Mathematical aspects of GPS RAIM

Diggelen, Frank van; Brown, Alison

doi:10.1109/plans.1994.303383

Cited by 18 publications

(11 citation statements)

References 2 publications

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“…and is the prediction pseudo-range which can be modeledas follow: (14) The coordinates of each observation satellite are calculated by broadcasted ephemeris. And represent the receiver prediction coordinates.…”

Section: B Gnss State Representation Modelmentioning

confidence: 99%

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Fault detection and exclusion for GNSS measurements using observations projection on information space

Mahmoud

Najjar

Naja

et al. 2015

2015 Fifth International Conference on Digital Information and Communication Technology and Its Applications (DICTAP)

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Faults in the GNSS measurements are the main reason for uncertainty positioning. Accuracy can thus be maximized by selecting only those observations least contaminated by faults to form the navigation solution (positioning) and discarding the rest. In this paper, we propose an algorithm to solve the problem of multi faults in the GNSS observations (pseudorange). The algorithm is based on observations projection on information space in order to detect and exclude the measurement faults and on Information Filter in order to estimate the position. The proposed method is tested using real data acquired with an experimental vehicle using low cost GNSS receiver in order to demonstrate its efficiency and its validity.

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Section: B Gnss State Representation Modelmentioning

confidence: 99%

“…A common method of estimating is to use the parity vector [14]. In our case, the parity vector is defined as:…”

Section: B Information On Position Errormentioning

confidence: 99%

Fault detection and exclusion for GNSS measurements using observations projection on information space

Mahmoud

Najjar

Naja

et al. 2015

2015 Fifth International Conference on Digital Information and Communication Technology and Its Applications (DICTAP)

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“…The purpose of RAIM is to detect the presence of unacceptably large position error and, further, to exclude the error source. Thus, the GPS navigation is allowed to continue (Diggelen and Brown 1994). An algorithm based on a single Kalman filter is proposed in this paper to speed up the failure detection and to reduce the incorrect exclusion rate (IER).…”

Section: Integritymentioning

confidence: 99%

“…According to Diggelen and Brown (1994), there exists a parity matrix P(k) satisfying P(k)H(k)=0 and P(k)P T (k) = I n)4 [here I n)4 stands for an identity matrix with dimension (n)4)·(n)4)]. Then the parity vector, p(k), can be represented as…”

Section: Integritymentioning

confidence: 99%

GBAS testbed development in Taiwan with a prototype GPS/GBAS receiver

Wang

Yang²

2006

GPS Solut

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“…In [9], the equivalence of the solution separation approach and the use of a RAIM estimate of the bias to correct the full solution is demonstrated. However, the connection between solution separation and other FDE methods is not explicitly shown.…”

Section: Snapshot Fde With Normalized Solution Separationmentioning

confidence: 99%

Fault Detection and Exclusion Using Normalized Solution Separation and Residual Monitoring Methods

Young

McGraw

2003

Navigation

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INTRODUCTIONBecause GPS signal-in-space integrity monitoring currently is inadequate for safety-of-life applications, real-time fault detection and exclusion (FDE) for navigation systems involving GPS is of considerable importance, especially in achieving primary means of navigation. Since the current assumptions about the GPS constellation and its measurement accuracy do not provide high enough availability of FDE to meet the primary-means objectives for all phases of flight, integration of GPS with inertial sensors for integrity monitoring has received considerable attention [1 -3]. GPS integrity algorithms can be classified into two broad categories based on the method employed for computing the navigation solution -snapshot approaches and filtered approaches. Snapshot approaches are generally based on least-squares (LS) methods, while filtered approaches generally utilize multiple Kalman filters with different fault hypothesis models.In addition to the snapshot vs. filtered classification, GPS integrity algorithms can be classified into two different categories based on the characteristics of their test statistics for the FDE function -range domain methods and position domain methods. For example, the solution separation algorithms in [1,2,4] are position domain methods, while the measurement residual algorithm in [3] is a range domain method.For snapshot algorithms, range domain methods are equivalent to position domain methods since variables in the range domain can be directly related to variables in the position domain and vice versa. For filtered algorithms, however, the relationship between test statistics in the range domain and their corresponding position errors cannot be clearly defined. This is the case because past measurements and statistics of the described system model also play a role in determining the current navigation solution. Therefore, it is more difficult to develop an analytical algorithm that relates the test statistic in the range domain to the horizontal protection level (HPL) or horizontal exclusion level (HEL) in the position domain.In this paper, we propose a hybrid FDE algorithm in which the fault detection function is based on a normalized solution separation scheme, and the fault exclusion function uses a measurement residual technique. Since the test statistic for the fault detection function is in the position domain, HPL can be analytically derived and is independent of failure types. HPL is also predictable without real measurementsan important operational requirement. In addition, with normalization, the proper probability levels for detection threshold, HPL, and horizontal uncertainty level (HUL) can be obtained. For fault exclusion, the test statistic for the fault exclusion function is in the range domain. Hence, there is no analytical equation for HEL that is independent of failure types, and the availability of the fault exclusion function needs to be determined by off-line covariance simulation. However, since HEL is required only for off-line Vol. 50, No. 3, Fall...

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Mathematical aspects of GPS RAIM

Cited by 18 publications

References 2 publications

Fault detection and exclusion for GNSS measurements using observations projection on information space

Fault detection and exclusion for GNSS measurements using observations projection on information space

GBAS testbed development in Taiwan with a prototype GPS/GBAS receiver

Fault Detection and Exclusion Using Normalized Solution Separation and Residual Monitoring Methods

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