Sampling Importance Resampling Particle Filter Research Articles

Vision-based particle filtering for quad-copter attitude estimation using multirate delayed measurements.

In this paper, the problem of attitude estimation of a quad-copter system equipped with a multi-rate camera and gyroscope sensors is addressed through extension of a sampling importance re-sampling (SIR) particle filter (PF). Attitude measurement sensors, such as cameras, usually suffer from a slow sampling rate and processing time delay compared to inertial sensors, such as gyroscopes. A discretized attitude kinematics in Euler angles is employed where the gyroscope noisy measurements are considered the model input, leading to a stochastic uncertain system model. Then, a multi-rate delayed PF is proposed so that when no camera measurement is available, the sampling part is performed only. In this case, the delayed camera measurements are used for weight computation and re-sampling. Finally, the efficiency of the proposed method is demonstrated through both numerical simulation and experimental work on the DJI Tello quad-copter system. The images captured by the camera are processed using the ORB feature extraction method and the homography method in Python-OpenCV, which is used to calculate the rotation matrix from the Tello's image frames.

An Efficient Estimation of Time‐Varying Parameters of Dynamic Models by Combining Offline Batch Optimization and Online Data Assimilation

AbstractIt is crucially important to estimate unknown parameters in process‐based models by integrating observation and numerical simulation. For many applications in earth system sciences, a parameter estimation method which allows parameters to temporally change is required. In the present paper, an efficient and practical method to estimate time‐varying parameters of relatively low dimensional models is presented. In the newly proposed method, called Hybrid Offline Online Parameter Estimation with Particle Filtering (HOOPE‐PF), an inflation method to maintain the spread of ensemble members in a Sampling‐Importance‐Resampling Particle Filter (SIRPF) is improved using a non‐parametric posterior probabilistic distribution of time‐invariant parameters obtained by comparing simulated and observed climatology. HOOPE‐PF outperforms the original SIRPF in synthetic experiments with toy models and a real‐data experiment with a conceptual hydrological model when an ensemble size is small. The advantage of HOOPE‐PF is that its performance is not greatly affected by the size of perturbation to be added to ensemble members to maintain their spread while it is important to get the optimal performance in the original particle filter. Since HOOPE‐PF is the extension of the existing particle filter which has been extensively applied to many models in earth system sciences such as land, ecosystem, hydrology, and paleoclimate reconstruction, HOOPE‐PF can be applied to improve the simulation of these process‐based models by considering time‐varying model parameters.

Characterization of Background Temperature Dynamics of a Multitemporal Satellite Scene through Data Assimilation for Wildfire Detection

Detection of an active fire in an image scene relies on an accurate estimation of the background temperature of the scene, which must be compared to the observed temperature, to decide on the presence of fire. The expected background temperature of a pixel is commonly derived based on spatial-contextual information that can overestimate the background temperature of a fire pixel and therefore results in the omission of a fire event. This paper proposes a method that assimilates brightness temperatures acquired from the Geostationary Earth Orbit (GEO) sensor MSG-SEVIRI into a Diurnal Temperature Cycle (DTC) model. The expected brightness temperatures are observational forecasts derived using the ensemble forecasting approach. The threshold on the difference between the observed and expected temperatures is derived under a Constant False Alarm Rate (CFAR) framework. The detection results are assessed against a reference dataset comprised of MODIS MOD14/MYD14 and EUMETSAT FIR products, and the performance is presented in terms of user’s and producer’s accuracies, and Precision-Recall and Receiver Operating Characteristic (ROC) graphs. The method has a high detection rate when the data assimilation is implemented with an Ensemble Kalman Filter (EnKF) and a Sampling Importance Resampling (SIR) particle filter, while the weak-constraint Four-Dimensional Variational Assimilation (4D-Var) has comparatively lower detection and false alarm rates according to the reference dataset. Consideration of the diurnal variation in the background temperature enables the proposed method to detect even low-power fires.

Online State of Charge Estimation of Lithium-Ion Cells Using Particle Filter-Based Hybrid Filtering Approach

Filtering based state of charge (SOC) estimation with an equivalent circuit model is commonly extended to Lithium-ion (Li-ion) batteries for electric vehicle (EV) or similar energy storage applications. During the last several decades, different implementations of online parameter identification such as Kalman filters have been presented in literature. However, if the system is a moving EV during rapid acceleration or regenerative braking or when using heating or air conditioning, most of the existing works suffer from poor prediction of state and state estimation error covariance, leading to the problem of accuracy degeneracy of the algorithm. On this account, this paper presents a particle filter-based hybrid filtering method particularly for SOC estimation of Li-ion cells in EVs. A sampling importance resampling particle filter is used in combination with a standard Kalman filter and an unscented Kalman filter as a proposal distribution for the particle filter to be made much faster and more accurate. Test results show that the error on the state estimate is less than 0.8% despite additive current measurement noise with 0.05 A deviation.

Data‐driven XGBoost‐based filter for target tracking

In recent years, the data-driven approach has been introduced in the field of target tracking as a powerful tool developing the end-to-end mapping relationship between input features and outputs. Typically, in data-driven methods, neural networks serve as a supplement of traditional Bayesian filters for improved estimation accuracy. However, these hybrid methods are somehow complicated to realise. In this study, inspired by the idea of direct-mapping from measurements to states, simpler method by developing a data-driven XGBoost-based Filter (DXGBF) is proposed. The DXGBF consists of four components, namely data generator, sliding window, centralisation strategy and XGBoost learner (XL). The data generator generates simulated data from the probabilistic model in the training phase. By intercepting the measurements, the sliding window enables DXGBF to track targets online. The centralisation strategy extracts the relevant kinematic information from different tracks that enables DXGBF to track randomly initialised targets. The XL is responsible for learning a function that mapping to estimate states. Simulation results show that the estimation accuracy of DXGBF is higher than those of Kalman filter, sampling importance resampling particle filter and the data-driven random-forest-based filter.

Oba Filter for Online-Adaptive Nonlinear State Estimation With Interference

Interference, such as jamming, is widely encountered in practical applications, such as target tracking. Kalman-based nonlinear filters may not be feasible for nonlinear state estimation with nonlinearly transformed interference. This paper presents an online-based adaptive (oba) filter, which we have named the oba filter (OF), for state filtering and prediction of nonlinear discrete dynamic models with estimate constraints, nonlinearly transformed interference and noise. In the OF, noises and interference are approximated by discrete noises and interference; states are quantized; some undesired state estimates, which are not in near vicinities of the actual state values, are detected by a confidence level, and then state quantization levels are updated at the times when undesired estimates occur by using the measurement model; and states are recursively estimated by a suboptimal implementation of multiple composite hypothesis testing. The OF can prevent some undesired state estimates and outperform the unscented Kalman, regularized, sampling importance resampling (SIR), and auxiliary SIR particle filters for some nonlinear models with noise and interference. It is also suitable for state estimation with either missing observations or estimate constraints.

Bayesian State Estimation for Markovian Jump Systems: Employing Recursive Steps and Pseudocodes

In this article, we review several existing Bayesian state-estimation algorithms for Markovian jump systems (MJSs) and illustrate their distinctive properties. Specifically, we analyze the jump Markov linear systems (JMLSs), for which autonomous multiple-model (AMM) algorithms, first-order generalized pseudo-Bayesian (GPB1) algorithms, secondorder generalized pseudo-Bayesian (GPB2) algorithms, interacting multiple-model (IMM) algorithms, and reweighed IMM (RIMM) algorithms are introduced. For nonlinear MJSs, we consider the sampling importance resampling (SIR) particle filter (PF) as well as the IMM PF to demonstrate how to handle nonlinearity in the framework of MJSs. For convenience, the realization codes of GPB1 and IMM algorithms and SIR PFs are provided.

Particle filter-based modulation domain infrared targets tracking

Faced with problems of low contrast, poor SNR, and relatively complicated tracking environment, stable infrared target tracking is worth researching for its many potential applications. In this paper, instead of traditional target tracking in the pixel domain, we propose a sampling importance resampling (SIR) particle filter method with indirect velocity measurements to track infrared targets in the modulation domain. The dominant amplitude modulation (AM) features used for tracking is extracted by decomposing the input image using an 18-channel Gabor filter bank followed by the application of the dominant component analysis approach. The dominant AM modulation features provide a significant partial texture characteristic of the target which can be separated from background with better discrimination. To take advantage of observed kinematics, we utilize the augmented state vector with indirect velocity information via combining the measurements of velocity in adjacent frames to the SIR particle filter framework, which weakens weights of particles with bad velocity estimates but still having association with the cluttered background or other moving objects. A dynamic template update strategy is also provided to prevent the tracker from appearance model drift. Experiments indicate that the proposed method is effective for raising the tracking accuracy compared with other tracking methods.

Selective Sampling Importance Resampling Particle Filter Tracking With Multibag Subspace Restoration.

The focus of this paper is a novel object tracking algorithm which combines an incrementally updated subspace-based appearance model, reconstruction error likelihood function and a two stage selective sampling importance resampling particle filter with motion estimation through autoregressive filtering techniques. The primary contribution of this paper is the use of multiple bags of subspaces with which we aim to tackle the issue of appearance model update. The use of a multibag approach allows our algorithm to revert to a previously successful appearance model in the event that the primary model fails. The aim of this is to eliminate tracker drift by undoing updates to the model that lead to error accumulation and to redetect targets after periods of occlusion by removing the subspace updates carried out during the period of occlusion. We compare our algorithm with several state-of-the-art methods and test on a range of challenging, publicly available image sequences. Our findings indicate a significant robustness to drift and occlusion as a result of our multibag approach and results show that our algorithm competes well with current state-of-the-art algorithms.

A local particle filter for high-dimensional geophysical systems

Abstract. A local particle filter (LPF) is introduced that outperforms traditional ensemble Kalman filters in highly nonlinear/non-Gaussian scenarios, both in accuracy and computational cost. The standard sampling importance resampling (SIR) particle filter is augmented with an observation-space localization approach, for which an independent analysis is computed locally at each grid point. The deterministic resampling approach of Kitagawa is adapted for application locally and combined with interpolation of the analysis weights to smooth the transition between neighboring points. Gaussian noise is applied with magnitude equal to the local analysis spread to prevent particle degeneracy while maintaining the estimate of the growing dynamical instabilities. The approach is validated against the local ensemble transform Kalman filter (LETKF) using the 40-variable Lorenz-96 (L96) model. The results show that (1) the accuracy of LPF surpasses LETKF as the forecast length increases (thus increasing the degree of nonlinearity), (2) the cost of LPF is significantly lower than LETKF as the ensemble size increases, and (3) LPF prevents filter divergence experienced by LETKF in cases with non-Gaussian observation error distributions.

Vehicle Tracking Based on Fusion of Magnetometer and Accelerometer Sensor Measurements With Particle Filtering

In this paper, we propose a method for vehicle tracking on roadways using measurements of magnetometers and accelerometers. The measurements are used to build a low-cost, low-complexity vehicle tracking sensor platform for highway traffic monitoring. First, the problem is formulated by introducing the process model for the motion of the vehicle on the road and two measurement models: one for each of the sensors. Second, it is shown how the measurements of the sensors can be fused using particle filtering. The standard sampling importance resampling (SIR) particle filter is extended for processing of multirate sensor measurements and models that employ unknown static parameters. The latter are treated by Rao–Blackwellization. The performance of the method is demonstrated by computer simulations. It is found that it is feasible to fuse the two sensors for vehicle tracking and that the proposed multirate particle filter performs better than particle filters that process only measurements of one of the sensors. The main contribution of this paper is the novel approach of fusing the measurements of road-mounted magnetometers and accelerometers for vehicle tracking and traffic monitoring.

Estimation of Tumor Size Evolution Using Particle Filters.

Cancer is characterized by the uncontrolled growth of cells with the ability of invading local organs and/or tissues and of spreading to other sites. Several kinds of mathematical models have been proposed in the literature, involving different levels of refinement, for the evolution of tumors and their interactions with chemotherapy drugs. In this article, we present the solution of a state estimation problem for tumor size evolution. A system of nonlinear ordinary differential equations is used as the state evolution model, which involves as state variables the numbers of tumor, normal and angiogenic cells, as well as the masses of the chemotherapy and anti-angiogenic drugs in the body. Measurements of the numbers of tumor and normal cells are considered available for the inverse analysis. Parameters appearing in the formulation of the state evolution model are treated as Gaussian random variables and their uncertainties are taken into account in the estimation of the state variables, by using an algorithm based on the auxiliary sampling importance resampling particle filter. Test cases are examined in the article dealing with a chemotherapy protocol for pancreatic cancer.

Tracking by local structural manifold learning in a new SSIR particle filter

We propose a new object tracking algorithm by local structural manifold learning in a selective sampling importance resampling (SSIR) particle filter framework. A new local structural manifold learning strategy is designed for the invariant appearance modeling in challenging conditions. The appearance of the object which has complex structure in the low-dimensional space is approximated with a set of local structural manifolds. The local structures of the appearance manifold are incrementally learned with changes in the appearance of the object. Unlike traditional particle filters which rely on random re-sampling for new particles generation, we propose a new SSIR particle filter, which integrates an auto-regressive filter to improve the process of samples generation. The distribution of the generated particle samples by our method is better than that of the traditional techniques. Experimental results on several challenging videos demonstrate the robustness and accuracy of our algorithm compared with other recent excellent tracking approaches.

Online state estimation for discrete nonlinear dynamic systems with nonlinear noise and interference

This paper presents a real-time recursive state filtering and prediction scheme (PR) for discrete nonlinear dynamic systems with nonlinear noise and random interference, such as undesired random jamming or clutter. The PR is based upon discrete noise approximation, state quantization, and a suboptimal implementation of multiple composite hypothesis testing. The PR outperforms both the sampling importance resampling (SIR) particle filter and auxiliary sampling importance resampling (ASIR) particle filter; whereas Kalman-based nonlinear filters are, in general, inadequate for state estimation of many nonlinear dynamic systems with nonlinear noise and interference. Moreover, the PR is more general than grid-based estimation approaches. It is also very suitable for state estimation with either constraints imposed on state estimates or missing observations.

Maneuvering target tracking from nautical radar images using particle-Kalman filters

In this paper, a new combined particle-Kalman filter (PF-KF)-based visual tracking approach is designed for maneuvering target tracking from X-band nautical radar images. Unlike existing target tracking approaches used by nautical radar, this approach incorporates a histogram-based visual tracking strategy to estimate the target position and velocity. It applies a sampling importance resampling (SIR) particle filter to obtain preliminary target positions, and then a Kalman filter to derive refined target position and velocity. A Bhattacharyya coefficient-based similarity function is employed to compare the reference target and candidate target models, which are constructed by a kernel-based histogram in radar images. An enhanced reference target model construction method that employs constant false alarm rate (CFAR) processing to enable automatic determination of reference region is proposed to improve the tracking stability and accuracy. Comparison of the target information obtained by the proposed PF-KF method from various field X-band nautical radar image sequences with those measured by GPS shows the proposed approach can provide a reliable and flexible online target tracking for nautical radar application. It is also shown that, in the scenario of strong sea clutter, the proposed approach outperforms the PF-only-based approach and the classical tracking approach which combines order-statistics (OS) CFAR processing and the Kalman filter.

State estimation in large-scale open channel networks using sequential Monte Carlo methods: Optimal sampling importance resampling and implicit particle filters

[1] This article investigates the performance of Monte Carlo-based estimation methods for estimation of flow state in large-scale open channel networks. After constructing a state space model of the flow based on the Saint-Venant equations, we implement the optimal sampling importance resampling filter to perform state estimation in a case in which measurements are available at every time step. Considering a case in which measurements become available intermittently, a random-map implementation of the implicit particle filter is applied to estimate the state trajectory in the interval between the measurements. Finally, some heuristics are proposed, which are shown to improve the estimation results and lower the computational cost. In the first heuristics, considering the case in which measurements are available at every time step, we apply the implicit particle filter over time intervals of a desired size while incorporating all the available measurements over the corresponding time interval. As a second heuristic method, we introduce a maximum a posteriori (MAP) method, which does not require sampling. It will be seen, through implementation, that the MAP method provides more accurate results in the case of our application while having a smaller computational cost. All estimation methods are tested on a network of 19 tidally forced subchannels and 1 reservoir, Clifton Court Forebay, in Sacramento-San Joaquin Delta in California, and numerical results are presented.

Improved particle filter based on fine resampling algorithm

In order to solve particle degeneracy phenomenon and simultaneously avoid sample impoverishment, this paper proposed an improved particle filter based on fine resampling algorithm for general case, called as particle filter with fine resampling (PF-FR). By introducing distance-comparing process and generating new particle based on optimized combination scheme, PF-FR filter performs better than generic sampling importance resampling particle filter (PF-SIR) both in terms of effectiveness and diversity of the particle system, hence, evidently improving estimation accuracy of the state in the nonlinear/non-Gaussian models. Simulations indicate that the proposed PF-FR algorithm can maintain the diversity of particles and thus achieve the same estimation accuracy with less number of particles. Consequently, PF-FR filter is a competitive choice in the applications of nonlinear state estimation.

A novel real-time adaptive suboptimal recursive state estimation scheme for nonlinear discrete dynamic systems with non-Gaussian noise

A real-time state filtering and prediction scheme which is adaptive, recursive, and suboptimal is proposed for discrete time nonlinear dynamic systems with either Gaussian or non-Gaussian noise. The proposed scheme (PR) estimates states adaptively whenever both the observation is available and there exists a non-zero and finite number of real state roots of the observation model, otherwise the PR estimates states non-adaptively. The PR state transition and observation functions are as general as the state transition and observation functions for particle filters. The PR is based upon discrete noise approximation, state quantization, and a suboptimal implementation of multiple hypothesis testing. The PR first detects state estimate divergence points along the time axis, and then state estimate divergences are prevented by introducing new admissible state quantization levels; whereas the extended Kalman filter (EKF), sampling importance resampling (SIR) particle filter (bootstrap filter), and auxiliary sampling importance resampling (ASIR) particle filter produce diverging state estimates from actual state values for many dynamic models. The PR uses state transition functions in order to calculate transition probabilities from gates to gates. If these transition probabilities are somehow available, then state transition functions are not needed for state estimation with the PR; whereas state transition functions are necessary for state estimation with both particle filters and the EKF. The PR is very suitable for state estimation with either constraints imposed on state estimates or missing observations. The PR is more general than grid-based estimation approaches. Monte Carlo simulations have shown the effectiveness of the PR, that is, the PR performance is better than the performances of the EKF, SIR, and ASIR particle filters for many nonlinear models with white Gaussian noise, four examples of which are presented in the paper.

Detection and Tracking of Moving Objects for Automotive Driver Assistance System

A method derived from the adaptive Sampling Importance Resampling particle filter is proposed to solve vehicle detection and tracking problems in laser range finder data. The originality of this approach lies in a joint detection and tracking of the objects. To this end, the solution is based on a matched filter which uses a predefined vehicle model. The non-linearity of the state equations is tackled by sequential Monte Carlo methods which are here the basis of our solution. A central point here is to calculate the weights of the matched particle filter, according to the vehicle model. The proposed approach is then applied to synthetic data from a road scenario. The efficiency of the method is shown in terms of estimation accuracies and detection.

A new real-time suboptimum filtering and prediction scheme for general nonlinear discrete dynamic systems with Gaussian or non-Gaussian noise

A new suboptimum state filtering and prediction scheme is proposed for nonlinear discrete dynamic systems with Gaussian or non-Gaussian disturbance and observation noises. This scheme is an online estimation scheme for real-time applications. Furthermore, this scheme is very suitable for state estimation under either constraints imposed on estimates or missing observations. State and observation models can be any nonlinear functions of the states, disturbance and observation noises as long as noise samples are independent, and the density functions of noise samples and conditional density functions of the observations given the states are available. State models are used to calculate transition probabilities from gates to gates. If these transition probabilities are known or can be estimated, state models are not needed for estimation. The proposed scheme (PR) is based upon state quantisation and multiple hypothesis testing. Monte Carlo simulations have shown that the performance of the PR, sampling importance resampling (SIR) particle filter and extended Kalman (EK) filter are all model-dependent, and that the performance of the PR is better than both the SIR particle filter and EK filter for some nonlinear models, simulation results of three of which are given in this article.