Allan Variance Analysis Research Articles

Quantification of nitrous acid (HONO) and nitrogen dioxide (NO2) in ambient air by broadband cavity-enhanced absorption spectroscopy (IBBCEAS) between 361 and 388 nm

Abstract. This work describes an incoherent broadband cavity-enhanced absorption spectroscopy (IBBCEAS) instrument for quantification of HONO and NO2 mixing ratios in ambient air. The instrument is operated in the near-ultraviolet spectral region between 361 and 388 nm. The mirror reflectivity and optical cavity transmission function were determined from the optical extinction observed when sampling air and helium. To verify the accuracy of this approach, Rayleigh scattering cross sections of nitrogen and argon were measured and found to be in quantitative agreement with literature values. The mirror reflectivity exceeded 99.98 %, at its maximum near 373 nm, resulting in an absorption path length of 6 km from a 1 m long optical cavity. The instrument precision was assessed through Allan variance analyses and showed minimum deviations of ±58 and ±210 pptv (1σ) for HONO and NO2, respectively, at an optimum acquisition time of 5 min. Measurements of HONO and NO2 mixing ratios in laboratory-generated mixtures by IBBCEAS were compared to thermal dissociation cavity ring-down spectroscopy (TD-CRDS) data and agreed within combined experimental uncertainties. Sample ambient air data collected in Calgary are presented.

MEMS-Based IMU Drift Minimization: Sage Husa Adaptive Robust Kalman Filtering

The Attitude Heading Reference System (AHRS) has been widely used to provide the position and orientation of a rigid body. A low cost MEMS based inertial sensor measurement unit (IMU) is a core device in AHRS. To improve the AHRS system performance, there is a need to develop (i) stochastic IMU error models and (ii) random noise minimization techniques. In this paper, we modify the Sage-Husa Adaptive Kalman Filter (SHAKF) to incorporate time-varying noise estimator and robustifier, termed as Modified Sage-Husa Adaptive Robust Kalman Filter (MSHARKF). In the proposed algorithm, a three segment approach is used to evaluate the adaptive scale factor followed by the learning statistics. The scale factor is iteratively updated in the MSHARKF equations. In addition, angle random walk (ARW) and bias instability (BI) errors are represented by state-space models. The proposed algorithm is applied to restrain the drift error and random noise in the MEMS IMUs signals. The performance of this algorithm is analyzed using Allan variance (AV) analysis for static signals whereas the Root Mean Square Error (RMSE) values are evaluated for dynamic signals. Experimental results demonstrate the effectiveness of MSHARKF in reducing the drift and random noise in static and dynamic conditions as compared with other existing algorithms. Finally, we present sufficient conditions for convergence proof of the MSHARKF algorithm.

Fiber optic gyro signal denoising based on variational mode decomposition and adaptive noise cancellation

The output signal of the fiber optic gyro (FOG) often contains a large amount of noise, which makes it difficult to model and calibrate. Therefore, it must be denoised. In this paper, an adaptive noise cancellation method based on variational mode decomposition (VMD) is proposed. The FOG signal was decomposed into a series of mode components with different center frequencies, and the correlation coefficient method was used to determine the number of decomposition layer. The low-frequency signal and the high-frequency noise components were distinguished by the frequency distribution of each component. They were respectively accumulated to use as the ready denoising signal and the reference noise, then obtaining the denoised signal by adaptive noise cancellation. Using FOG measured data, the proposed method was taken into experiment compared with traditional methods. Allan variance analysis verified that the proposed method effectively suppresses the noise in the FOG signal.

Measurement of nitric oxide from cigarette burning using TDLAS based on quantum cascade laser

Nitric oxide (NO) is an important product released by cigarette burning with significantly negative effects to both environment and human health, but it is hard to be measured in-situ in the process of burning. In this paper, we report a tunable diode laser absorption spectroscopy (TDLAS) set-up using a quantum cascade laser emitting at 5.24 μm to continuously determine the emitted NO mass in cigarette smoke during burning. Wavelength modulation spectroscopy was applied to improve the detection sensitivity and robustness of the measurement system. A simple single-pass gas cell with a volume of 28 cm3 was used to record the absorption spectra, and then the mass of NO was derived based on the measured line strength. Allan variance analysis demonstrated that the limit of detection of system reached 28 ppb over 180 s integration time. Due to the low effective volume, the rise time and the fall time were rapid with 3 s and 6 s, respectively. An adaptive Kalman filter was used to reduce the noise on the concentration measurement. As a result, the measurement precision is improved by a factor of 4.5. For accurate determination the total NO mass, the emissions of mainstream (MS) and sidestream (SS) of a burning cigarette were individually measured at the same continuous flow rate. The recorded results of three types of cigarettes revealed that the NO mass emitted in the MS is correlated with the sampling flow rate, while the NO mass emitted by the same cigarette in the SS is hardly influenced by at different smoke flow rates. And different cigarette types with identical physical dimensions emit approximately equivalent mass of NO. This work provides a promising method for determining the mass of emitted NO and other compositions of cigarettes smoke.

In situ, portable and robust laser sensor for simultaneous measurement of ammonia, water vapor and temperature in denitrification processes of coal fired power plants

Simultaneous measurement of the ammonia, flue gas temperature and water vapor concentration in denitrification (deNOx) processes is of great importance for improving the deNOx efficiency of coal-fired power plants (CFPPs) and maximizing energy conservation and emission reduction. A portable, robust, low-cost and low-power laser sensor was developed based on wavelength modulation spectroscopy (WMS) with a single near infrared diode laser, which covers the optimized NH3 spectral line at 6612.73 cm−1 and H2O line pair at 6612.02 and 6609.85 cm−1. A calibration-free for WMS with varied modulation amplitude (WMS-VMA) was proposed to improve the performance of the tri-spectral line analysis. A probe, based on Herriott cell structure, coupled with deformation resistance, dust-proof, air-tight and anti-seismic, was design to adapt to the harsh environment of CFPPs. Lab-based sensor evaluation showed that the measurement accuracies for the temperature, H2O and NH3 concentration are 2.9 %, 4.8 % and 5.1 %, respectively. Allan variance analysis shows that the sensor has good stability, and the measurement sensitivity at five-second resolution are 0.1 ppm and 0.03 % for NH3 and H2O concentration, respectively. Furthermore, the feasibility of the sensor system was also verified by field tests at both deNOx inlet and outlet in a practical CFPP, denoting great potential of ammonia injection optimization in deNOx process.

Two Correlated Interferometric Optical Fiber Systems Applied to the Mining Activity Recordings

In order to meet new directions of research in the field of rotational seismology, a registration of rotation phenomena from mining seismic shocks was carried out by two interferometric optical systems. Applied instruments are based on the Sagnac effect and measure the rotation rate in a direct way. Systems have a wide measuring range both in the case of signal amplitude as well as frequency range. Allan variance analysis has indicated that they have proper parameters for the rotational seismology investigation (angle random walk equals 3.20 · 10−8 rad/√s, as well as bias instability equals 2.41 · 10−8 rad/s). Moreover, regarding applied special electronic processing, they provide rotation rate as an output instead of a change of an angle like in commercially available fiber optic gyroscopes. The optical head of the constructed systems uses depolarized light in order to avoid polarization effect. Systems are remotely controlled by the Internet and adapted to an independent power supply which makes them fully autonomous. Correlation between data gathered by two systems applied in a geophysical observatory in Ksiąz, Poland, have been calculated according to the person's correlation coefficient.

Evaluation of ambient ammonia measurements from a research aircraft using a closed-path QC-TILDAS operated with active continuous passivation

Abstract. A closed-path quantum-cascade tunable infrared laser direct absorption spectrometer (QC-TILDAS) was outfitted with an inertial inlet for filter-less separation of particles and several custom-designed components including an aircraft inlet, a vibration isolation mounting plate, and a system for optionally adding active continuous passivation for gas-phase measurements of ammonia (NH3) from a research aircraft. The instrument was then deployed on the NSF/NCAR C-130 aircraft during research flights and test flights associated with the Western wildfire Experiment for Cloud chemistry, Aerosol absorption and Nitrogen (WE-CAN) field campaign. The instrument was configured to measure large, rapid gradients in gas-phase NH3, over a range of altitudes, in smoke (e.g., ash and particles), in the boundary layer (e.g., during turbulence and turns), in clouds, and in a hot aircraft cabin (e.g., average aircraft cabin temperatures expected to exceed 30 ∘C during summer deployments). Important design goals were to minimize motion sensitivity, maintain a reasonable detection limit, and minimize NH3 “stickiness” on sampling surfaces to maintain fast time response in flight. The observations indicate that adding a high-frequency vibration to the laser objective in the QC-TILDAS and mounting the QC-TILDAS on a custom-designed vibration isolation plate were successful in minimizing motion sensitivity of the instrument during flight. Allan variance analyses indicate that the in-flight precision of the instrument is 60 ppt at 1 Hz corresponding to a 3σ detection limit of 180 ppt. Zero signals span ±200, or 400 pptv total, with cabin pressure and temperature and altitude in flight. The option for active continuous passivation of the sample flow path with 1H,1H-perfluorooctylamine, a strong perfluorinated base, prevented adsorption of both water and basic species to instrument sampling surfaces. Characterization of the time response in flight and on the ground showed that adding passivant to a “clean” instrument system had little impact on the time response. In contrast, passivant addition greatly improved the time response when sampling surfaces became contaminated prior to a test flight. The observations further show that passivant addition can be used to maintain a rapid response for in situ NH3 measurements over the duration of an airborne field campaign (e.g., ∼2 months) since passivant addition also helps to prevent future buildup of water and basic species on instrument sampling surfaces. Therefore, we recommend the use of active continuous passivation with closed-path NH3 instruments when rapid (>1 Hz) collection of NH3 is important for the scientific objective of a field campaign (e.g., sampling from aircraft or another mobile research platform). Passivant addition can be useful for maintaining optimum operation and data collection in NH3-rich and humid environments or when contamination of sampling surfaces is likely, yet frequent cleaning is not possible. Passivant addition may not be necessary for fast operation, even in polluted environments, if sampling surfaces can be cleaned when the time response has degraded.

VCSEL-Based Atmospheric Trace Gas Sensor Using First Harmonic Detection

This paper presents a measurement system based on the first harmonic in tunable diode laser absorption spectroscopy using a vertical-cavity surface-emitting laser to measure the atmospheric CO2 and H2O concentrations. The developed system separates the residual amplitude modulation signal from the harmonics and then eliminates it. A digital signal processing is developed to autonomously infer the wavelength and light intensities of the laser. The gas concentrations are determined without extra calibration. The long-term measurements are taken to validate the precision and accuracy of the system. Based on the Allan variance analysis, the broad wavelength scanning enhances the measurement precision, and the first-harmonic detection can achieve about two times as high precision as the traditional second-harmonic detection. The field measurements implemented in early spring of 2018 in Munich were compared with the commercial nondispersive infrared (NDIR) sensor. The outcomes have revealed that our system has high accuracy for the gas concentration measurements and high consistency with the NDIR sensor. The diurnal variations of CO2 concentration have demonstrated that CO2 concentration in urban areas is affected by the biosphere and meteorological conditions and the daily anthropogenic activities. Furthermore, the air trajectory analysis based on the HYSPLIT model has found that the CO2 emission sources primarily come from the southeast of Munich. The developed system described in this paper has a great potential for in situ trace gas concentration measurements, the analysis on the polluted gas distributions, and the verification of the pollutant transport model in urban areas.

Adaptive etalon suppression technique for long‐term stability improvement in high index contrast waveguide‐based laser absorption spectrometers

The authors present an adaptive algorithm based on a non-linear regression model for mitigating time-varying etalon drifts in line-scanned optical absorption spectrometers. By dynamically varying the etalon spectral background using physically realistic degrees of freedom, the authors’ dynamic etalon fitting-routine (DEF-R) significantly increases the spectral baseline recalibration interval as compared to conventional fringe subtraction models. They provide an empirical demonstration of the efficacy of DEF-R using an on-chip 10 cm silicon waveguide for near-infrared methane absorption spectroscopy at 6057 cm−1, which suffers significant etalon spectral noise due to reflections and multi-path interference from stochastic line-edge roughness imperfections. They demonstrate the corresponding improvement in both spectral clean-up and long-term stability via Allan-variance analysis. For the sensor presented here, application of DEF-R enables Gaussian-noise limited performance for more than 102 s and provides almost an order-of-magnitude improvement in stability time with respect to conventional baseline subtraction. Although DEF-R is applied here to an on-chip sensor embodiment, they envision their technique to be applicable to any absorption sensor limited by time-varying etalon drifts.

Error characteristics analysis and calibration testing for MEMS IMU gyroscope

Microelectromechanical systems’ (MEMS) inertial measurement unit (IMU) is widely used in many scenarios for its small size, low weight, and low-power consumptions. However, it possesses relatively low positioning accuracy compared with other high-grade IMUs, as errors accumulate quickly over time. This paper mainly focuses on the error characteristics of the gyro part of MEMS IMU by analyzing different kinds of error parameters. As there is no published standard for MEMS gyro error characterization, three dominant error parameters are selected and investigated, namely, scale factor, in-run bias stability, and angular random walk. In addition, Allan variance analysis is deployed as an important part of the scheme with relative results presented in this paper. Not only is theoretical analysis presented, but experimental verification is also carried out correspondingly with an ADIS16490 MEMS IMU. By comparison, we find that the results of in-run bias stability exceed the given features by up to ten times, while the rest of the results agree quite well with the given features. Possible reasons for the exceeding part are given. Calibration testing results not only provide concrete characterization for MEMS gyro errors, but also enhance the importance of overall calibration of MEMS IMU before use.

Design of a Micromachined Z-axis Tunneling Magnetoresistive Accelerometer with Electrostatic Force Feedback.

This paper presents the design, simulation, fabrication and experiments of a micromachined z-axis tunneling magnetoresistive accelerometer with electrostatic force feedback. The tunneling magnetoresistive accelerometer consists of two upper differential tunneling magnetoresistive sensors, a middle plane main structure with permanent magnetic films and lower electrostatic feedback electrodes. A pair of lever-driven differential proof masses in the middle plane main structure is used for sensitiveness to acceleration and closed-loop feedback control. The tunneling magnetoresistive effect with high sensitivity is adopted to measure magnetic field variation caused by input acceleration. The structural mode and mass ratio between inner and outer proof masses are optimized by the Ansys simulation. Simultaneously, the magnetic field characteristic simulation is implemented to analyze the effect of the location of tunneling magnetoresistive sensors, magnetic field intensity, and the dimension of permanent magnetic film on magnetic field sensitivity, which is beneficial for the achievement of maximum sensitivity. The micromachined z-axis tunneling magnetoresistive accelerometer fabricated by the standard deep dry silicon on glass (DDSOG) process has a device dimension of 6400 μm (length) × 6400 μm (width) × 120 μm (height). The experimental results demonstrate the prototype has a maximal sensitivity of 8.85 mV/g along the z-axis sensitive direction under the gap of 1 mm. Simultaneously, Allan variance analysis illustrate that a noise floor of 86.2 μg/Hz0.5 is implemented in the z-axis tunneling magnetoresistive accelerometer.

Long-Term Stable Online Acetylene Detection by a CEAS System with Suppression of Cavity Length Drift.

A trace acetylene (C2H2) detection system was demonstrated using the cavity-enhanced absorption spectroscopy (CEAS) technique and a near-infrared distributed feedback (NIR-DFB) laser. A Fabry–Perot (F–P) cavity with an effective optical path length of 49.7 m was sealed and employed as a gas absorption cell. Co-axis cavity alignment geometry was adopted to acquire a larger transmitted light intensity and a higher sensitivity compared with off-axis geometry. The laser frequency was locked to the cavity fundamental mode (TEM00 mode) by using the Pound–Drever–Hall (PDH) technique continuously. By introducing a cavity length-locking loop, the drift of the cavity length was suppressed, and the stability of the system was enhanced. To demonstrate the efficacy of the system, a C2H2 absorption spectrum near 6534.36 cm−1 was acquired by tuning the laser operation temperature. Measurements of C2H2 samples with different concentrations were carried out, and a good linear relationship between C2H2 concentration and the cavity-transmitted signal voltage was observed. The measurement results showed the system could work stably for more than 2 h without major fluctuations. The Allan variance analysis results demonstrated a detection limit of 9 parts-per-billion (ppb) with an averaging time of 11 s corresponding to a minimum detectable absorption coefficient of 1.1 × 10−8 cm−1.

A regression‐based methodology to improve estimation of inertial sensor errors using Allan variance data

This research proposes a novel, autonomous, regression-based methodology for Allan variance analysis of inertial measurement unit (IMU) sensors. Current methods for Allan variance analysis have been rooted in the human-based interpretation of linear trends, referred to as the slope method. The slope method is so prolific; it is referenced among electrical and electronics engineering standards for IMU error analysis. However, the graphical nature and visual-inspection–based use of the method limit its ability to be programmed as a generalized algorithm, which hinders the autonomy desired in modern-day navigation computations. Using nonlinear regression with a ridge-regression initial guess, the proposed method is shown to produce comparable results to the gold standard slope method when using standard-length data collections and outperforms the slope method when the amount of available data is limited. This development directly enables accurate navigation solutions for all vehicles in land, air, sea, and space operations.

A single-pass RGB differential photoacoustic spectrometer (RGB-DPAS) for aerosol absorption measurement at 473, 532, and 671 nm

In this study, we describe a newly developed three-wavelength differential photoacoustic spectrometer, which we denote RGB-DPAS, for aerosol absorption measurement in the visible spectral range: 671 nm (red), 532 nm (green), and 473 nm (blue). This instrument utilizes the differential photoacoustic spectrometric (DPAS) technique, which simultaneously measures light absorption signals due to total particulate matter + gaseous samples and those of gaseous samples alone. The difference between the photoacoustic signals recorded from the two nearly identical acoustic cells (<0.2% variability in physical dimensions) yields the aerosol photoacoustic signals at the three wavelengths. This measurement approach eliminates the interferences from light-absorbing gaseous species as well as low-frequency ambient acoustic noise. In this study, we demonstrate the linearity of the RGB-DPAS signal response to the number concentration of the synthetic carbon black particles at electrical mobility diameter (Dm) = 350 nm, which is used as a calibration surrogate. Based on the Allan variance analysis, detection limits (2σ) of 0.20 Mm−1 at 671 nm, 0.22 Mm−1 at 532 nm, and 0.90 Mm−1 at 473 nm have been achieved in 100 s data acquisition for the RGB-DPAS instrument.Copyright © 2018 American Association for Aerosol Research

Open-loop fiber-optic gyroscope with a double sensitivity employing a polarization splitter and Faraday rotator mirror.

In this Letter, a novel open-loop fiber-optic gyroscope configuration with a double sensitivity is proposed. By employing a polarization-maintaining Faraday rotator mirror and a polarization beamsplitter/combiner, light waves propagate twice along the same fiber coil in two orthonormal polarization directions. The reciprocity of the configuration has been verified in theory. The Allan variance analysis of the gyro prototype exhibits 0.03°/h bias stability over 5.5h in the laboratory environment.

A 3D-Printed Microresonator Based on the Quartz-Enhanced Photoacoustic Spectroscopy Sensor for Methane Detection

A 3D-printed microresonator based on a quartz tuning fork has been developed. The sensor performance is evaluated by detection of methane with a fiber-coupled distributed feedback diode laser. In combination with wavelength modulation spectroscopy, a minimum detectable concentration of 15.6 ppb by volume is achieved at atmospheric pressure with an 8-mW average optical excitation power and a lock-in amplifier time constant of 1 s, which corresponds to a 1σ normalized noise equivalent absorption coefficient of 5·10–9 cm–1·W/Hz1/2. An Allan variance analysis shows that the system has long-term stability and can serve as the basis for a portable gas analyzer. Approaches to improve the current sensor performance are also discussed. This design greatly reduces the time of manufacturing the microresonator.

Advanced Photonic Sensors Based on Interband Cascade Lasers for Real-Time Mouse Breath Analysis.

A multiparameter gas sensor based on distributed feedback interband cascade lasers emitting at 4.35 μm and ultrafast electro-spun luminescence oxygen sensors has been developed for the quantification and continuous monitoring of 13CO2/12CO2 isotopic ratio changes and oxygen in exhaled mouse breath samples. Mid-infrared absorption spectra for quantitatively monitoring the enrichment of 13CO2 levels were recorded in a miniaturized dual-channel substrate-integrated hollow waveguide using balanced ratiometric detection, whereas luminescence quenching was used for synchronously detecting exhaled oxygen levels. Allan variance analysis verified a CO2 measurement precision of 1.6‰ during a 480 s integration time. Routine online monitoring of exhaled mouse breath was performed in 14 mechanically ventilated and instrumented mice and demonstrated the feasibility of online isotope-selective exhaled breath analysis within microliters of probed gas samples using the reported combined sensor platform.

Intelligent GNSS/INS integrated navigation system for a commercial UAV flight control system

Owing to the increase in civil applications using quadcopters, commercial flight control systems such as Pixhawk are a popular solution to provide the sensing and control functions of an unmanned aerial vehicle (UAV). A low-cost global navigation satellite system (GNSS) receiver is crucial for the low-cost flight control system. However, the accuracy of GNSS positioning is severely degraded by the notorious multipath effect in mega-urbanized cities. The multipath effect cannot be eliminated but can be mitigated; hence, the GNSS/inertial navigation system (INS) integrated navigation is a popular approach to reduce this error. This study proposes an adaptive Kalman filter for adjusting the noise covariance of GNSS measurements under different positioning accuracies. The adaptive tuning is based on a proposed accuracy classification model trained by a supervised machine-learning method. First, principal component analysis is employed to identify the significant GNSS accuracy related features. Subsequently, the positioning accuracy model is trained based on a random forest learning algorithm with the labeled real GNSS dataset encompassing most scenarios concerning modern urban areas. To reduce the cases of misclassifying the GNSS accuracy, a fuzzy logic algorithm is employed to consider the GNSS accuracy propagation. Additionally, the process noise covariance of the INS is determined using the Allan variance analysis. The positioning performance of the proposed adaptive Kalman filter is compared with both a conventional Kalman filter and the positioning solution provided by the commercial flight control system, Pixhawk 2. The results show that the proposed adaptive Kalman filter using random forest with fuzzy logic can achieve a better classification of GNSS accuracy compared to the others. The overall positioning result improved by approximately 50% compared with the onboard solution.

Using Allan variance to improve stochastic modeling for accurate GNSS/INS integrated navigation

MEMS-based integrated system of a global navigation satellite system (GNSS) and an inertial navigation system (INS) has been widely used in various navigation applications. However, such integration encounters some major limitations. On the one hand, the noisy MEMS-based INS undermines the accuracy with time during the frequently occurring GNSS outages caused by signal blockage or attenuation in certain situations such as urban canyon, tunnels, and high trees. On the other hand, the model mismatch between actual GNSS error and the assumed one would also degrade the obtained accuracy even with continuous GNSS aiding. To improve the overall performance for GNSS/MEMS-INS, better error models can be obtained using Allan variance (AV) analysis technique for modeling inertial sensor errors instead of the commonly recommended auto-regressive processes, and on the other hand, the measurement update in Kalman filter is improved using innovation filtering and AV calculation. The performance of each method and the combined algorithm is evaluated by a field test with either differential GNSS (DGNSS) or single-point positioning (SPP) as external aid. In addition to the considerable navigation enhancement brought by each method, the experimental results show the combined algorithm accomplishes overall accuracy improvements by about 18% (position), 8% (velocity), and 38% (attitude) for integration with DGNSS, and by about 15% (position), 75% (velocity), and 77% (attitude) for that with SPP, compared with corresponding traditional counterparts.

A procedure for the significance testing of unmodeled errors in GNSS observations

It is a crucial task to establish a precise mathematical model for global navigation satellite system (GNSS) observations in precise positioning. Due to the spatiotemporal complexity of, and limited knowledge on, systematic errors in GNSS observations, some residual systematic errors would inevitably remain even after corrected with empirical model and parameterization. These residual systematic errors are referred to as unmodeled errors. However, most of the existing studies mainly focus on handling the systematic errors that can be properly modeled and then simply ignore the unmodeled errors that may actually exist. To further improve the accuracy and reliability of GNSS applications, such unmodeled errors must be handled especially when they are significant. Therefore, a very first question is how to statistically validate the significance of unmodeled errors. In this research, we will propose a procedure to examine the significance of these unmodeled errors by the combined use of the hypothesis tests. With this testing procedure, three components of unmodeled errors, i.e., the nonstationary signal, stationary signal and white noise, are identified. The procedure is tested by using simulated data and real BeiDou datasets with varying error sources. The results show that the unmodeled errors can be discriminated by our procedure with approximately 90% confidence. The efficiency of the proposed procedure is further reassured by applying the time-domain Allan variance analysis and frequency-domain fast Fourier transform. In summary, the spatiotemporally correlated unmodeled errors are commonly existent in GNSS observations and mainly governed by the residual atmospheric biases and multipath. Their patterns may also be impacted by the receiver.