virtually eliminated by forming single differences, the baseline-related errors such as line biases are still present in the single-differenced carrier phase measurements. It is, therefore, difficult to resolve the single-differenced integer ambiguities due to the line biases. By forming double differences, the line biases of the single-differenced carrier phase measurements can be effectively removed. However, the main disadvantages of this method lie in the fact that the double-differenced measurements are mathematically correlated and consequently the attitude obtained from the double differences is noisy. This paper presents a new algorithm through which both single and double differences are used simultaneously to resolve these problems in real-time. The solution of the integer ambiguities can be obtained by searching for the most likely grid point in the attitude domain that is independent of the correlation with the double differences. Next, the line biases and corresponding single difference integer ambiguities can be resolved on the fly by using the noisy attitude solution obtained from the previous double difference procedure. In addition, the relationship between the physical signal path difference and the line bias is formed. A new method is also applied to derive the attitude angles through finding the optimal solution of the attitude matrix element. The proposed new procedure is validated using ground and flight tests. Results have demonstrated that the new algorithm is effective and can satisfy the requirement of real-time applications.

Local Height Determination Using GPS-Monitored Atmospheric Path Delays

National satellite control points, or any fixed points determined rel- ative to a known control point, can serve as monitoring stations when equipped with dual-frequency global positioning system (GPS) receivers. The available mon- itoring station coordinates are used to advantage to derive time-varying ionospheric and tropospheric path delays from the observed carrier phase data. Distinguishing atmospheric parameters from geometric positions is necessary in many cases be- cause the relative tropospheric zenith delays are strongly correlated with the inter- station height differences. In addition, GPS users may work with the single-fre- quency receivers that track satellite signals for only a few minutes at a time. The algorithm in this paper is based on the cosine functions of double-difference carrier phase measurements. After removing the first-order temporal and spatial iono- spheric effects, the relative tropospheric delays are found to have correlation co- efficients of up to 0.85, with the Saastamoinen model delays using some standard values for atmospheric pressure, temperature, and humidity. When comparing the 19 GPS-derived orthometric heights with the independently leveled heights, in a 5.5 3 4.0 km 2 area, the use of GPS-monitored atmospheric path delays led to an improved root-mean-square height error of 61.48 cm.

The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation

The GPS double difference carrier phase measurements are ambiguous by an unknown integer number of cycles. High precision relative GPS positioning based on short observational timespan data, is possible, when reliable estimates of the integer double difference ambiguities can be determined in an efficient manner. In this contribution a new method is introduced that enables very fast integer least-squares estimation of the ambiguities. The method makes use of an ambiguity transformation that allows one to reformulate the original ambiguity estimation problem as a new problem that is much easier to solve. The transformation aims at decorrelating the least-squares ambiguities and is based on an integer approximation of the conditional least-squares transformation. This least-squares ambiguity decorrelation approach, flattens the typical discontinuity in the GPS-spectrum of ambiguity conditional variances and returns new ambiguities that show a dramatic improvement in correlation and precision. As a result, the search for the transformed integer least-squares ambiguities can be performed in a highly efficient manner.