On the probability density function of the GNSS ambiguity residuals

Integer GNSS ambiguity resolution involves estimation and validation of the unknown integer carrier phase ambiguities. A problem then is that the classical theory of linear estimation does not apply to the integer GPS model, and hence rigorous validation is not possible when use is made of the classical results. As with the classical theory, a first step for being able to validate the integer GPS model is to make use of the residuals and their probabilistic properties. The residuals quantify the inconsistency between data and model, while their probabilistic properties can be used to measure the significance of the inconsistency. Existing validation methods are often based on incorrect assumptions with respect to the probabilistic properties of the parameters involved. In this contribution we will present and evaluate the joint probability density function (PDF) of the multivariate integer GPS carrier phase ambiguity residuals. The residuals and their properties depend on the integer estimation principle used. Since it is known that the integer least-squares estimator is the optimal choice from the class of admissible integer estimators, we will only focus on the PDF of the ambiguity residuals for this estimator. Unfortunately the PDF cannot be evaluated exactly. It will therefore be shown how to obtain a good approximation. The evaluation will be completed by some examples

GNSS multi-frequency receiver single-satellite measurement validation method

A method is presented for real-time validation of GNSS measurements of a single receiver, where data from each satellite are independently processed. A geometry- free observation model is used with a reparameterized form of the unknowns to overcome rank deficiency of the model. The ionosphere error and non-constant biases such as multipath are assumed changing relatively smoothly as a function of time. Data validation and detection of errors are based on statistical testing of the observation residuals using the detection–identification–adaptation approach. The method is applicable to any GNSS with any number of frequencies. The performance of validation method was evaluated using multi-frequency data from three GNSS (GPS, GLONASS, and Galileo) that span 3 days in a test site at Curtin University, Australia. Performance of the method in detection and identification of outliers in code observations, and detection of cycle slips in phase data were examined. Results show that the success rates vary according to precision of observations and their number as well as size of the errors. The method capability is demonstrated when processing four IOV Galileo satellites in a single-point-positioning mode and in another test by comparing its performance with Bernese software in detection of cycle slips in precise point-positioning processing using GPS data

Integer Least-squares Theory for the GNSS Compass

Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is the key to high-precision positioning and attitude determination. In this contribution, we develop new integer least-squares (ILS) theory for the GNSS compass model, together with efficient integer search strategies. It extends current unconstrained ILS theory to the nonlinearly constrained case, an extension that is particularly suited for precise attitude determination. As opposed to current practice, our method does proper justice to the a priori given information. The nonlinear baseline constraint is fully integrated into the ambiguity objective function, thereby receiving a proper weighting in its minimization and providing guidance for the integer search. Different search strategies are developed to compute exact and approximate solutions of the nonlinear constrained ILS problem. Their applicability depends on the strength of the GNSS model and on the length of the baseline. Two of the presented search strategies, a global and a local one, are based on the use of an ellipsoidal search space. This has the advantage that standard methods can be applied. The global ellipsoidal search strategy is applicable to GNSS models of sufficient strength, while the local ellipsoidal search strategy is applicable to models for which the baseline lengths are not too small. We also develop search strategies for the most challenging case, namely when the curvature of the non-ellipsoidal ambiguity search space needs to be taken into account. Two such strategies are presented, an approximate one and a rigorous, somewhat more complex, one. The approximate one is applicable when the fixed baseline variance matrix is close to diagonal. Both methods make use of a search and shrink strategy. The rigorous solution is efficiently obtained by means of a search and shrink strategy that uses non-quadratic, but easy-to-evaluate, bounding functions of the ambiguity objective function. The theory presented is generally valid and it is not restricted to any particular GNSS or combination of GNSSs. Its general applicability also applies to the measurement scenarios (e.g. single-epoch vs. multi-epoch, or single-frequency vs. multi-frequency). In particular it is applicable to the most challenging case of unaided, single frequency, single epoch GNSS attitude determination. The success rate performance of the different methods is also illustrated

IRNSS/NavIC and GPS: a single- and dual-system L5 analysis

The Indian Regional Navigation Satellite System (IRNSS) has recently (May 2016) become fully operational. In this contribution, for the fully operational IRNSS as a stand-alone system and also in combination with GPS, we provide a first assessment of L5 integer ambiguity resolution and positioning performance. While our empirical analyses are based on the data collected by two JAVAD receivers at Curtin University, Perth, Australia, our formal analyses are carried out for various onshore locations within the IRNSS service area. We study the noise characteristics (carrier-to-noise density, measurement precision, time correlation), the integer ambiguity resolution performance (success rates and ambiguity dilution of precision), 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 GPS L5-data have a lower noise level than that of IRNSS L5-data, particularly in case of the code data. The underlying model in our assessments varies from stand-alone IRNSS (L5) to IRNSS (Formula presented.) GPS (L5), from unconstrained to height-constrained and from kinematic to static. Significant improvements in ambiguity resolution and positioning performance are achievable upon integrating L5-data of IRNSS with GPS

Theory of carrier phase ambiguity resolution

Carrier phase ambiguity resolution is the key to high precision Global Navigation Satellite System (GNSS) positioning and navigation. It applies to a great variety of current and future models of GPS, modernized GPS and Galileo. A proper handling of carrier phase ambiguity resolution requires a proper understanding of the underlying theory of integer inference. In this contribution a brief review is given of the probabilistic theory of integer ambiguity estimation. We describe the concept of ambiguity pull-in regions, introduce the class of admissible integer estimators, determine their probability mass functions and show how their variability affect the uncertainty in the so-called ‘fixed’ baseline solution. The theory is worked out in more detail for integer least-squares and integer bootstrapping. It is shown that the integer least-squares principle maximizes the probability of correct integer estimation. Sharp and easy-to-compute bounds are given for both the ambiguity success rate and the baseline’s probability of concentration. Finally the probability density function of the ambiguity residuals is determined. This allows one for the first time to formulate rigorous tests for the integerness of the parameters

An assessment of smartphone and low-cost multi-GNSS single-frequency RTK positioning for low, medium and high ionospheric disturbance periods

The emerging GNSSs make single-frequency (SF) RTK positioning possible. In this contribution two different types of low-cost (few hundred USDs) RTK receivers are analyzed, which can track L1 GPS, B1 BDS, E1 Galileo and L1 QZSS, or any combinations thereof, for a location in Dunedin, New Zealand. These SF RTK receivers can potentially give competitive ambiguity resolution and positioning performance to that of more expensive (thousands USDs) dual-frequency (DF) GPS receivers. A smartphone implementation of one of these SF receiver types is also evaluated. The least-squares variance component estimation (LS-VCE) procedure is first used to formulate a realistic stochastic model, which assures that our receivers at hand can achieve the best possible ambiguity resolution and RTK positioning performance. The best performing low-cost SF RTK receiver types are then assessed against DF GPS receivers and survey-grade antennas. Real data with ionospheric disturbances at low, medium and high levels are analyzed, while making use of the ionosphere-weighted model. It will be demonstrated that when the presence of the residual ionospheric delays increases, instantaneous RTK positioning is not possible for any of the receivers, and a multi-epoch model is necessary to use. It is finally shown that the low-cost SF RTK performance can remain competitive to that of more expensive DF GPS receivers even when the ionospheric disturbance level reaches a Kp-index of 7-, i.e. for a strong geomagnetic storm, for the baseline at hand

Lattice-relaxation of zeolites

Quantum-chemical cluster calculations as well as solid-state chemical lattice-calculations indicate that zeolitic SiO2- and AlPO4-structures are flexible structures. The structures reflect the subtle balance of electrostatic and covalent interactions. The different electrostatic interactions lower the symmetry of layered AlPO4-structures compared to that of the corresponding SiO2-compounds. The result is a smaller zeolite-channel dimension for the AlPO4-structure compared to that of the corresponding SiO2-network. Deprotonation of the zeolite-lattice leads to large local changes in geometry that changes acidity compared to that predicted for a non-flexible lattice. Changes in lattice vibrational frequencies are consistent with the theoretically predicted relaxation of the zeolite-lattic

Effect of warm-up and precooling on pacing during a 15-km cycling time trial in the heat

PURPOSE:The best way to apply precooling for endurance exercise in the heat is still unclear. Therefore, we analyzed the effect of different preparation regimes on pacing during a 15-km cycling time trial in the heat.METHODS:Ten male subjects completed four 15-km time trials (30°C), preceded by different preparation regimes: 10 min cycling (WARM-UP), 30 min scalp cooling of which 10 min cycling (SC+WARM-UP), ice slurry ingestion (ICE), and ice slurry ingestion + 30 min scalp cooling (SC+ICE).RESULTS:No differences were observed in finish time and mean power output, although power output was lower for WARM-UP than for SC+ICE during km 13-14 (17±16 and 19±14 W, respectively) and for ICE during km 13 (16±16 W). Rectal temperature at the start of the time trial was lower for both ICE (~36.7°C) than both WARM-UP (~37.1°C) conditions and remained lower during the first part of the trial. Skin temperature and thermal sensation were lower at the start for SC+ICE.CONCLUSIONS:The preparation regime providing the lowest body heat content and sensation of coolness at the start (SC+ICE) was most beneficial for pacing during the latter stages of the time trial, although overall performance did not differ

Розробка нейромережевої інтелектуальної системи для прогнозування енергетичних центрів плямових зображень у процесах профілювання лазерного променя

Здійснено розробку нейромережевої інтелектуальної системи для прогнозування енергетичних центрів (ЕЦ) плямових зображень у процесах профілювання лазерного променя (ЛП). Обґрунтовано актуальність задачі прогнозування координат ЕЦ профілю ЛП. Розглянуто методи прогнозування та обґрунтовано доцільність застосування нейромережевої моделі. Здійснено комп’ютерне моделювання системи прогнозування, а також на основі отриманих результатів сформульовано вимоги та здійснено програмну реалізацію інтелектуальної системи.Выполнено разработку нейросетевой интеллектуальной системы для прогнозирования энергетических центров (ЭЦ) пятенных зображений в процесах профилирования лазерного луча (ЛЛ). Обоснована актуальность задачи прогнозирования координат ЭЦ профиля ЛЛ. Рассмотрены методы прогнозирования и обоснована целесообразность применения нейросетевой модели. Выполнено компьютерное моделирование системы прогнозирования, а также на основе полученных результатов сформулированы требования и выполнено программную реализацию интеллектуальной системы.The development of a neural net intellectual system for energy centers (EC) spot images forecasting in the processes of laser beam profiling (LB) is done. Actuality of the problem of coordinates forecasting of EC of laser beam profile is proved. Methods of forecasting are considered and the appropriateness of usage the neural net model is justified. Computer simulation of forecasting system is carried out and also on the basis of the obtained results the requirements are formulated and software implementation of intelligent system is performed

N-acetylaspartic acid in cerebrospinal fluid of multiple sclerosis patients determined by gas-chromatography-mass spectrometry

Background: Axonal degeneration is considered to play a major role in the development of clinical disability in multiple sclerosis (MS). N-AcetylAspartic Acid (NAA) is a neuron-specific marker constantly identified in MR-spectroscopy studies of the normal and MS brain. To our knowledge there are no studies available that evaluated NAA in cerebrospinal fluid (CSF) as a possible marker for disease severity. Objective: To evaluate CSF concentrations of NAA in MS in relation to disease phenotype, clinical measures of disability and MRI markers of disease burden. Methods: NAA concentrations were determined in CSF of 46 patients with MS (26 relapsing remitting (RRMS), 12 secondary progressive (SPMS) and 8 primary progressive (PPMS)). Prior to lumbar puncture, MS-patients underwent MRI and clinical examination, including the Expanded Disability Status Scale (EDSS) and the MS Functional Composite (MSFC). Additionally, CSF concentrations of NAA were determined in 12 patients with other neurological diseases (OND). Results: Median CSF NAA concentration was 0.74 (IQR: 0.59-0.94) in RRMS , 0.54 (IQR: 0.35-0.73) in SPMS and 0.83 μmol/l (IQR: 0.56-1.03) in PPMS patients. SPMS patients had a significantly lower NAA concentration than RRMS patients. NAA concentrations correlated with EDSS (r = )0.37, p = 0.016), MSFC (r = 0.41, p = 0.010), normalised brain volume (r = 0.49, p = 0.001), T2 lesion load (r = )0.35, p = 0.021) and black hole lesion load (r = )0.47, p = 0.002). No differences were observed between OND (median: 0.57 IQR: 0.28-0.73) and MS patients. Conclusions: CSF NAA concentration in MS patients is related to clinical performance and MRI measures of disease burden and may therefore be an important neuron specific marker of disease severity and possibly progression