Nonlinear Particle Filter Research Articles

Statistical modelling of digital elevation models for GNSS-based navigation

ABSTRACT Recently, smart mobility has become a important activity in transportation systems such as public, autonomous and shared transports. These systems require reliable navigation applications that lead to precise localisation and optimised route. The GPS system may face problems such as signal degradation caused by conical effects, affecting the reliability and accuracy of the signal, or signal loss in poor visibility environments. By using other sensors, the vehicle location system can overcome these GPS problems. This work focuses on the estimation of the inclination, which will be used to optimise the route planning for the EV or HEV especially in order to control the energy consumption. This paper presents a multi-sensor fusion method, based on GNSS, INS, OSM and DEM data fused using a non-linear particle filter, to estimate and improve the slopes of road segments. A new statistical modelling of the DEM errors related to the spatial sampling of elevation data is proposed. This method is based on the definition of a geometrical window, called Adjacent Sliding Window (ASW), which dynamically selects the elevation data in the vicinity of the road. The proposed method is evaluated in a suburban transport network. The experimental results show the benefits of the vehicle attitude and road slope estimation accuracies.

Hierarchical estimation of vehicle state and tire forces for distributed in-wheel motor drive electric vehicle without previously established tire model

In this paper, a hierarchical estimator combined with the nonlinear observer and particle filter (PF) is proposed to accurately estimate the vehicle state and tire forces of distributed in-wheel motor drive electric vehicles (DIMDEVs) when the traditional tire models are not available. The proposed estimator consists of lower and upper layers. The lower layer, i.e. longitudinal tire force nonlinear observer (LTFNO) aims at estimating the longitudinal force based on the available drive/brake torques and rotational speed of wheels. The convergence of LTFNO is proved by the invariant set principle. The upper layer receives these estimated longitudinal tire forces from LTFNO and estimates the vehicle state including lateral tire forces based on an expert model (EM). The designed EM utilizes basic knowledge and rules about tire characteristics to approximate the unknown lateral tire force. The upper estimator combines with EM (EEM) to further improve the accuracy. The EEM takes the modeling errors and disturbances into account and avoids the usage of complex established tire models. Then PF is applied in the upper layer to complete the estimation, which only needs measurable longitudinal/lateral accelerations and yaw rate signals. Finally, the effectiveness of the designed hierarchical estimator is verified by Carsim and Simulink co-simulations. The results show the proposed strategy can accurately estimate the vehicle state and tire forces in real-time.

Trading information, price discreteness, and volatility estimation

This paper investigates the challenging problem of volatility estimation using high-frequency financial data when both price discreteness and structural random market microstructure noise, i.e., a known function of trading information and a finite-dimensional parameter vector, are present. Under this setup, we propose a novel approach that features both nonlinear least squares and particle filters for the estimation of integrated volatility. Theoretical underpinnings are provided justifying the effectiveness of our method. Both simulation and empirical results show the clear advantage of our approach over a number of existing methods.

A Nonlinear Data-Driven Towed Array Shape Estimation Method Using Passive Underwater Acoustic Data

Large-aperture towed linear hydrophone array has been widely used for beamforming-based signal enhancement in passive sonar systems; however, its performance can drastically decrease due to the array distortion caused by rapid tactical maneuvers of the towed platform, oceanic currents, hydrodynamic effects, etc. In this paper, an enhanced data-driven shape array estimation scheme is provided in the passive underwater acoustic data, and a novel nonlinear outlier-robust particle filter (ORPF) method is proposed to acquire enhanced estimates of time delays in the presence of distorted hydrophone array. A conventional beamforming technique based on a hypothetical array is first used, and the detection of the narrow-band components is sequentially carried out so that the corresponding amplitudes and phases at these narrow-band components can be acquired. We convert the towed array estimation problem into a nonlinear discrete-time filtering problem with the joint estimates of amplitudes and time-delay differences, and then propose the ORPF method to acquire enhanced estimates of the time delays by exploiting the underlying properties of slowly changing time-delay differences across sensors. The proposed scheme fully exploits directional radiated noise targets as sources of opportunity for online array shape estimation, and thus it requires neither the number nor direction of sources to be known in advance. Both simulations and real experimental data show the effectiveness of the proposed method.

Robust linearly constrained extended Kalman filter for mismatched nonlinear systems

SummaryStandard state estimation techniques, ranging from the linear Kalman filter (KF) to nonlinear extended KF (EKF), sigma‐point or particle filters, assume a perfectly known system model, that is, process and measurement functions and system noise statistics (both the distribution and its parameters). This is a strong assumption which may not hold in practice, reason why several approaches have been proposed for robust filtering, mainly because the filter performance is particularly sensitive to different model mismatches. In the context of linear filtering, a solution to cope with possible system matrices mismatch is to use linear constraints. In this contribution we further explore the extension and use of recent results on linearly constrained KF for robust nonlinear filtering under both process and measurement model mismatch. We first investigate how linear equality constraints can be incorporated within the EKF and derive a new linearly constrained extended KF (LCEKF). Then we detail its use to mitigate parametric modeling errors in the nonlinear process and measurement functions. Numerical results are provided to show the performance improvement of the new LCEKF for robust vehicle navigation.

Velocity estimation of flexible dynamics systems using virtual sensing

In this paper, multiple virtual sensors derived from the equations of motion of a flexible dynamics system, are utilized to form a novel virtual sensing system able to estimate the angular and translation velocities. Measuring only the elastic displacement of the flexible body by a strain gauge, angular velocities are estimated by the first virtual sensor composed of a kinetics equation related to the flexibility, and the nonlinear Kalman and particle filters. Moreover, for translational velocities to be also estimated, specific forces are measured by accelerometers. The second virtual sensor including the equation of translational motion, is added to the virtual sensing system, leading not only the velocities to be estimated with high performance but the accumulated errors of the sensors to be corrected.

SOC Estimation of a Rechargeable Li-Ion Battery Used in Fuel Cell Hybrid Electric Vehicles—Comparative Study of Accuracy and Robustness Performance Based on Statistical Criteria. Part II: SOC Estimators

The purpose of this paper is to analyze the accuracy of three state of charge (SOC) estimators of a rechargeable Li-ion SAFT battery based on two accurate Li-ion battery models, namely a linear RC equivalent electrical circuit (ECM) and a nonlinear Simscape generic model, developed in Part 1. The battery SOC of both Li-ion battery models is estimated using a linearized adaptive extended Kalman filter (AEKF), a nonlinear adaptive unscented Kalman filter (AUKF) and a nonlinear and non-Gaussian particle filter estimator (PFE). The result of MATLAB simulations shows the efficiency of all three SOC estimators, especially AEKF, followed in order of decreasing performance by AUKF and PFE. Besides, this result reveals a slight superiority of the SOC estimation accuracy when using the Simscape model for SOC estimator design. Overall, the performance of all three SOC estimators in terms of accuracy, convergence of response speed and robustness is excellent and is comparable to state of the art SOC estimation methods.

Intelligent estimation for electric vehicle mass with unknown uncertainties based on particle filter

Vehicle mass is one of the most critical parameters in the vehicle control system, based on the discrete vehicle longitudinal dynamic equation after the forward Euler approximation, non-linear particle filter is introduced to estimate the vehicle mass intelligently, and it gains a competitive advantage that statistical characteristics of noise and uncertainties in the system are not necessary to be known or supposed in advance. As a sort of recursive, Bayesian state estimator, vehicle mass is regarded as a constant state variable to constitute the discrete state-space equation, motor torque is selected as input signal, and the measurable vehicle speed is selected to constitute the observation equation, parameters such as rolling resistance coefficient, air drag coefficient and road slop are considered as high-power noise and uncertainties. The performance of the proposed vehicle mass estimator is tested by several groups of load and the results demonstrate that the output of the particle filter based vehicle mass estimator can converge to the real value and keep steady.

A Dynamic State-of-Charge Estimation Method for Electric Vehicle Lithium-Ion Batteries

With the increasing environmental concerns, plug-in electric vehicles will eventually become the main transportation tools in future smart cities. As a key component and the main power source, lithium-ion batteries have been an important object of research studies. In order to efficiently control electric vehicle powertrains, the state of charge (SOC) of lithium-ion batteries must be accurately estimated by the battery management system. This paper aims to provide a more accurate dynamic SOC estimation method for lithium-ion batteries. A dynamic Thevenin model with variable parameters affected by the temperature and SOC is established to model the battery. An unscented Kalman particle filter (UPF) algorithm is proposed based on the unscented Kalman filter (UKF) algorithm and the particle filter (PF) algorithm to generate nonlinear particle filter according to the advantages and disadvantages of various commonly used filtering algorithms. The simulation results show that the unscented Kalman particle filter algorithm based on the dynamic Thevenin model can predict the SOC in real time and it also has strong robustness against noises.

An ensemble framework for time delay synchronization.

Synchronization based state estimation tries to synchronize a model with the true evolution of a system via the observations. In practice, an extra term is added to the model equations which hampers growth of instabilities transversal to the synchronization manifold. Therefore, there is a very close connection between synchronization and data assimilation. Recently, synchronization with time‐delayed observations has been proposed, in which observations at future times are used to help synchronize a system that does not synchronize using only present observations, with remarkable successes. Unfortunately, these schemes are limited to small‐dimensional problems.In this article, we lift that restriction by proposing an ensemble‐based synchronization scheme. Tests were performed using the Lorenz'96 model for 20‐, 100‐ and 1000‐dimension systems. Results show global synchronization errors stabilizing at values of at least an order of magnitude lower than the observation errors, suggesting that the scheme is a promising tool to steer model states to the truth. While this framework is not a complete data assimilation method, we develop this methodology as a potential choice for a proposal density in a more comprehensive data assimilation method, like a fully nonlinear particle filter.

Determination of Target Angular Coordinates in Passive Locator via Particle Filter

The article deals with solving a problem of the passive angle track on target from a spacecraft (SC) via measuring one angle. A main idea of the passive track is to use the angle data to estimate the unknown position of a target. For estimation, methods based on the Kalman filter and its modifications are often used. However, here there is a problem that the linearized filters can easily diverge, when maneuvering. Therefore, in this paper, we propose to solve the problem of passive one angle track on target using a nonlinear particle filter (PF). The problem under consideration is represented as a Bayesian one of the recursive estimation that is aimed at estimating a state dynamics of the observed angle. It is described through defining the transient and conditional probability densities, and its general solution is represented as a procedure prediction-correction. The PF algorithm allows solving such a problem by representing a posteriori probability density of the estimated value by a set of generated points with weights generated according to the algorithm of sequential importance sampling and regenerated according to the algorithm of regeneration with systematic residual resampling. In such an algorithm at each subsequent time iteration there is a recursively updated set of weighted points according to which the posterior distribution of the state vector is approximated. The article in detail describes a developed algorithm of passive tracking and gives its diagrammatic representation. The flowchart diagram can be divided into the following steps: initialization, regeneration, filtering, and extrapolation. The first provides initial generation of a set of points and weights, regeneration allows avoiding the degeneracy of the set, and filtering enables direct estimates. Extrapolation, however, plays a separate important role in correcting the given functional laws. Further, the class hierarchy software implementation is shown as one combined flexible, portable module. The developed module has been simulated using the real experimental data for the cases of linear and nonlinear variation of the true angle. The accuracy of tracking a target was evaluated by a criterion of the squared estimation error of the measured angle against the true one. Based on the results of the simulation, a conclusion can be drawn that the proposed algorithm is sufficiently fast convergent, which indicates that its using is expedient.

Target Detection Method Before Tracking based on Particle Filter

infrared dim target detection and tracking technology is one of the core technologies in infrared imaging system, and also a hot research topic. When the SNR is low, the tracking technique has a unique advantage. This paper studies the algorithm of track before detect based on particle filter, gives the basic theory of particle filter and its improved algorithm, and through the simulation of the particle filter technology examples, results show the superior performance in nonlinear and non particle filter under the background of Gauss.

Enhancing Relative Positioning Accuracy in Vehicle-to-Vehicle Safety: Multivehicle Kinematics and Nonlinear Particle Filtering Approach

Unsatisfactory relative positioning accuracy is a bottleneck in collision avoidance applications of vehicle-to-vehicle communication. Previous efforts focused mainly on either enhancing absolute GPS data precision or experimenting with positioning techniques alternative to GPS, such as real-time kinematics, Doppler measurements, or integration of GPS with ultrawideband ranging radios. This paper proposes a new approach that is independent from the sources and precisions of raw data. Based on a multivehicle kinematics model adapted from a multirobot domain, the method can predict vehicles’ distances and bearings by fully utilizing the shared real-time motion data from dedicated short-range communications’ basic safety message packets. Three types of nonlinear filters were proposed and compared to minimize the errors caused by raw data noise and system timing inaccuracies. Experiments indicated that the extended Kalman filter failed to estimate a highly nonlinear process, unscented Kalman filter dysfunctions, if the statistical features of errors were misestimated; only the particle filter maintained satisfactory and stable accuracies in both high-nonlinearity and error-unknown situations. The combination of the kinematics model and particle filtering can serve as an algorithmic complement to various approaches focused on data sources to enhance relative positioning precision.

Structural changes in the Czech, Slovak and euro area economies during the Great Recession

Abstract The goal of this paper is to identify and compare the most important changes in the structure of the Czech economy, as a small open economy with independent monetary policy, the Slovak economy, as a small open economy that entered monetary union, and the economy of the euro area, which has a common monetary policy, during the turbulent period of the Great Recession, the subsequent anaemic recovery and recent disinflationary period. Structural changes are identified with the help of nonlinear dynamic stochastic models of general equilibrium with time-varying parameters. The model parameters are estimated using Bayesian methods and a nonlinear particle filter. The results confirm the similarity of the Czech and Slovak economies and show that in certain respects the structure of the Czech economy might be closer to that of the euro area than that of Slovakia. The time-varying estimates reveal many similarities between the parameter changes in the Czech economy and those in the euro area. In Slovakia, the situation during the Great Recession was dominated by the country’s adoption of the euro, which caused large deviations in its Calvo parameters.

Moving target parameter estimation for MIMO radar based on the improved particle filter

In this paper, a novel independent partition Rao-Blackwellized particle filter (IPRBPF) is proposed to estimate the moving target parameters in MIMO radar. Firstly, noticing that the likelihood function is a nonlinear function of the nonlinear position parameters, and that the target motion equation is a linear function of linear parameters such as velocity, acceleration and etc. The nonlinear particle filter is proposed to estimate the nonlinear position parameters and the linear Kalman filter is proposed to estimate the linear parameters. Then a new MIMO radar parameter estimation algorithm based on Rao-Blackwellized particle filter is obtained. Furtherly, considering that the computational complexity will increase dramatically with the targets’ state dimension in the case of multiple targets, the independent partition sampling is put forward to improve the performance of our algorithm, then the IPRBPF algorithm is obtained. Compared with the existing methods, the proposed algorithm can achieve the lower computational complexity and the higher accuracy of parameter estimation. Simulation results demonstrate the advantages of the proposed algorithm.

A robust dynamic state estimation for droop controlled islanded microgrids

This paper proposes a nonlinear particle filter (PF) method for dynamic state estimation in droop-controlled islanded microgrids (IMGs). The PFs are normally applied to systems that (1) have highly nonlinear system dynamics, and (2) do not require the additive process or observation noise to be Gaussian. This flexibility allows the PFs to handle noisy measurements from a range of varied distributions, thereby increasing its robustness. To that end, a nonlinear dynamic state model has been developed in this work for droop-controlled IMGs. Additive noise has been incorporated into the state model to account for the error in its accuracy. Monte Carlo simulations have been conducted to verify that the PF accurately tracks the IMG state variables in spite of using significantly corrupted state and observation values. A comparison between the PF and unscented Kalman filter (UKF) has been carried out to test the effectiveness and robustness of the proposed methodology.

Two Second-Order Nonlinear Extended Kalman Particle Filter Algorithms

In algorithms of nonlinear Kalman filter, the so-called extended Kalman filter algorithm actually uses first-order Taylor expansion approach to transform a nonlinear system into a linear system. It is obvious that this algorithm will bring some systematic deviations because of ignoring nonlinearity of the system. This paper presents two extended Kalman filter algorithms for nonlinear systems, called second-order nonlinear Kalman particle filter algorithms, by means of second-order Taylor expansion and linearization approximation, and correspondingly two recursive formulas are derived. A simulation example is given to illustrate the effectiveness of two algorithms. It is shown that the extended Kalman particle filter algorithm based on second-order Taylor expansion has a more satisfactory performance in reducing systematic deviations and running time in comparison with the extended Kalman filter algorithm and the other second-order nonlinear Kalman particle filter algorithm.

The Particle Filter Sample Impoverishment Problem in the Orbit Determination Application

The paper aims at discussing techniques for administering one implementation issue that often arises in the application of particle filters: sample impoverishment. Dealing with such problem can significantly improve the performance of particle filters and can make the difference between success and failure. Sample impoverishment occurs because of the reduction in the number of truly distinct sample values. A simple solution can be to increase the number of particles, which can quickly lead to unreasonable computational demands, which only delays the inevitable sample impoverishment. There are more intelligent ways of dealing with this problem, such as roughening and prior editing, procedures to be discussed herein. The nonlinear particle filter is based on the bootstrap filter for implementing recursive Bayesian filters. The application consists of determining the orbit of an artificial satellite using real data from the GPS receivers. The standard differential equations describing the orbital motion and the GPS measurements equations are adapted for the nonlinear particle filter, so that the bootstrap algorithm is also used for estimating the orbital state. The evaluation will be done through convergence speed and computational implementation complexity, comparing the bootstrap algorithm results obtained for each technique that deals with sample impoverishment.

Usefulness of Nonlinear Interpolation and Particle Filter in Zigbee Indoor Positioning

Abstract The key to fingerprint positioning algorithm is establishing effective fingerprint information database based on different reference nodes of received signal strength indicator (RSSI). Traditional method is to set the location area calibration multiple information sampling points, and collection of a large number sample data what is very time consuming. With Zigbee sensor networks as platform, considering the influence of positioning signal interference, we proposed an improved algorithm of getting virtual database based on polynomial interpolation, while the pre-estimated result was disposed by particle filter. Experimental result shows that this method can generate a quick, simple fine-grained localization information database, and improve the positioning accuracy at the same time.

Numerical analysis of rating transition matrix depending on latent macro factor via nonlinear particle filter method

We propose a new nonlinear filtering model for a better estimation of credit rating transition matrix consistent with the hypothesis that rating transition intensities as well as dynamics of financial asset prices depend on some unobservable macroeconomic factor. We attempt a branching particle filter method to numerically obtain the conditional distribution of the latent factor. For an illustration, we analyze a rating transition history of Japanese enterprises. As a result, we realize that our model can capture some contagion effect of credit events and an interpolative role of financial market information on the rating transition intensities.