Ps-LAMBDA: Ambiguity success rate evaluation software for interferometric applications

Verhagen, Sandra; Li, Bofeng; Teunissen, Peter

doi:10.1016/j.cageo.2013.01.014

Cited by 106 publications

(61 citation statements)

References 42 publications

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“…It is clear, that the lower bounds are also valid for the optimal partial integer estimator. The analysis in Verhagen et al (2013) shows that the success rates of integer BS are a tight lower bound for the ILS success rates if a prior decorrelation function is used. The idea of using BS success rates for selecting the subset I with a given reliability constraint was introduced in Teunissen et al (1999) and used for PAR in, e.g., Khanafseh and Pervan (2010), Verhagen et al (2011), Odijk et al (2014, and Nardo et al (2016).…”

Section: Criteria For Selecting the Integer Subsetmentioning

confidence: 99%

Optimal Estimation of a Subset of Integers with Application to GNSS

Brack

2016

Artificial Satellites

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ABSTRACT. The problem of integer or mixed integer/real valued parameter estimation in linear models is considered. It is a well-known result that for zero-mean additive Gaussian measurement noise the integer least-squares estimator is optimal in the sense of maximizing the probability of correctly estimating the full vector of integer parameters. In applications such as global navigation satellite system ambiguity resolution, it can be beneficial to resolve only a subset of all integer parameters. We derive the estimator that leads to the highest possible success rate for a given integer subset and compare its performance to suboptimal integer mappings via numerical studies. Implementation aspects of the optimal estimator as well as subset selection criteria are discussed.

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Section: Criteria For Selecting the Integer Subsetmentioning

confidence: 99%

Optimal Estimation of a Subset of Integers with Application to GNSS

Brack

2016

Artificial Satellites

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“…(2011) and Verhagen and Teunissen, (2013). However the performance of the success rate is still not fully understood.…”

Section: E I Wa N G a N D O T H E R S Vol 69mentioning

confidence: 99%

“…Combined with the decorrelation procedure, the IB success rate is considered as a tight lower bound of the ILS success rate (Thomsen, 2000;Verhagen 2003;Feng and Wang 2011;Verhagen et al, 2013). 3.3.2.…”

Section: Introduction Global Navigation Satellite Systems (Gnss) Promentioning

confidence: 99%

Impact of Decorrelation on Success Rate Bounds of Ambiguity Estimation

et al. 2016

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Reliability is an important performance measure of navigation systems and this is particularly true in Global Navigation Satellite Systems (GNSS). GNSS positioning techniques can achieve centimetre-level accuracy which is promising in navigation applications, but can suffer from the risk of failure in ambiguity resolution. Success rate is used to measure the reliability of ambiguity resolution and is also critical in integrity monitoring, but it is not always easy to calculate. Alternatively, success rate bounds serve as more practical ways to assess the ambiguity resolution reliability. Meanwhile, a transformation procedure called decorrelation has been widely used to accelerate ambiguity estimations. In this study, the methodologies of bounding integer estimation success rates and the effect of decorrelation on these success rate bounds are examined based on simulation. Numerical results indicate decorrelation can make most success rate bounds tighter, but some bounds are invariant or have their performance degraded after decorrelation. This study gives a better understanding of success rate bounds and helps to incorporate decorrelation procedures in success rate bounding calculations. K E Y

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“…Considering that in the real applications, one usually accepts the fixed solution only when its success rate is close to 1 (say, >99%), one can use these two bounds to easily evaluate the success rate. For more information about the performance of the other approximations and bounds, one can refer to [13,23,24].…”

Section: =Ils [Default] 2=ib 3=ir Optionmentioning

confidence: 99%

GNSS Integer Ambiguity Estimation and Evaluation: LAMBDA and Ps-LAMBDA

Verhagen

Teunissen

2013

Lecture Notes in Electrical Engineering

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Abstract. Successful integer carrier-phase ambiguity resolution is crucial for high precision GNSS applications. It includes both integer estimation and evaluation. For integer estimation, the LAMBDA method has been applied in a wide variety of GNSS applications. The method's popularity stems from its numerical efficiency and statistical optimality. However, before conducting ambiguity resolution, one needs to infer how reliable the fixed solution can expected to be, as incorrect fixed ambiguity solutions often lead to unacceptable positioning errors. In this paper, two Matlab software tools are introduced for the evaluation and integer estimation: Ps-LAMBDA and an updated version of LAMBDA. Evaluation of the integer solution is based on the ambiguity success rate. Since this probability of correct integer estimation is generally difficult to compute, easy-to-use approximations and bounds of the ambiguity success rate are provided by the Ps-LAMBDA software. This success rate tool is valuable not only for inferring whether to fix the ambiguities but also for design and research purposes. For the actual integer estimation, the updated version of the LAMBDA software, provides now more options of integer estimation and integer search, including the searchand-shrink strategy. In addition, the Fixed Failure-rate Ratio Test (FF-RT) and the Fixed Critical-value Ratio Test (FC-RT) are incorporated for users to validate the significance of the fixed solution. Using these two software tools together allows for the combined execution of integer estimation and evaluation, thus benefiting multi-frequency, multi-GNSS applications.

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Ps-LAMBDA: Ambiguity success rate evaluation software for interferometric applications

Cited by 106 publications

References 42 publications

Optimal Estimation of a Subset of Integers with Application to GNSS

Optimal Estimation of a Subset of Integers with Application to GNSS

Impact of Decorrelation on Success Rate Bounds of Ambiguity Estimation

GNSS Integer Ambiguity Estimation and Evaluation: LAMBDA and Ps-LAMBDA

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