Observation Noise Research Articles

Improved CKF Collaborative Positioning Algorithm Between UAVs Based on UWB/IMU

Abstract Addressing the challenges of position information solution among multiple Unmanned Aerial Vehicles (UAVs) and the issue of low relative navigation accuracy, an improved collaborative localization algorithm based on the Cubature Kalman Filter (CKF) is proposed. It utilizes a tightly coupled approach to construct a relative ranging model equipped with Ultra-Wideband (UWB) and Inertial Measurement Unit (IMU) sensors, enabling the correction of self-navigation information. The cosine similarity function is utilized to determine the reliability of the observations, and the observation noise matrix is adaptively adjusted based on the new interest vector from each iteration, thereby refining the positioning trajectory for collaborative navigation. Simulation experiments results demonstrate that the improved CKF collaborative localization algorithm significantly enhances the relative positioning accuracy between UAVs, effectively reduces the maximum relative positioning error, and exhibits strong anti-interference capabilities. It is more suitable for indoor multi-UAV and multi-sensor collaborative localization.

Downscaling using CDAnet under observational and model noise: the Rayleigh-Bénard convection paradigm

Downscaling using CDAnet under observational and model noise: the Rayleigh-Bénard convection paradigm

Deep Learning‐Based Optical Flow in Fine‐Scale Deformation Mapping of Sea Ice Dynamics

AbstractOptical methods deployed for studying motion and deformation of objects often struggle to distinguish small displacements hidden behind observational noise. In geophysical applications, this has limited analysis to lower spatial and temporal resolutions, while reliable extraction of high‐resolution data is required for understanding material deformation and failure. In this work, we propose a novel method for determining deformation for noisy observational data using deep learning‐based optical flow. To enable higher estimate accuracy, we introduce a novel initialization technique considering contextual information. This allows an unprecedentedly high‐resolution description of motion in radar imagery. We use the proposed technique on verification cases to compare with the currently used methodologies and on ship radar observations on sea ice deformation. The outcome of our work is an open‐source end‐to‐end tool for determining full‐field Lagrangian deformation fields for data sets with small pixel displacements and high observational noise.

A State Estimation of Dynamic Parameters of Electric Drive Articulated Vehicles Based on the Forgetting Factor of Unscented Kalman Filter with Singular Value Decomposition

In this paper, a state estimation method of distributed electric drive articulated vehicle dynamics parameters based on the forgetting factor unscented Kalman filter with singular value decomposition (SVD-UKF) is proposed. The 7DOF nonlinear dynamics model of a distributed electric drive articulated vehicle is established. The unscented Kalman filter algorithm is the foundation, with singular value decomposition replacing the Cholesky decomposition. A forgetting factor is introduced to dynamically adapt the observation noise covariance matrix in real time, resulting in a centralized parameter state estimator for the articulated vehicle. The proposed parameter state estimation method based on the forgetting factor SVD-UKF is simulated and compared with the unscented Kalman filter (UKF) estimation method. Key dynamic parameters are estimated, such as the lateral and longitudinal velocities and accelerations, angular velocity, articulated angle, wheel speeds, and longitudinal and lateral tire forces of both the front and rear vehicle bodies. The results show that the proposed forgetting factor SVD-UKF method outperforms the traditional UKF method. Furthermore, a prototype vehicle test is conducted to compare the estimated values of various dynamic parameters with the actual values, demonstrating minimal errors. This verifies the effectiveness of the proposed dynamic parameter estimation method for articulated vehicles.

A laser tracking attitude dynamic measurement method based on real-time calibration and AEKF with a multi-factor influence analysis model

Abstract To address the limitations of six-degree-of-freedom (6-DOF) visual tracking systems in terms of low dynamic performance and the inability to perform measurements under light occlusion, this paper proposes a novel laser tracking attitude dynamic measurement method integrating vision and inertial measurement unit (IMU). A tailored real-time calibration model is developed to enable precise alignment of the vision and IMU coordinate systems during dynamic operations. To overcome the limitations of extended Kalman filter (EKF) that rely on static noise assumptions in complex dynamic measurement scenarios, this study proposes an adaptive mechanism based on multi-factor influence analysis. Through dynamic monitoring of visual observation noise, an adaptive EKF algorithm is designed to enhance performance under varying conditions. When integrated into a vision/IMU fusion system, the algorithm significantly enhances the system’s sensitivity to variations in visual sensor observation noise caused by changes in lighting and motion states. This capability allows rapid adjustment of filtering parameters, leading to substantial improvements in filtering accuracy and stability. Simulation results demonstrate that the proposed algorithm outperforms traditional EKF in fusion measurement accuracy when tested in simulated noise environments featuring sinusoidal and random jump signals. Furthermore, the fusion measurement accuracy is mainly influenced by the data density of the visual sensor and the measurement distance. Finally, the proposed method was validated on a precision turntable. Experimental results reveal that at a 3 m measurement distance and within a 0°–25° angular range, when the turntable rotates at a constant speed of 5°/s along a single axis, the maximum absolute deviation in repeatability of the fused attitude measurements was below 0.11°, and the system is capable of achieving a high measurement frequency of 100 Hz.

Probabilistic estimation of rheological properties in subduction zones using sequences of earthquakes and aseismic slip

Abstract Constraining the effective rheology of major faults contributes to improving our understanding of the physics of plate boundary deformation. Geodetic observations over the earthquake cycle are often used to estimate key rheological parameters, assuming specific laboratory-informed classes of viscous or frictional rheological models. However, differentiating between various rheological model classes using only observations of a single earthquake (coseismic and postseismic deformation) is difficult—especially in the presence of coarse spatiotemporal sampling, inherent observational noise, and non-uniqueness of the inverted properties. In this study, we present a framework to estimate key rheological parameters of a subduction zone plate interface using simulations of sequences of earthquakes and aseismic slip, constrained by pre- and postseismic surface displacement timeseries. Our simplified forward model consists of a two-dimensional subduction zone, represented by a discretized planar fault or narrow shear zone, divided into a locked, shallow region (“asperity”) experiencing periodically imposed coseismic events, and a stress-driven creeping section governed by power-law viscoelasticity or rate-dependent friction. Our inverse model fits the rheological parameters of the interface to surface displacement timeseries in a Bayesian probabilistic way. We validate that our proposed framework can successfully recover depth-dependent profiles of effective viscosity using a synthetic dataset of pre- and postseismic observations. Our first set of numerical experiments show that our framework is only mildly sensitive to uncertainties in the rupture history or assumed coseismic slip, making it robust enough to be applied to real observations of subduction zones. Our second set of tests considers the similarities of surface displacement timeseries between synthetic models that model the plate interface either as a shear zone described by power-law viscosity, or a surface described by rate-dependent friction. Here, we find that the ability to fit surface observations using functional or mechanical models assuming frictional behavior does not constitute sufficient evidence to actually infer frictional behavior at depth, as the surface expressions are virtually indistinguishable from deformation generated from models with depth-variable power-law viscous behavior. Based on our numerical experiments, we conclude that studies that aim to infer the mechanical behavior and rheological properties at depth in subduction zones should consider the surface expression from time periods representative of the entire seismic cycle. Graphical Abstract

Ensemble Methods for Parameter Estimation of WRF‐Hydro

AbstractThe WRF‐Hydro hydrological model has been used in many applications in the past with some level of history matching in the majority of these studies. In this study, we use the iterative Ensemble Smoother (iES), a powerful parameter estimation methodology implemented in the open‐source PEST++ software. The iES provides an ensemble solution with an uncertainty bound instead of a single best estimate which has been the common approach in the previous WRF‐Hydro studies. We discuss the importance of accounting for observation noise which results in a wider spread in the model solution. We investigate the impact of constructing objective functions by differentially weighting the observations to tune the model response toward model outputs appropriate for a specific application. Results confirm the necessity of differentially weighting the observations before calculation of the objective function as the optimization algorithm struggles with calculating parameter updates with uniform weighting. We also show that we achieve better model performance in terms of verification metrics with higher emphasis on the high flow events, when the objective function is tuned toward an application where the extreme events are of importance. We then investigate the impact of estimating more parameters, in particular we estimate a larger number of snow parameters. Results show a large improvement in the model performance. In summary, our study demonstrates the efficacy of employing iES alongside differential weighting of observations, highlighting its potential to enhance hydrological model parameter estimation.

VarNMF: non-negative probabilistic factorization with source variation.

Non-negative matrix factorization (NMF) is a powerful tool often applied to genomic data to identify non-negative latent components that constitute linearly mixed samples. It is useful when the observed signal combines contributions from multiple sources, such as cell types in bulk measurements of heterogeneous tissue. NMF accounts for two types of variation between samples - disparities in the proportions of sources and observation noise. However, in many settings, there is also a non-trivial variation between samples in the contribution of each source to the mixed data. This variation cannot be accurately modeled using the NMF framework. We present VarNMF, a probabilistic extension of NMF that explicitly models this variation in source values. We show that by modeling sources as non-negative distributions, we can recover source variation directly from mixed samples without observing any of the sources directly. We apply VarNMF to a cell-free ChIP-seq dataset of two cancer cohorts and a healthy cohort, demonstrating that VarNMF provides a better estimation of the data distribution. Moreover, VarNMF extracts cancer-associated source distributions that decouple the tumor characteristics from the amount of tumor contribution, and identify patient-specific disease behaviors. This decomposition highlights the inter-tumor variability that is obscured in the mixed samples. Code is available at https://github.com/Nir-Friedman-Lab/VarNMF.

Modified Bott-Parker Method for Gravimetric Moho Modeling

Determining the detailed Moho topography is crucial for understanding the Earth's geodynamic processes. Inversion of the Moho depth in the frequency-domain from gravity observations is an effective tool for this purpose. However, existing inversion methods such as the Parker-Oldenburg (P-O) and Bott-Parker (B-P) methods face challenges including non-convergence and noise amplification. We have developed a modified B-P (mB-P) method to estimate the Moho depth with variable density contrast from gravity data. The proposed method casts exponential density-based Parker’s formula into the iterative continuation theoretical framework, allowing the use of an adaptive filter that has been proven effective in iterative continuation studies. This modification retains the efficiency of the B-P method while offering improved control over solution stability. Gauss-Fast Fourier Transform was adopted to improve the precision of the forward and inverse Fourier transforms in the inversion process. Furthermore, the mathematical connection between the P-O and B-P methods was established. Specifically, the B-P method acts as a low-pass filter to reduce the downward continuation effect in the P-O method and recovers the nonlinear topography through the nonlinearity of the fitting function. Synthetic inversion tests demonstrate that the proposed method achieves superior inversion accuracy compared to the P-O and B-P methods under 3% gravity observations noise and significantly outperforms the P-O method in terms of computational efficiency. We applied the mB-P method to estimate the Moho depth beneath the Tibetan Plateau using satellite gravity data and seismic data, achieving reasonable agreement between the gravimetric model and seismic data.

Improving the Calibration of Low-Cost Sensors Using Data Assimilation.

In the context of smart agriculture, accurate soil moisture monitoring is crucial to optimise irrigation, improve water usage efficiency and increase crop yields. Although low-cost capacitive sensors are used to make monitoring affordable, these sensors face accuracy challenges that often result in inefficient irrigation practices. This paper presents a method for calibrating capacitive soil moisture sensors through data assimilation. The method was validated using data collected from a farm in Dos Hermanas, Seville, Spain, which utilises a drip irrigation system. The proposed solution integrates the Hydrus 1D model with particle filter (PF) and the Iterative Ensemble Smoother (IES) to continuously update and refine the model and sensor calibration parameters. The methodology includes the implementation of physical constraints, ensuring that the updated parameters remain within physically plausible ranges. Soil moisture was measured using low-cost SoilWatch 10 capacitive sensors and ThetaProbe ML3 high-precision sensors as a reference. Furthermore, a comparison was carried out between the PF and IES methods. The results demonstrate that the data assimilation approach markedly enhances the precision of sensor readings, aligning them closely with reference measurements and model simulations. The PF method demonstrated superior performance, achieving an 84.8% improvement in accuracy compared to the raw sensor readings. This substantial improvement was measured against high-precision reference sensors, confirming the effectiveness of the PF method in calibrating low-cost capacitive sensors. In contrast, the IES method showed a 68% improvement in accuracy, which, while still considerable, was outperformed by the PF. By effectively mitigating observation noise and sensor biases, this approach proves robust and practical for large-scale implementations in precision agriculture.

Numerical investigation on aerodynamic noise of rigid coaxial rotor in forward flight with lift-offset

A computational fluid dynamics (CFD) solver based on Reynolds-averaged Navier–Stokes (RANS) equations and high-efficiency trim model is used to simulate the unsteady aerodynamics of coaxial rotor. Farassat 1 A equations are adopted for predicting rotor far-field aerodynamic noise. Forward flight cases of a two-bladed rigid coaxial rotor in different advance ratios and lift-offsets (LOS) are conducted. Sound pressure histories of different observation points and noise radiation maps are analyzed. Results indicate that, the intensity of rotor thickness noise moves towards the advancing side in the rotor disk plane, with the increase of advance ratio. Due to the superposition effect, the thickness noise of coaxial rotor is symmetrical, which is different with the single rotor. At low advance ratio, loading noise of the rigid coaxial rotor is enhanced near the blade-crossing azimuths caused by the unsteady interaction of the twin rotors. The enhancement turns weak with the increase of advance ratio. At high advance ratio, increasing LOS tends to enhance the rotor-self BVI noise, while weakening the inter-rotor interaction noise. At certain flight states, appropriate LOS can reduce the overall noise radiation intensity of rigid coaxial rotor.

Asynchronous event stream noise filtering for high-frequency structure deformation measurement

Large-scale structures suffer high-frequency deformations due to complex loads. However, harsh lighting conditions and high equipment costs limit measurement methods based on traditional high-speed cameras. This paper proposes a method to measure high-frequency deformations by exploiting an event camera and LED markers. First, observation noise is filtered based on the characteristics of the event stream generated by LED markers blinking and spatiotemporal correlation. Then, LED markers are extracted from the event stream after differentiating between motion-induced events and events from LED blinking, which enables extracting high-speed moving LED markers. Ultimately, high-frequency planar deformations are measured by a monocular event camera. Experimental results confirm the accuracy of our method in measuring high-frequency planar deformations.

A Comprehensive Analysis of Factors Affecting GNSS Observation Noise

Observation noise is one of the most significant error sources in the Global Navigation Satellite System (GNSS). It can be influenced by various factors. Analyzing these factors is crucial for developing a stochastic model for GNSS navigation and positioning. This process ensures that the statistical properties of the observational data are accurately characterized, leading to more reliable and precise positioning results. Previous research has predominantly focused on code type and PPP techniques, often limited by the inability to separately assess observation types across different frequency bands due to ionospheric delay. If based on short baseline, these studies were generally constrained by limited experimental data. This study provides a detailed analysis of the affecting factor on observation noise, including elevation, SNR (signal-to-noise ratio), different receiver and antenna type, different GNSS system, and different frequency bands etc. In addition, environmental effects on observation noise are investigated by comparison between short baseline and zero baseline.

Multi-Sensor Fusion for Wheel-Inertial-Visual Systems Using a Fuzzification-Assisted Iterated Error State Kalman Filter.

This paper investigates the odometry drift problem in differential-drive indoor mobile robots and proposes a multi-sensor fusion approach utilizing a Fuzzy Inference System (FIS) within a Wheel-Inertial-Visual Odometry (WIVO) framework to optimize the 6-DoF localization of the robot in unstructured scenes. The structure and principles of the multi-sensor fusion system are developed, incorporating an Iterated Error State Kalman Filter (IESKF) for enhanced accuracy. An FIS is integrated with the IESKF to address the limitations of traditional fixed covariance matrices in process and observation noise, which fail to adapt effectively to complex kinematic characteristics and visual observation challenges such as varying lighting conditions and unstructured scenes in dynamic environments. The fusion filter gains in FIS-IESKF are adaptively adjusted for noise predictions, optimizing the rule parameters of the fuzzy inference process. Experimental results demonstrate that the proposed method effectively enhances the localization accuracy and system robustness of differential-drive indoor mobile robots in dynamically changing movements and environments.

21cmlstm: A Fast Memory-based Emulator of the Global 21 cm Signal with Unprecedented Accuracy

Neural network (NN) emulators of the global 21 cm signal need an emulation error much less than the observational noise in order to be used to perform unbiased Bayesian parameter inference. To this end, we introduce 21cmLSTM—a long short-term memory (LSTM) NN emulator of the global 21 cm signal that leverages the intrinsic correlation between frequency channels to achieve exceptional accuracy compared to previous emulators, which are all feedforward, fully connected NNs. LSTM NNs are a type of recurrent NN designed to capture long-term dependencies in sequential data. When trained and tested on the same simulated set of global 21 cm signals as the best previous emulators, 21cmLSTM has an average relative rms error of 0.22%—equivalently 0.39 mK—and comparably fast evaluation time. We perform seven-dimensional Bayesian parameter estimation analyses using 21cmLSTM to fit global 21 cm signal mock data with different adopted observational noise levels, σ 21. The posterior 1σ rms error is ≈three times less than σ 21 for each fit and consistently decreases for tighter noise levels, showing that 21cmLSTM can sufficiently exploit even very optimistic measurements of the global 21 cm signal. We have made the emulator, code, and data sets publicly available so that 21cmLSTM can be independently tested and used to retrain and constrain other 21 cm models.

Model free data assimilation with Takens embedding

In many practical scenarios, the dynamical system is not available and standard data assimilation methods are not applicable. Our objective is to construct a data-driven model for state estimation without the underlying dynamics. Instead of directly modeling the observation operator with noisy observation, we establish the state space model of the denoised observation. Through data assimilation techniques, the denoised observation information could be used to recover the original model state. Takens’ theorem shows that an embedding of the partial and denoised observation is diffeomorphic to the attractor. This gives a theoretical base for estimating the model state using the reconstruction map. To realize the idea, the procedure consists of offline stage and online stage. In the offline stage, we construct the surrogate dynamics using dynamic mode decomposition with noisy snapshots to learn the transition operator for the denoised observation. The filtering distribution of the denoised observation can be estimated using adaptive ensemble Kalman filter, without knowledge of the model error and observation noise covariances. Then the reconstruction map can be established using the posterior mean of the embedding and its corresponding state. In the online stage, the observation is filtered with the surrogate dynamics. Then the online state estimation can be performed utilizing the reconstruction map and the filtered observation. Furthermore, the idea can be generalized to the nonparametric framework with nonparametric time series prediction methods for chaotic problems. The numerical results show the proposed method can estimate the state distribution without the physical dynamical system.

Polyak’s Method Based on the Stochastic Lyapunov Function for Justifying the Consistency of Estimates Produced by a Stochastic Approximation Search Algorithm under an Unknown-But-Bounded Noise

In 1976–1977, Polyak published in the journal Avtomatica i Telemekhanika (Automation and Remote Control) two remarkable papers on how to study the properties of estimates of iterative pseudogradient algorithms. The first paper published in 1976 considered the general case based on the stochastic Lyapunov function, and the second one considered the linear case. The assumptions formulated in these papers and the estimates obtained in them can still be considered the state-of-the art. In the current paper, Polyak’s approach is applied to the study of the properties of estimates of a (randomized) stochastic approximation search algorithm for the case of unknown-but-bounded noise in observations. The obtained asymptotic estimates were already known earlier, and exact estimates for a finite number of observations are published for the first time.

Master-slave coupling scheme for synchronization and parameter estimation in the generalized Kuramoto-Sivashinsky equation.

The problem of estimating the constant parameters of the Kuramoto-Sivashinsky (KS) equationfrom observed data has received attention from researchers in physics, applied mathematics, and statistics. This is motivated by the various physical applications of the equationand also because it often serves as a test model for the study of space-time pattern formation. Remarkably, most existing inference techniques rely on statistical tools, which are computationally very costly yet do not exploit the dynamical features of the system. In this paper, we introduce a simple, online parameter estimation method that relies on the synchronization properties of the KS equation. In particular, we describe a master-slave setup where the slave model is driven by observations from the master system. The slave dynamics are data-driven and designed to continuously adapt the model parameters until identical synchronization with the master system is achieved. We provide a simple analysis that supports the proposed approach and also present and discuss the results of an extensive set of computer simulations. Our numerical study shows that the proposed method is computationally fast and also robust to initialization errors, observational noise, and variations in the spatial resolution of the numerical scheme used to integrate the KS equation.

Pollution Source Detection With Low‐Cost Low‐Accuracy Sensors Through Coupling Forward Data Assimilation and Inverse Optimization

AbstractData uncertainty affects the accuracy of pollution source detection (PSD), particularly in the background of low‐cost water quality sensing and low‐accuracy data challenge. This study aims to develop a novel PSD method to use low‐accuracy sensor data, namely, the method of coupled forward data Assimilation and inverse Optimization in PSD (A&O‐PSD). This approach primarily employs filtering strategies to handle observation errors and extract hidden trend information during forward water quality data assimilation, and then optimal estimation of pollution source information through inverse optimization with enhanced trend information matching, avoiding the non‐Gaussian distribution challenge of pollution source information. Both real‐world pollution events and semi‐synthetic cases were used to evaluate the methodology and compare its performance with the traditional optimization approach (T‐PSD). The results indicated that T‐PSD is significantly affected by observational and parameter noise, engendering noticeable biases in PSD under the low‐accuracy sensor conditions. In contrast, the A&O‐PSD could accomplish the estimation task of PSD in real‐world pollution events, with improved robustness against noise interference. Furthermore, A&O‐PSD achieved an accuracy improvement of over 10% compared to T‐PSD in estimating pollution source locations within the typical noise distribution range of most low‐accuracy sensors currently available, making it possible to use low‐accuracy data that would otherwise be unusable in T‐PSD. Overall, the A&O‐PSD method, combined with low‐cost low‐accuracy water quality sensing, offers an effective solution for watershed environmental management.

Reconstructing Attractors of a Conceptual Airfoil System via Next Generation Reservoir Computing

Reconstructing attractors of airfoil systems from observations facilitates understanding of aeroelasticity, especially the onset of flutter. However, it is generally difficult due to observation noise and the nonlinear nature of the underlying dynamics. In this study, a hybrid strategy is proposed which incorporates data preprocessing and next generation reservoir computing (NG-RC) for reconstructing attractors of an airfoil system. This approach first estimates the system states from noisy observations via a state estimation method and then trains the NG-RC model to predict the responses of the airfoil system. The NG-RC employs nonlinear functions of past states to approximate the dynamics, requiring less training data and fewer hyperparameters than the conventional reservoir computing. To reduce the model complexity, both L2 and smoothed L1 norm penalties are introduced to promote the sparsity of trainable weights, where the optimal weights are determined by simple iterative optimization. Simulation results show that the proposed method can predict various vibration patterns and reconstruct the attractors of the airfoil system from limited, noisy observations. The smoothed L1 norm penalty can lead to sparser weights and, in some cases, enhance performance. The findings support applications of the present method like flutter boundary prediction and flight accident analysis.