Sigma inflation for the local area augmentation of GPS

Pervan, Boris; Sayim, Irfan

doi:10.1109/7.976966

Cited by 18 publications

(17 citation statements)

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“…The data broadcasts rate has to be increased accordingly, and this will become a datalink bandwidth burden for the master station. The finite sample size demands a counterbalance between uncertainties in test statistics and susceptible of correlation coefficient between multiple reference receivers (Pervan and Sayim 2001). There are many candidate estimation methods that could deal with the sample size problem.…”

Section: The ML Based Position Domain Mrccmentioning

confidence: 99%

Multiple reference consistency check for LAAS: a novel position domain approach

Quddus

Ison

et al. 2011

GPS Solut

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Since the traditional Maximum Likelihood (ML) based range domain MultipleReference Consistency Check (MRCC) has limitations in satisfying the integrity requirement of CAT II/III for civil aviation, a Kalman filter based position domain method has been developed for fault detection and exclusion in Local Area Augmentation System (LAAS) MRCC process. The position domain approach developed in this paper seek to address the limitations of range domain based MRCC by focusing not only on improving the performance of the fault detection but also on the integrity risk requirement for MRCC. In addition, the issue of the stability of the Kalman filter in relation to the position domain approach is considered. GPS ranging corrections from multiple reference receivers are fused by the adaptive Kalman filter at the master station for detecting and excluding the single reference receiver' failure. The performance of the developed Kalman filter based MRCC algorithm has been compared with the traditional ML based method using experimental data. The results reveal that the Vertical Protection Level (VPL) is slightly better in the ML based method compared to the developed Kalman filter based approach under the faultfree case. However, the availability is better in the proposed method relative to the ML based approach under the single-fault case. In addition, a better fault-tolerant positioning result is obtained even if different fault types are considered under the single-fault case. In particular, the algorithm can be a candidate option as an augmentable complement for the traditional MRCC and can be implemented in a master station element of the LAAS integrity monitoring architecture.

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Section: The ML Based Position Domain Mrccmentioning

confidence: 99%

Multiple reference consistency check for LAAS: a novel position domain approach

Quddus

Ison

et al. 2011

GPS Solut

View full text Add to dashboard Cite

show abstract

“…The details of the computation of inflation factors from an integrity risk perspective are provided in reference (Pervan and Sayim, 2001), but for clarity in exposition here, inflation factors will be directly generated using a 99 . 9% confidence interval.…”

Section: A D a P T I V E B I N N I N G M E T H O D Thementioning

confidence: 99%

Synthesis of Empirical and Theoretical Approaches Toward the Establishment of GBAS σ_{pr_gnd}

2005

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The objective of this paper is to describe recent progress in the area of the Ground Based Augmentation System (GBAS) s pr_ gnd establishment to ensure aircraft precision approach navigation integrity. In particular, this paper details: (1) the development and testing of a new adaptive binning algorithm for processing GBAS reference station empirical data to account for ranging error non-stationarity; (2) an introduction of a practical empirical method to quantify and compensate for the effects of seasonal variations of ranging error ; and (3) the synthesis of these empirical results with existing theoretical ground-multipath models toward a quantitative establishment s pr_ gnd for GBAS.2. Expanding bin. 3. Sigma estimation.

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“…In contrast to the impulse response coefficients in (5), these coefficients are vector-valued since the G subsystem, which maps {v k } to {u k }, is single-input, multiple-output. Assuming zero initial conditions (u 0 ¼ 0), it follows from (12) that…”

Section: Application To Spherically Symmetric Overboundingmentioning

confidence: 99%

“…Navigation systems based on DGPS such as the Local Area Augmentation System (LAAS) [2] and other ground-based augmentation systems utilize filters to smooth the pseudo-range corrections generated by reference receiver processing. The filtering operation introduces time-correlation of the noise that cannot be accounted for with conventional overbounding techniques (e.g., [3][4][5]). This makes it difficult to show that the system design satisfies navigation integrity requirements since the effect of time-correlated errors on the probability density function (PDF) of the filter output is not modelled.…”

Section: Introductionmentioning

confidence: 99%

A Proof of the Spherically Symmetric Overbounding Theorem For Linear Systems

Pulford

2008

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Rife and Gebre‐Egziabher's recent paper [1] considers linear mappings of random variables from spherically symmetric probability distributions in the context of overbounding correlated ranging errors. This theory has potential implications for ensuring the integrity of differential GPS (DGPS) navigation systems. We first give a succinct rederivation of their preliminary result. The extension to a cascade of two discrete‐time, linear time‐invariant filters, the main result in [1], is then formulated using a precise definition of spherical symmetry for scalar random processes. The relationship between the input and output probability densities when the input density is spherically symmetric is derived using linear systems theory. This yields an alternative statement of the spherically symmetric overbounding theorem in terms of the system matrices. A precise definition is given of the filter impulse response coefficients and the multi‐dimensional convolution operation that is needed to ensure the validity of the overbounding theorem in [1]. The equivalence between the two representations is formally proved. Numerical simulations are provided that support the derived results.

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Sigma inflation for the local area augmentation of GPS

Cited by 18 publications

References 1 publication

Multiple reference consistency check for LAAS: a novel position domain approach

Multiple reference consistency check for LAAS: a novel position domain approach

Synthesis of Empirical and Theoretical Approaches Toward the Establishment of GBAS σ_{pr_gnd}

A Proof of the Spherically Symmetric Overbounding Theorem For Linear Systems

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Sigma inflation for the local area augmentation of GPS

Cited by 18 publications

References 1 publication

Multiple reference consistency check for LAAS: a novel position domain approach

Multiple reference consistency check for LAAS: a novel position domain approach

Synthesis of Empirical and Theoretical Approaches Toward the Establishment of GBAS σpr_gnd

A Proof of the Spherically Symmetric Overbounding Theorem For Linear Systems

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Synthesis of Empirical and Theoretical Approaches Toward the Establishment of GBAS σ_{pr_gnd}