On optimal filtering of GPS dual frequency observations without using orbit information

Successful carrier phase ambiguity resolution is the key to high-precision positioning with Global Navigation Satellite Systems (GNSS). The ambiguity dilution of precision (ADOP) is a well-known scalar measure which can be used to infer the strength of the GNSS model for carrier phase ambiguity resolution. In this contribution we present analytical closed-form expressions for the ADOP. This will be done for a whole class of different multifrequency single baseline models. These models include the geometry-fixed, the geometry-free and the geometry-based models, respectively. And within the class of geometry-based models, we discriminate between short and long observation time spans, and between stationary and moving receivers. The easy-to-use ADOP expressions can be applied to infer the contribution of various GNSS model factors. They comprise, for instance, the type, the number and the precision of the GNSS observations, the number and selection of frequencies, the presence of atmospheric disturbances, the length of the observation time span and the length of the baseline.

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“…To account for these weights, we may for example use an exponential function cf. Euler and Goad (1991):…”

Section: Time Correlation and Number Of Samplesmentioning

confidence: 99%

ADOP in closed form for a hierarchy of multi-frequency single-baseline GNSS models

Odijk

Teunissen

2008

J Geod

109

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“…so as to capture the elevation dependency, where h is the elevation of the satellite in degrees (Euler and Goad 1991). Incorporation of this elevation dependency in the LS-VCE allows one to estimate the zenith-referenced standard deviations of the undifferenced code and phase observables, r p and r u .…”

Section: Estimated Precision (Time Correlation)mentioning

confidence: 99%

GLONASS CDMA L3 ambiguity resolution and positioning

2016

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A first assessment of GLONASS CDMA L3 ambiguity resolution and positioning performance is provided. Our analyses are based on GLONASS L3 data from the satellite pair SVNs 755-801, received by two JAVAD receivers at Curtin University, Perth, Australia. In our analyses, four different versions of the two-satellite model are applied: the geometry-free model, the geometry-based model , the height-constrained geometry-based model, and the geometry-fixed model. We study the noise characteristics (carrier-to-noise density, measurement precision), the integer ambiguity resolution performance (success rates and distribution of the ambiguity residuals), and the positioning performance (ambiguity float and ambiguity fixed). The results show that our empirical outcomes are consistent with their formal counterparts and that the GLONASS data have a lower noise level than that of GPS, particularly in case of the code data. This difference is not only seen in the noise levels but also in their onward propagation to the ambiguity time series and ambiguity residuals distribution.

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“…This model is similar to the Euler and Goad elevation-dependent model (Euler and Goad, 1991), and is expressed as follows Therefore, the exponential elevation-dependent model was implemented to express the dependence of the GPS observable precision on the satellite elevation angle (Amiri-Simkooei et al, 2015). 17).…”

Section: Estimation Of Components Ofmentioning

confidence: 99%

On the Realistic Stochastic Model of GPS Observables: Implementation and Performance

Zangeneh-Nejad

Amiri-Simkooei

Sharifi

et al. 2015

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:High-precision GPS positioning requires a realistic stochastic model of observables. A realistic GPS stochastic model of observables should take into account different variances for different observation types, correlations among different observables, the satellite elevation dependence of observables precision, and the temporal correlation of observables. Least-squares variance component estimation (LS-VCE) is applied to GPS observables using the geometry-based observation model (GBOM). To model the satellite elevation dependent of GPS observables precision, an exponential model depending on the elevation angles of the satellites are also employed. Temporal correlation of the GPS observables is modelled by using a first-order autoregressive noise model. An important step in the high-precision GPS positioning is double difference integer ambiguity resolution (IAR). The fraction or percentage of success among a number of integer ambiguity fixing is called the success rate. A realistic estimation of the GNSS observables covariance matrix plays an important role in the IAR. We consider the ambiguity resolution success rate for two cases, namely a nominal and a realistic stochastic model of the GPS observables using two GPS data sets collected by the Trimble R8 receiver. The results confirm that applying a more realistic stochastic model can significantly improve the IAR success rate on individual frequencies, either on L1 or on L2. An improvement of 20% was achieved to the empirical success rate results. The results also indicate that introducing the realistic stochastic model leads to a larger standard deviation for the baseline components by a factor of about 2.6 on the data sets considered.* Corresponding author INTRODCTIONGPS data processing is usually performed by the least squares adjustment method for which both the functional and stochastic models must be correctly specified. The functional model, describing the mathematical relation between the observations and the unknown parameters, is usually well known either in the relative positioning or in the single/precise point positioning (Seeber, 2003;Hofmann-Wellenhof et al., 2008;Leick, 2004; Teunissen and Kleusberg, 1998;Rizos, 1997). However, the stochastic model, expressing the statistical characteristics of the GPS observations by means of a covariance matrix, is still a challenging problem. Misspecification in the stochastic model leads to unreliable and suboptimal estimates. The realistic stochastic model should thus be utilized aiming at obtaining reliable least squares estimates.There are a few common stochastic models for GPS observables: (1) Equal-weight stochastic model in which identical variances for each measurement type are chosen (i.e. the same variance for the code and the same variance for the phase observations). This structure ignores the correlations among different observables, (2) Satellite elevation-angle dependent model in which the observations weighting procedure is performed using trigonometric or exponential functions. T...

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On optimal filtering of GPS dual frequency observations without using orbit information

Cited by 266 publications

References 2 publications

ADOP in closed form for a hierarchy of multi-frequency single-baseline GNSS models

ADOP in closed form for a hierarchy of multi-frequency single-baseline GNSS models

GLONASS CDMA L3 ambiguity resolution and positioning

On the Realistic Stochastic Model of GPS Observables: Implementation and Performance

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