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Integrity Monitoring for Carrier Phase Ambiguities
- Shaojun Feng, Washington Ochieng, Jaron Samson, Michel Tossaint, Manuel Hernandez-Pajares, J. Miguel Juan, Jaume Sanz, Àngela Aragón-Àngel, Pere Ramos-Bosch, Marti Jofre
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- Journal:
- The Journal of Navigation / Volume 65 / Issue 1 / January 2012
- Published online by Cambridge University Press:
- 25 November 2011, pp. 41-58
- Print publication:
- January 2012
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- Article
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The determination of the correct integer number of carrier cycles (integer ambiguity) is the key to high accuracy positioning with carrier phase measurements from Global Navigation Satellite Systems (GNSS). There are a number of current methods for resolving ambiguities including the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method, which is a combination of least-squares and a transformation to reduce the search space. The current techniques to determine the level of confidence (integrity) of the resolved ambiguities (i.e. ambiguity validation), usually involve the construction of test statistics, characterisation of their distribution and definition of thresholds. Example tests applied include ratio, F-distribution, t-distribution and Chi-square distribution. However, the assumptions that underpin these tests have weaknesses. These include the application of a fixed threshold for all scenarios, and therefore, not always able to provide an acceptable integrity level in the computed ambiguities. A relatively recent technique referred to as Integer Aperture (IA) based on the ratio test with a large number of simulated samples of float ambiguities requires significant computational resources. This precludes the application of IA in real time.
This paper proposes and demonstrates the power of an integrity monitoring technique that is applied at the ambiguity resolution and positioning stages. The technique has the important benefit of facilitating early detection of any potential threat to the position solution, originating in the ambiguity space, while at the same time giving overall protection in the position domain based on the required navigation performance. The proposed method uses the conventional test statistic for ratio testing together with a doubly non-central F distribution to compute the level of confidence (integrity) of the ambiguities. Specifically, this is determined as a function of geometry and the ambiguity residuals from least squares based ambiguity resolution algorithms including LAMBDA. A numerical method is implemented to compute the level of confidence in real time.
The results for Precise Point Positioning (PPP) with simulated and real data demonstrate the power and efficiency of the proposed method in monitoring both the integrity of the ambiguity computation and position solution processes. Furthermore, due to the fact that the method only requires information from least squares based ambiguity resolution algorithms, it is easily transferable to conventional Real Time Kinematic (RTK) positioning.
Carrier Phase-based RAIM Algorithm Using a Gaussian Sum Filter
- Ho Yun, Youngsun Yun, Changdon Kee
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- Journal:
- The Journal of Navigation / Volume 64 / Issue 1 / January 2011
- Published online by Cambridge University Press:
- 26 November 2010, pp. 75-90
- Print publication:
- January 2011
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- Article
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Carrier phase measurements are used to provide high-accuracy estimates of position. For safety-of-life navigation applications such as precision approach and landing, integrity plays a critical role. Carrier phase-based Receiver Autonomous Integrity Monitoring (CRAIM) has been investigated for many years (Pervan et al, 1998; Feng et al, 2007). Assuming that the carrier phase error has a Gaussian distribution, conventional CRAIM algorithms were directly derived from the Pseudorange-based RAIM (PRAIM). However, the actual carrier phase error does not exactly follow the Gaussian distribution, hence the performance of the conventional CRAIM algorithm is not optimal.
To approach this problem, this paper proposes a new CRAIM algorithm that uses Gaussian sum filters. A Gaussian sum filter can deal with any non-Gaussian error distribution and accurately present the posterior distributions of states. In this paper, a new method of making a Gaussian mixture model, which follows the true error distribution, is introduced. Additionally an integrity monitoring algorithm, using a Gaussian sum filter, is described in detail. The simulation results show that the proposed algorithm can have about 18% smaller Minimum Detectable Bias (MDB) and generates about 20% lower protection levels than those of the conventional CRAIM algorithm. In other words, by considering a non-Gaussian carrier phase error distribution, the new algorithm can improve the accuracy and the availability.