Particle Filtering Scheme Research Articles

Estimating multi-scale irrigation amounts using multi-resolution soil moisture data: A data-driven approach using PrISM

Irrigated agriculture is the primary driver of freshwater use and is continuously expanding. Precise knowledge of irrigation amounts is critical for optimizing water management, especially in semi-arid regions where water is a limited resource. This study proposed to adapt the PrISM (Precipitation inferred from Soil Moisture) methodology to detect and estimate irrigation events from soil moisture remotely sensed data. PrISM was originally conceived to correct precipitation products, assimilating Soil Moisture (SM) observations into an antecedent precipitation index (API) formula, using a particle filter scheme. This novel application of PrISM uses initial precipitation and SM observations to detect instances of water excess in the soil (not caused by precipitation) and estimates the amount of irrigation, along with its uncertainty. This newly proposed approach does not require extensive calibration and is adaptable to different spatial and temporal scales. The objective of this study was to analyze the performance of PrISM for irrigation amount estimation and compare it with current state-of-the-art approaches. To develop and test this methodology, a synthetic study was conducted using SM observations with various noise levels to simulate uncertainties and different spatial and temporal resolutions. The results indicated that a high temporal resolution (less than 3 days) is crucial to avoid underestimating irrigation amounts due to missing events. However, including a constraint on the frequency of irrigation events, deduced from the system of irrigation used at the field level, could overcome the limitation of low temporal resolution and significantly reduce underestimation of irrigation amounts. Subsequently, the developed methodology was applied to actual satellite SM products at different spatial scales (1 km and 100 m) over the same area. Validation was performed using in situ data at the district level of Algerri-Balaguer in Catalunya, Spain, where in situ irrigation amounts were available for various years. The validation resulted in a total Pearson’s correlation coefficient (r) of 0.80 and a total root mean square error (rmse) of 7.19 mm∕week for the years from 2017 to 2021. Additional validation was conducted at the field level in the Segarra-Garrigues irrigation district using in situ data from a field where SM profiles and irrigation amounts were continuously monitored. This validation yielded a total bi-weekly r of 0.81 and a total rmse of −9.34 mm∕14-days for the years from 2017 to 2021. Overall, the results suggested that PrISM can effectively estimate irrigation from SM remote sensing data, and the methodology has the potential to be applied on a large scale without requiring extensive calibration or site-specific knowledge.

Wind and Actuator Fault Estimation for a Quadrotor UAV Based on Two-Stage Particle Filter

This paper investigates the problems of wind and actuator fault estimation for a quadrotor unmanned aerial vehicle (UAV). To effectively assess the safety and reliability of a quadrotor UAV in the presence of unknown wind disturbances, a two-stage particle filter (TSPF) scheme is proposed to obtain the simultaneous estimation of winds and actuator faults that may degrade the performance of the vehicle. In this scheme, the first-stage particle filter is used to estimate the states of the quadrotor UAV, and the second-stage particle filter is designed to produce estimates of unknown parameters, including the wind disturbances and actuator faults. To mitigate the degeneracy and impoverishment issues, the second-stage particle filter admits a parallel implementation of increased particle samplings for the wind and actuator fault estimation. Finally, simulation results are presented to demonstrate the effectiveness of the proposed scheme.

A genetic particle filter scheme for univariate snow cover assimilation into Noah-MP model across snow climates

Abstract. Accurate snowpack simulations are critical for regional hydrological predictions, snow avalanche prevention, water resource management, and agricultural production, particularly during the snow ablation period. Data assimilation methodologies are increasingly being applied for operational purposes to reduce the uncertainty in snowpack simulations and to enhance their predictive capabilities. This study aims to investigate the feasibility of using a genetic particle filter (GPF) as a snow data assimilation scheme designed to assimilate ground-based snow depth (SD) measurements across different snow climates. We employed the default parameterization scheme combination within the Noah-MP (with multi-parameterization) model as the model operator in the snow data assimilation system to evolve snow variables and evaluated the assimilation performance of the GPF using observational data from sites with different snow climates. We also explored the impact of measurement frequency and particle number on the filter updating of the snowpack state at different sites and the results of generic resampling methods compared to the genetic algorithm used in the resampling process. Our results demonstrate that a GPF can be used as a snow data assimilation scheme to assimilate ground-based measurements and obtain satisfactory assimilation performance across different snow climates. We found that particle number is not crucial for the filter's performance, and 100 particles are sufficient to represent the high dimensionality of the point-scale system. The frequency of measurements can significantly affect the filter-updating performance, and dense ground-based snow observational data always dominate the accuracy of assimilation results. Compared to generic resampling methods, the genetic algorithm used to resample particles can significantly enhance the diversity of particles and prevent particle degeneration and impoverishment. Finally, we concluded that the GPF is a suitable candidate approach for snow data assimilation and is appropriate for different snow climates.

ParticleAugment: Sampling-based data augmentation

We present an automated data augmentation approach for image classification. The problem is formulated as a Monte Carlo sampling problem where the goal is to approximate the optimal augmentation policies using a policy mixture distribution. We propose a particle filter scheme for the policy search where the probability of applying a set of augmentation operations forms the state of the filter. The policy performance is measured based on the loss function difference between a reference model and the actual model. This performance measure is then used to re-weight the particles and finally update the policy distribution. In our experiments, we show that our formulation for automated augmentation reaches promising results on CIFAR-10, CIFAR-100, and ImageNet datasets using the standard network architectures for this problem. By comparing with the related work, our method reaches a balance between the computational cost of policy search and the model performance. The source code of our approach is publicly available.

Real-time estimation and prediction of unsteady flows using reduced-order models coupled with few measurements

The estimation and prediction of unsteady flows in real time offers significant advantages for the monitoring and active control of complex hydrodynamic and aerodynamic systems, such as wind turbine blades, hydrofoils and aircraft wings. A new data assimilation algorithm is proposed for the estimation and prediction of unsteady flows, coupling in real time onboard measurements and fluid dynamics simulations at minimal computational expense. The procedure combines a Proper Orthogonal Decomposition Galerkin method, a model under location uncertainty stochastic closure, and a particle filtering scheme. The algorithm is validated using case studies of two- and three-dimensional wake flows at low and moderate Reynolds numbers respectively. Following an initial learning window to train the algorithm, and using only a single measurement point, our method is shown to perform well against conventional reduced data assimilation algorithms for up to 14 vortex shedding cycles.

Numerical simulation-aided particle filter-based damage prognosis using Lamb waves

Damage prognosis generally resorts to a damage evolution model and the current damage state to predict the future state and the remaining useful life (RUL). As a properly defined damage-sensitive statistical feature extracted from the Lamb waves can be used to online quantify the damage state, it is here exploited within a particle filter (PF) scheme to perform damage prognosis in structural health monitoring. An accurate mapping between the damage state and this feature would require a sufficient set of experimental Lamb waves collected in correspondence of different damage levels occurring during the run-to-failure process, which, however, is not usually available in real practice due to the high costs and the complex logistics involved in such experimental campaigns. In order to deal with this issue, this paper develops a new numerical simulation-aided particle filter-based damage prognosis framework, where the process equation is still built on the basis of available physical knowledge about the degradation process, whereas the measurement equation is built by means of a data-driven modeling approach using the features extracted from the numerically simulated Lamb waves. The PF framework serves as the state estimation tool which allows to identify the damage state and the parameters in the two equations. The future damage states and the RUL can finally be predicted by projecting the PF estimates in the future using the process equation. The proposed framework is demonstrated with reference to experimental studies of fatigue crack growth in aluminum lug structures with online Lamb wave monitoring.

Ego-Lane Index Estimation Based on Lane-Level Map and LiDAR Road Boundary Detection.

Correct ego-lane index estimation is essential for lane change and decision making for intelligent vehicles, especially in global navigation satellite system (GNSS)-challenged environments. To achieve this, we propose an ego-lane index estimation approach in an urban scenario based on particle filter (PF). The particles are initialized and propagated by dead reckoning with inertial measurement unit (IMU) and odometry. A lane-level map is used to navigate the particles taking advantage of topologic and geometric information of lanes. GNSS single-point positioning (SPP) can provide position estimation with meter-level accuracy in urban environments, which can limit drift introduced by dead reckoning for updating the weight of each particle. Light detection and ranging (LiDAR) is a common sensor in an intelligent vehicle. A LiDAR-based road boundary detection method provides distance measurements from the vehicle to the left/right road boundaries, which provides a measurement for importance weighting. However, the high precision of the LiDAR measurements may put a tight constraint on the distribution of particles, which can lead to particle degeneration with sparse particle sets. To deal with this problem, we propose a novel step that shifts particles laterally based on LiDAR measurements instead of importance weighting in the traditional PF scheme. We tested our methods on an urban expressway at a low traffic volume period to ensure road boundaries can be detected by LiDAR measurements at most time steps. Experimental results prove that our improved PF scheme can correctly estimate ego-lane index at all time steps, while the traditional PF scheme produces wrong estimations at some time steps.

Two-Stage Bayesian Optimization for Scalable Inference in State-Space Models.

State-space models (SSMs) are a rich class of dynamical models with a wide range of applications in economics, healthcare, computational biology, robotics, and more. Proper analysis, control, learning, and decision-making in dynamical systems modeled by SSMs depend on the accuracy of the inferred/learned model. Most of the existing inference techniques for SSMs are capable of dealing with very small systems, unable to be applied to most of the large-scale practical problems. Toward this, this article introduces a two-stage Bayesian optimization (BO) framework for scalable and efficient inference in SSMs. The proposed framework maps the original large parameter space to a reduced space, containing a small linear combination of the original space. This reduced space, which captures the most variability in the inference function (e.g., log likelihood or log a posteriori), is obtained by eigenvalue decomposition of the covariance of gradients of the inference function approximated by a particle filtering scheme. Then, an exponential reduction in the search space of parameters during the inference process is achieved through the proposed two-stage BO policy, where the solution of the first-stage BO policy in the reduced space specifies the search space of the second-stage BO in the original space. The proposed framework's accuracy and speed are demonstrated through several experiments, including real metagenomics data from a gut microbial community.

Implicit Equal-Weights Variational Particle Smoother

Under the motivation of the great success of four-dimensional variational (4D-Var) data assimilation methods and the advantages of ensemble methods (e.g., Ensemble Kalman Filters and Particle Filters) in numerical weather prediction systems, we introduce the implicit equal-weights particle filter scheme in the weak constraint 4D-Var framework which avoids the filter degeneracy through implicit sampling in high-dimensional situations. The new variational particle smoother (varPS) method has been tested and explored using the Lorenz96 model with dimensions N x = 40 , N x = 100 , N x = 250 , and N x = 400 . The results show that the new varPS method does not suffer from the curse of dimensionality by construction and the root mean square error (RMSE) in the new varPS is comparable with the ensemble 4D-Var method. As a combination of the implicit equal-weights particle filter and weak constraint 4D-Var, the new method improves the RMSE compared with the implicit equal-weights particle filter and LETKF (local ensemble transformed Kalman filter) methods and enlarges the ensemble spread compared with ensemble 4D-Var scheme. To overcome the difficulty of the implicit equal-weights particle filter in real geophysical application, the posterior error covariance matrix is estimated using a limited ensemble and can be calculated in parallel. In general, this new varPS performs slightly better in ensemble quality (the balance between the RMSE and ensemble spread) than the ensemble 4D-Var and has the potential to be applied into real geophysical systems.

SLFNs interpolation fingerprint particle filter-based shared bicycle tracking algorithm

In order to improve the performance of traditional fingerprint detection method in the process of tracking the shared bicycle, the inertial sensor is used for data measurement. The particle filter (PF) method is a widely used sensor fusion algorithm, but the initialisation and weighting processes are problematic in shared bicycle positioning systems. In this paper, a new PF scheme is proposed, and it can produces smooth and stable localised knowledge. However, the feed-forward network that uses the single hidden layer is used to simulate the estimation and improvement of the performance of multiple probability to achieve the distinction of similar fingerprints. At the same time, the random sample consensus algorithm (RANSAC) is used to initialise the algorithm so as to reduce the convergence time. Experiments show that the tracking error of this scheme is less than 1.2 m, which is superior to the selected comparison method.

Particle filtering‐based adaptive training of neural networks for real‐time structural damage diagnosis and prognosis

Real-time failure diagnosis and prognosis play key roles in prognostics and health management of critical engineering assets. Physics-based (or empirical–phenomenological) and data-driven methods have been proposed in the literature to solve damage diagnosis and prognosis challenges. Among data-driven methods, neural networks have often successfully proven their regression capabilities for the complex, nonlinear problems typical of this field research field. Indeed, the need to resort to machine learning techniques (e.g., neural networks) becomes stronger when physics-based (or empirical–phenomenological) models are lacking for describing the degradation behavior of the systems under consideration. In this work, we propose to exploit the flexibility offered by neural networks in order to adaptively, and in real time, learn from the monitored structure and derive models for diagnosis and prognosis of structural components subject to damage processes. To this aim, neural networks are embedded within a particle filtering scheme, and the training of the network is performed sequentially and in real time, as observations become available during the damage evolution. The structural health monitoring tool is capable of sequentially updating itself using the observations gathered during the system's operation, avoiding the typical limitations associated to off-line training schemes, which are, in general, not capable of capturing possible changes in the dynamical degradation behavior, when not properly included in the training patterns. For validation and comparison purposes, the method is demonstrated on simulated fatigue crack growths and real crack evolution dynamics observed in a metallic aeronautical panel loaded with a changing-amplitude fatigue load, during an accelerated laboratory test.

Magnetic-Based Indoor Localization Using Smartphone via a Fusion Algorithm

The detection of indoor location based on magnetic fields collected by embedded sensors in smartphones has been progressed rapidly. Most current approaches rely on the particle filter (PF) scheme which combines the pedestrian dead reckoning (PDR) technique with patterns of previously recorded magnetic field intensity. The key challenges include inherent blindness and particle degradation problems. Here, a fusion algorithm combining the extended Kalman filter (EKF) and the PF scheme is proposed to address these issues. EKF is first used to reduce the possible location regions by fusing the PDR and magnetic field intensity results. The particle generation, update, and resampling processes are conducted afterward, and the final position is calculated by using the weighted mean of particles. As such, the blindness and particle degradation problems are alleviated by using particles in the reduced location regions at each processing step. Experiments show a localization accuracy of 1-2m when the user walks smoothly, which is better than those of traditional PF schemes, especially in cases under heavy magnetic distortions by using a reduced number of particles.

A particle filter scheme for multivariate data assimilation into a point-scale snowpack model in an Alpine environment

Abstract. The accuracy of hydrological predictions in snow-dominated regions deeply depends on the quality of the snowpack simulations, with dynamics that strongly affect the local hydrological regime, especially during the melting period. With the aim of reducing the modelling uncertainty, data assimilation techniques are increasingly being implemented for operational purposes. This study aims to investigate the performance of a multivariate sequential importance resampling – particle filter scheme, designed to jointly assimilate several ground-based snow observations. The system, which relies on a multilayer energy-balance snow model, has been tested at three Alpine sites: Col de Porte (France), Torgnon (Italy), and Weissfluhjoch (Switzerland). The implementation of a multivariate data assimilation scheme faces several challenging issues, which are here addressed and extensively discussed: (1) the effectiveness of the perturbation of the meteorological forcing data in preventing the sample impoverishment; (2) the impact of the parameter perturbation on the filter updating of the snowpack state; the system sensitivity to (3) the frequency of the assimilated observations, and (4) the ensemble size.The perturbation of the meteorological forcing data generally turns out to be insufficient for preventing the sample impoverishment of the particle sample, which is highly limited when jointly perturbating key model parameters. However, the parameter perturbation sharpens the system sensitivity to the frequency of the assimilated observations, which can be successfully relaxed by introducing indirectly estimated information on snow-mass-related variables. The ensemble size is found not to greatly impact the filter performance in this point-scale application.

A Dual Particle Filter-Based Fault Diagnosis Scheme for Nonlinear Systems

In this paper, a dual estimation methodology is developed for both time-varying parameters and states of a nonlinear stochastic system based on the particle filtering scheme. Our developed methodology is based on a concurrent implementation of state and parameter estimation filters as opposed to using a single filter to simultaneously estimate the augmented states and parameters. The convergence and stability properties of our proposed dual estimation strategy are shown formally to be guaranteed under certain conditions. The advantage of our developed dual estimation method is justified by handling simultaneously and efficiently both the state and time-varying parameters of a nonlinear system. This is accomplished in the context of a health monitoring scheme that employs a unified approach to fault detection (FD), isolation, and identification in a single framework. The performance capabilities of our proposed FD methodology is demonstrated and evaluated by its application to a gas turbine engine through providing state and parameter estimation objectives under simultaneous and concurrent component fault scenarios. Extensive simulation results are provided to substantiate and justify the superiority of our proposed FD methodology when compared with another well-known alternative diagnostic technique that is available in the literature.

A Support Vector Learning-Based Particle Filter Scheme for Target Localization in Communication-Constrained Underwater Acoustic Sensor Networks.

Target localization, which aims to estimate the location of an unknown target, is one of the key issues in applications of underwater acoustic sensor networks (UASNs). However, the constrained property of an underwater environment, such as restricted communication capacity of sensor nodes and sensing noises, makes target localization a challenging problem. This paper relies on fractional sensor nodes to formulate a support vector learning-based particle filter algorithm for the localization problem in communication-constrained underwater acoustic sensor networks. A node-selection strategy is exploited to pick fractional sensor nodes with short-distance pattern to participate in the sensing process at each time frame. Subsequently, we propose a least-square support vector regression (LSSVR)-based observation function, through which an iterative regression strategy is used to deal with the distorted data caused by sensing noises, to improve the observation accuracy. At the same time, we integrate the observation to formulate the likelihood function, which effectively update the weights of particles. Thus, the particle effectiveness is enhanced to avoid “particle degeneracy” problem and improve localization accuracy. In order to validate the performance of the proposed localization algorithm, two different noise scenarios are investigated. The simulation results show that the proposed localization algorithm can efficiently improve the localization accuracy. In addition, the node-selection strategy can effectively select the subset of sensor nodes to improve the communication efficiency of the sensor network.

Contribution to Real-Time Estimation of Crop Phenological States in a Dynamical Framework Based on NDVI Time Series: Data Fusion With SAR and Temperature

In this study, a methodology based in a dynamical framework is proposed to incorporate additional sources of information to normalized difference vegetation index (NDVI) time series of agricultural observations for a phenological state estimation application. The proposed implementation is based on the particle filter (PF) scheme that is able to integrate multiple sources of data. Moreover, the dynamics-led design is able to conduct real-time ( online ) estimations, i.e., without requiring to wait until the end of the campaign. The evaluation of the algorithm is performed by estimating the phenological states over a set of rice fields in Seville (SW, Spain). A Landsat-5/7 NDVI series of images is complemented with two distinct sources of information: SAR images from the TerraSAR-X satellite and air temperature information from a ground-based station. An improvement in the overall estimation accuracy is obtained, especially when the time series of NDVI data is incomplete. Evaluations on the sensitivity to different development intervals and on the mitigation of discontinuities of the time series are also addressed in this work, demonstrating the benefits of this data fusion approach based on the dynamic systems.

Improved particle filter based on WLAN RSSI fingerprinting and smart sensors for indoor localization

Received Signal Strength Indicator (RSSI) is affected significantly by multi-path fading, building structure and obstacles in indoor environments, which lead to similar fingerprints problem and noise. To improve the performance of traditional fingerprinting method, the measurements provided by inertial sensors can be leveraged. Particle filter (PF) method is a widely chosen algorithm for sensor fusion. However, the initialization and weighting process are problematic in indoor positioning systems. This paper proposes a new PF scheme which yield a smooth and stable localization experience. To differentiate similar fingerprints, a single-hidden layer feed-forward networks (SLFNs) is used to model the multiple probabilistic estimations and improve the performance of the PF. Meanwhile, a new initialization algorithm using Random Sample Consensus (RANSAC) is presented to reduce the convergence time. Experimental measurements were carried out to determine the performance of the proposed algorithm. The results indicate that the positioning error of proposed scheme falls to less than 1.2 m which is better than the error reported in comparable approaches.

Simulation Study of the Particle Filter and the EKF for State Estimation of a Large-scale DAE-system with Multi-rate Sampling

In the present contribution we study the application of the Particle Filter (PF) and of the Extended Kalman Filter (EKF) incorporating measurements at different sampling rates for the state estimation of a large-scale model. We investigate a model of an intensified chemical process (a reactive distillation (RD) process) that is represented by a nonlinear DAE-system and has more than 100 states. The EKF and PF schemes are studied for two different cases. The performance of each of the estimation method is compared first for the case where the estimator uses a model which is identical to the process Secondly, the model used by the estimator is considered to be parametrically different from the model used to simulate the process. The effect of model-plant mismatch on the mean squared estimation error is studied for both state estimation methods. The goal is to give arguments for the selection of either of the methods to be used at the real process unit fulfilling the requirements of accurate estimation and real-time capability.

Online object tracking via bounded error distance

Online object tracking is a very important issue in computer vision and video processing, which has many potential applications. This paper presents a novel tracking method based on the proposed bounded error distance with subspace representation. First, the tracked object is assumed to be consisted of a principle component analysis (PCA) subspace and a bounded error distance is adopted to handle outliers. Then, the relationship between the proposed bounded error distance and the sparsity constraint is revealed, based on which the representation model is relaxed into a convex L1 regularization model. Finally, a tracking framework is developed by combining the proposed bounded error model with subspace representation within the particle filter scheme. We conduct many experiments on ten challenging image sequences and compare our tracker with eight state-of-the-art tracking methods. Both qualitative and quantitative evaluations on some challenging video clips show that our tracker performs better than other tracking algorithms.

Inferring Metrical Structure in Music Using Particle Filters

In this paper, we propose a new state-of-the-art particle filter (PF) system to infer the metrical structure of musical audio signals. The new inference method is designed to overcome the problem of PFs in multi-modal probability distributions, which arise due to tempo and phase ambiguities in musical rhythm representations. We compare the new method with a hidden Markov model (HMM) system and several other PF schemes in terms of performance, speed and scalability on several audio datasets. We demonstrate that using the proposed system the computational complexity can be reduced drastically in comparison to the HMM while maintaining the same order of beat tracking accuracy. Therefore, for the first time, the proposed system allows fast meter inference in a high-dimensional state space, spanned by the three components of tempo, type of rhythm, and position in a metric cycle.