Magnetometers provide compass information, and are widely used for navigation, orientation and alignment of objects. As magnetometers are affected by sensor biases and eventually by systematic ...distortions of the Earth magnetic field, a calibration is needed. In this paper, a method for calibration of magnetometers with three Global Navigation Satellite System (GNSS) receivers is presented. We perform a least-squares estimation of the magnetic flux and sensor biases using GNSS-based attitude information. The attitude is obtained from the relative positions between the GNSS receivers in the North-East-Down coordinate frame and prior knowledge of these relative positions in the platform's coordinate frame. The relative positions and integer ambiguities of the periodic carrier phase measurements are determined with an integer least-squares estimation using an integer decorrelation and sequential tree search. Prior knowledge on the relative positions is used to increase the success rate of ambiguity fixing. We have validated the proposed method with low-cost magnetometers and GNSS receivers on a vehicle in a test drive. The calibration enabled a consistent heading determination with an accuracy of five degrees. This precise magnetometer-based attitude information allows an instantaneous GNSS integer ambiguity fixing.
A method is described for joint precise point positioning and attitude determination with tight coupling of two single-frequency low-cost global navigation satellite system receivers and an inertial ...sensor. The sensor fusion is performed with an extended Kalman filter. The carrier phase ambiguities are determined in a constrained tree search using soft a priori information on the antenna distance. A code multipath parameter is determined for each satellite to improve the accuracy. Ionospheric corrections are estimated also by single-frequency receivers.
Model predictive control is a promising approach to reduce the CO2 emissions in the building sector. However, the vast modeling effort hampers the widescale practical application. Here, data-driven ...process models, like artificial neural networks, are well-suited to automatize the modeling. However, the underlying data set strongly determines the quality and reliability of artificial neural networks. In general, the validity domain of a machine learning model is limited to the data that was used to train it. Predictions based on system states outside that domain, so-called extrapolations, are unreliable and can negatively influence the control quality.
We present a safe operation approach combined with online learning to deal with extrapolation in data-driven model predictive control. Here, the k-nearest neighbor algorithm is used to detect extrapolation to switch to a robust fallback controller. By continuously retraining the artificial neural networks during operation, we successively increase the validity domain of the artificial neural networks and the control quality.
We apply the approach to control a building energy system provided by the BOPTEST framework. We compare controllers based on two data sets, one with extensive system excitation and one with baseline operation. The system is controlled to a fixed temperature set point in baseline operation. Therefore, the artificial neural networks trained on this data set tend to extrapolate in other operating points. We show that safe operation in combination with online learning significantly improves performance.
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•We introduce safe operation for online learning data-driven model predictive control.•Novelty Detection is used to check the reliability of artificial neural networks.•Continuously retraining the process models and detector increases the validity domain.•The methodology achieves significant improvements when only poor initial data is available.
The building sector significantly contributes to climate change. To improve its carbon footprint, applications like model predictive control and predictive maintenance rely on system models. However, ...the high modeling effort hinders practical application. Machine learning models can significantly reduce this modeling effort. To ensure a machine learning model’s reliability in all operating states, it is essential to know its validity domain. Operating states outside the validity domain might lead to extrapolation, resulting in unpredictable behavior. This paper addresses the challenge of identifying extrapolation in data-driven building energy system models and aims to raise knowledge about it. For that, a novel approach is proposed that calibrates novelty detection algorithms towards the machine learning model. Suitable novelty detection algorithms are identified through a literature review and a benchmark test with 15 candidates. A subset of five algorithms is then evaluated on building energy systems. First, on two-dimensional data, displaying the results with a novel visualization scheme. Then on more complex multi-dimensional use cases. The methodology performs well, and the validity domain could be approximated. The visualization allows for a profound analysis and an improved understanding of the fundamental effects behind a machine learning model’s validity domain and the extrapolation regimes.
The availability of in situ snow water equivalent (SWE), snowmelt and run-off measurements is still very limited especially in remote areas as the density of operational stations and field ...observations is often scarce and usually costly, labour-intense and/or risky. With remote sensing products, spatially distributed information on snow is potentially available, but often lacks the required spatial or temporal requirements for hydrological applications. For the assurance of a high spatial and temporal resolution, however, it is often necessary to combine several methods like Earth Observation (EO), modelling and in situ approaches. Such a combination was targeted within the business applications demonstration project SnowSense (2015–2018), co-funded by the European Space Agency (ESA), where we designed, developed and demonstrated an operational snow hydrological service. During the run-time of the project, the entire service was demonstrated for the island of Newfoundland, Canada. The SnowSense service, developed during the demonstration project, is based on three pillars, including (i) newly developed in situ snow monitoring stations based on signals of the Global Navigation Satellite System (GNSS); (ii) EO snow cover products on the snow cover extent and on information whether the snow is dry or wet; and (iii) an integrated physically based hydrological model. The key element of the service is the novel GNSS based in situ sensor, using two static low-cost antennas with one being mounted on the ground and the other one above the snow cover. This sensor setup enables retrieving the snow parameters SWE and liquid water content (LWC) in the snowpack in parallel, using GNSS carrier phase measurements and signal strength information. With the combined approach of the SnowSense service, it is possible to provide spatially distributed SWE to assess run-off and to provide relevant information for hydropower plant management in a high spatial and temporal resolution. This is particularly needed for so far non, or only sparsely equipped catchments in remote areas. We present the results and validation of (i) the GNSS in situ sensor setup for SWE and LWC measurements at the well-equipped study site Forêt Montmorency near Quebec, Canada and (ii) the entire combined in situ, EO and modelling SnowSense service resulting in assimilated SWE maps and run-off information for two different large catchments in Newfoundland, Canada.
Real-time kinematic (RTK) positioning with Global Navigation Satellite System (GNSS) signals is widely used, e.g., for surveying, agriculture, and potentially for autonomous vehicles and unmanned air ...vehicles in the future. In this paper, an extended RTK positioning for significant height differences between two low-cost GNSS receivers with patch antennas is presented. In this case, the classical model for double difference measurements needs to be extended, i.e., a differential tropospheric zenith delay and pseudorange multipath errors need to be estimated besides the baseline and carrier phase integer ambiguities. The increased number of unknowns results in an ill-conditioned system of observation equations and a substantial correlation between the state estimates. We introduce prior information on the differential tropospheric zenith delay based on the differential air pressure and exploit the temporal correlation of pseudorange multipath errors. Moreover, a criterion for the integer ambiguity candidate vector selection is provided, which is robust over phase multipath and unavoidable errors in the float ambiguity covariance matrix. The proposed method is validated with two low-cost GNSS modules that were placed at the Zugspitzplatt (2601 m a.s.l.) and Eibsee (1018 m a.s.l.). The obtained estimates for the baseline and differential tropospheric zenith delay show a high repeatability over several independent ambiguity fixings. The residuals of the fixed carrier phase measurements are within 2 cm for almost all satellites, which confirms both the measurement model and the ambiguity fixing.
This work analyzes the design and performance of a planar ionospheric gradient monitor, based on differential carrier phase-only measurements between the elements of an antenna array. Small ...ionospheric disturbances are one of the potential threats to aerospace navigation and have to be monitored to prevent an excessive degradation of the position estimates. A carrier phase-based ionospheric gradient monitor enhances bias detection capabilities with respect to monitors that only exploit pseudorange measurements, provided that the ambiguous nature of the phase observations and the measurement error statistics are correctly handled. In this work we introduce a statistical test for detecting small ionospheric gradients, and we derive the analytical expression of the test probability distribution function for single- and two-baseline antenna arrays. A theoretical evaluation of the performance of the ionospheric gradient monitor is provided through inspection of the associated acceptance region, which defines the magnitudes of ionospheric gradient that cannot be detected with given integrity requirements. Due to the integer ambiguity of the carrier-phase measurements, multiple undesirable acceptance regions are produced. We provide a method to reduce the number and size of such regions.
For numerous hydrological applications, information on snow water equivalent (SWE) and snow liquid water content (LWC) are fundamental. In situ data are much needed for the validation of model and ...remote sensing products; however, they are often scarce, invasive, expensive, or labor‐intense. We developed a novel nondestructive approach based on Global Positioning System (GPS) signals to derive SWE, snow height (HS), and LWC simultaneously using one sensor setup only. We installed two low‐cost GPS sensors at the high‐alpine site Weissfluhjoch (Switzerland) and processed data for three entire winter seasons between October 2015 and July 2018. One antenna was mounted on a pole, being permanently snow‐free; the other one was placed on the ground and hence seasonally covered by snow. While SWE can be derived by exploiting GPS carrier phases for dry‐snow conditions, the GPS signals are increasingly delayed and attenuated under wet snow. Therefore, we combined carrier phase and signal strength information, dielectric models, and simple snow densification approaches to jointly derive SWE, HS, and LWC. The agreement with the validation measurements was very good, even for large values of SWE (>1,000 mm) and HS (> 3 m). Regarding SWE, the agreement (root‐mean‐square error (RMSE); coefficient of determination (R2)) for dry snow (41 mm; 0.99) was very high and slightly better than for wet snow (73 mm; 0.93). Regarding HS, the agreement was even better and almost equally good for dry (0.13 m; 0.98) and wet snow (0.14 m; 0.95). The approach presented is suited to establish sensor networks that may improve the spatial and temporal resolution of snow data in remote areas.
Key Points
Snow water equivalent, liquid water content, and snow height were simultaneously derived with one sensor setup only
This continuous and nondestructive approach for bulk snow cover properties determination is based on GPS signals travelling through snowpack
The correlation with validation data for three entire winter seasons encompassing dry‐snow accumulation and wet‐snow melting periods is high
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