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In vehicle navigation, it is quite common that the dynamic system is subject to various constraints, which increases the difficulty in nonlinear filtering. To address this issue, this paper presents a new constrained cubature particle filter (CCPF) for vehicle navigation. Firstly, state constraints are incorporated in the importance sampling process of the traditional cubature particle filter to enhance the accuracy of the importance density function. Subsequently, the Euclidean distance is employed to optimize the resampling process by adjusting particle weights to avoid particle degradation. Further, the convergence of the proposed CCPF is also rigorously proved, showing that the posterior probability function is converged when the particle number N → ∞. Our experimental results and the results of a comparative analysis regarding GNSS/DR (Global Navigation Satellite System/Dead Reckoning)-integrated vehicle navigation demonstrate that the proposed CCPF can effectively estimate system state under constrained conditions, leading to higher estimation accuracy than the traditional particle filter and cubature particle filter.

The state of charge (SOC) is an important parameter for batteries, especially those for electric vehicles. Since SOC cannot be obtained directly by measurement, SOC estimation methods are required. In this paper, three model-based methods, including the extended particle filter (EPF), cubature particle filter (CPF), and unscented particle filter (UPF), are compared in terms of complexity, accuracy, and robustness. The second-order resistor-capacitor (RC) equivalent circuit model is selected as the circuit model of the lithium-ion battery, and the parameters of the model are obtained by off-line identification. Then, the City test is applied to compare the performance of the methods. The experimental results show that the EPF method exhibits low complexity and fast running speed, but poor accuracy and robustness. Compared with the EPF method, the complexity of the CPF and UPF methods is relatively high, but these models offer improved accuracy and robustness.

This paper presents a new particle filter algorithm (MultiPDF) for state estimation of nonlinear systems. The proposed method is a modification of the standard particle filter approach. Due to the strong need for the acceleration of calculations and an improvement in the estimation quality of state estimation, the authors propose a method which enables one to divide the main particle filter into smaller sub-filters with an accordingly smaller number of particles for each one of them. The algorithm has been implemented for various numbers of particles and subordinate parallel filters. Estimation quality has been checked for nine nonlinear objects (both one- and multidimensional) and evaluated through the quality index, average root-mean-squared error. The computation time of the particle filter algorithm for several hardware configurations has been compared. Based on the obtained results, it can be concluded that, besides the computation acceleration, the parallelization of the particle filter’s operation also improves the estimation quality.

Particle number concentration (PN) in vehicle exhaust and ambient air describes the number of ultrafine particles (UFPs) below 500 nm, which are recognized as a toxic and carcinogenic component of pollution and are regulated in several countries. Metal nuclei, ash, and organic matter contribute significantly to the ultrafine particle size fraction and, thus, to the particle number concentration. Exhaust gas filtration is increasingly being used worldwide to significantly reduce this pollution, both on diesel particulate filter (DPF) and gasoline particulate filter (GPF) engines. In recent years, the EU has also funded research projects dealing with the possibilities of retrofitting gasoline vehicles with GPFs. This paper presents the results and compares the PN emissions of different vehicles. An original equipment manufacturer (OEM) diesel car with a DPF is considered as a benchmark. The PN emissions of this car are compared with a CNG car without filtration and with gasoline cars equipped with GPFs. It can be concluded that the currently used GPFs still have some potential to improve their filtration efficiency and that a modern CNG car would still have remarkable possibilities to reduce PN emissions with an improved quality GPF.

Bayesian methods for dynamic models in marketing have so far been parametric. For instance, it is invariably assumed that model errors emerge from normal distributions. Yet using arbitrary distributional assumptions can result in false inference, which in turn misleads managers. The author therefore presents a set of flexible Bayesian nonparametric (NP) dynamic models that treat error densities as unknown but assume that they emerge from Dirichlet process mixtures. Although the methods address misspecification in dynamic linear models, the main innovation is a particle filter algorithm for nonlinear state-space models. The author used two advertising studies to confirm the benefits of the methods when strict error assumptions are untenable. In both studies, NP models markedly outperformed benchmarks in terms of fit and forecast results. In the first study, the benchmarks understated the effects of competitive advertising on own brand awareness. In the second study, the benchmark inflated ad quality, and consequently, the effects of past advertising appeared 36% higher than that predicted by the NP model. In general, these methods should be valuable wherever state-space models appear (e.g., brand and advertising dynamics, diffusion of innovation, dynamic discrete choice).

The ensemble Kalman filter (EnKF) is a reliable data assimilation tool for high-dimensional meteorological problems. On the other hand, the EnKF can be interpreted as a particle filter, and particle filters (PF) collapse in high-dimensional problems. We explain that these seemingly contradictory statements offer insights about how PF function in certain high-dimensional problems, and in particular support recent efforts in meteorology to 'localize' particle filters, i.e. to restrict the influence of an observation to its neighbourhood.

Terrain-referenced navigation (TRN) uses topographic data to correct drift errors due to dead-reckoning or inertial navigation. While it has long been applied to aerial vehicle applications, TRN can be more useful for navigation in underwater environments where global positioning system signals are not available. TRN requires a geometric description of undulating terrain surface as a mathematical function or a look-up table, which leads to a nonlinear estimation problem. In this study, three nonlinear filter algorithms for underwater TRN are considered: 1) extended Kalman filter, 2) particle filter, and 3) Rao-Blackwellized particle filter. The performance of these three filters is compared through navigation simulations with actual bathymetry data.

The adaptive iterated particle filter (AIPF) is presented, where the importance density function is updated iteratively by the particle filter itself when necessary. By using a simulated annealing algorithm with an adaptive annealing parameter, the current measurement can be quickly incorporated into the sampling process, resulting in greatly improved sampling efficiency. Simulation results demonstrate the improved performance of the AIPF over the sampling importance resampling filter, unscented Kalman particle filter and auxiliary particle filter.

An essential type of Bayesian recursive filters known as the sequential Monte Carlo (alias, the particle filter) is used to estimate hidden Markov target states from noisy sensor data. Utilising sensor data and a collection of weighted particles, the filter makes an approximation of the posterior probability density of the target state. These particles are made to recursively propagate in time and are then updated using the incoming sensor information. The auxiliary particle filter improves over the traditional particle filter by guiding particles into regions of importance of the probability density using a lookahead scheme. This facilitates in the use of fewer particles and improved accuracy. However, when the sensor observations are extremely informative and the state transition noise is strong, the filter suffers badly. This is because the high state transition noise causes the particles that are determined to be important by the lookahead step could guide themselves to unimportant regions of the posterior in the final sampling process. Recent improvements of the auxiliary particle filter explored better weighting strategies but the said problem has not been explored closely. This paper seeks to solve the problem by adopting an auxiliary lookahead technique with two predictive support points to estimate the particles that will be located in regions of high importance after final sampling. The proposed method is successfully tested using a nonlinear model using simulations.

This research proposes an accurate vehicular positioning system which can achieve lane-level performance in urban canyons. Multiple passive sensors, which include Global Navigation Satellite System (GNSS) receivers, onboard cameras and inertial sensors, are integrated in the proposed system. As the main source for the localization, the GNSS technique suffers from Non-Line-Of-Sight (NLOS) propagation and multipath effects in urban canyons. This paper proposes to employ a novel GNSS positioning technique in the integration. The employed GNSS technique reduces the multipath and NLOS effects by using the 3D building map. In addition, the inertial sensor can describe the vehicle motion, but has a drift problem as time increases. This paper develops vision-based lane detection, which is firstly used for controlling the drift of the inertial sensor. Moreover, the lane keeping and changing behaviors are extracted from the lane detection function, and further reduce the lateral positioning error in the proposed localization system. We evaluate the integrated localization system in the challenging city urban scenario. The experiments demonstrate the proposed method has sub-meter accuracy with respect to mean positioning error.