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Sequential Bayesian filters in non-linear dynamic systems require the recursive estimation of the predictive and posterior distributions. This paper introduces a Bayesian filter called the adaptive kernel Kalman filter (AKKF). With this filter, the arbitrary predictive and posterior distributions of hidden states are approximated using the empirical kernel mean embeddings (KMEs) in reproducing kernel Hilbert spaces (RKHSs). In parallel with the KMEs, some particles, in the data space, are used to capture the properties of the dynamical system model. Specifically, particles are generated and updated in the data space, while the corresponding kernel weight mean vector and covariance matrix associated with the feature mappings of the particles are predicted and updated in the RKHSs based on the kernel Kalman rule (KKR). Simulation results are presented to confirm the improved performance of our approach with significantly reduced particle numbers, by comparing with the unscented Kalman filter (UKF), particle filter (PF) and Gaussian particle filter (GPF). For example, compared with the GPF, the proposed approach provides around 5% logarithmic mean square error (LMSE) tracking performance improvement in the bearing-only tracking (BOT) system when using 50 particles., Comment: The manuscript has been accepted for publication as a regular paper in the IEEE Transactions on Signal Processing

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.

Estimation models from connected vehicles often assume low level parameters such as arrival rates and market penetration rates as known or estimate them in real-time. At low market penetration rates, such parameter estimators produce large errors making estimated queue lengths inefficient for control or operations applications. In order to improve accuracy of low level parameter estimations, this study investigates the impact of connected vehicles information filtering on queue length estimation models. Filters are used as multilevel real-time estimators. Accuracy is tested against known arrival rate and market penetration rate scenarios using microsimulations. To understand the effectiveness for short-term or for dynamic processes, arrival rates, and market penetration rates are changed every 15 min. The results show that with Kalman and Particle filters, parameter estimators are able to find the true values within 15 min and meet and surpass the accuracy of known parameter scenarios especially for low market penetration rates. In addition, using last known estimated queue lengths when no connected vehicle is present performs better than inputting average estimated values. Moreover, the study shows that both filtering algorithms are suitable for real-time applications that require less than 0.1 second computational time.

The understanding of nonlinear, high dimensional flows, e.g, atmospheric and ocean flows, is critical to address the impacts of global climate change. Data Assimilation techniques combine physical models and observational data, often in a Bayesian framework, to predict the future state of the model and the uncertainty in this prediction. Inherent in these systems are noise (Gaussian and non-Gaussian), nonlinearity, and high dimensionality that pose challenges to making accurate predictions. To address these issues we investigate the use of both model and data dimension reduction based on techniques including Assimilation in Unstable Subspaces, Proper Orthogonal Decomposition, and Dynamic Mode Decomposition. Algorithms that take advantage of projected physical and data models may be combined with Data Analysis techniques such as Ensemble Kalman Filter and Particle Filter variants. The projected Data Assimilation techniques are developed for the optimal proposal particle filter and applied to the Lorenz'96 and Shallow Water Equations to test the efficacy of our techniques in high dimensional, nonlinear systems., 30 pages, 13 figures, 3 tables To appear in Computers & Mathematics with Applications, 2021,ISSN 0898-1221

New clustering methods are proposed to develop novel particle filters with Gaussian mixture models (PFGMM). In the PFGMM, the propagated samples are clustered to recover a Gaussian mixture model (GMM) using a clustering algorithm, which plays a fundamental role in the filter's performance. Two clustering methods are introduced that simultaneously minimize the covariance of each of the GMM components and maximize the likelihood function. Under the scenarios considered in this paper, it is shown through numerical simulation that the PFGMMs with the proposed clustering algorithms lead to better performance than the PFGMM employing the K-means or the expectation-maximization (EM) algorithms as well as the regularized particle filter (RPF) and the Gaussian sum particle filter (GSPF).

The introduction of data-driven inertial navigation provides new opportunities that the pedestrian dead reckoning could not well provide for constraining inertial system error drift on smartphones, and has been considered as another promising approach to meet the requirement of location-based services. However, indoor localization systems based on a single technology still have their limitations, such as the drift of inertial navigation and the received signal strength fluctuation of Bluetooth, making them unable to provide reliable positioning. To exploit the complementary strengths of each technology, this paper proposes a feasible fusion framework by utilizing a particle filter to integrate data-driven inertial navigation with localization based on Bluetooth Low Energy (BLE). For data-driven inertial navigation, under the premise of using the deep neural network with great potential in model-free generalization to regress pedestrian motion characteristics, we effectively combined the method of using gravity to stabilize inertial measurement units data to make the network more robust. Experimental results show that in the test of different smartphone usages, the proposed data-driven inertial navigation and BLE-based localization technology have good results in modeling user’s movement and positioning respectively. And due to this, the proposed fusion algorithm has almost unaffected by the usages of smartphones. Compared with BLE-based localization that achieved a good mean positional error (MPE) of 1.76m, for the four usages of texting, swinging, calling and pocket, the proposed fusion algorithm reduced the MPE by 32.35%, 20.51%, 20.74%, and 45.37%, respectively, and can further improve localization accuracy on the basis of existing fusion method.

Real-time high-precision navigation has many applications, such as pedestrian navigation, emergency rescue, and vehicle networks. In practice, the measurement models are often non-linear, and sequential Bayesian filters, such as Kalman and particle filter, suffer from accumulative errors, which cannot provide long-time high-precision services for localization. To solve arbitrary noise distribution, this paper proposes a Gaussian condensation filter algorithm to achieve high-precision localization in a non-Gaussian noise environment. To this end, we proposed an error-ellipse re-sampling-based Gaussian condensation filter (EER-GCF), which establishes error-ellipses with different confidence probabilities and implements a re-sampling algorithm based on the sampling points’ geometrical positions. Furthermore, a cooperative constrained Gaussian condensation filter (CEER-GCF) is proposed to enhance information fusion in the multi-target network. This study accomplishes cooperative tracking based on spatial-temporal constraints to enhance error correction. Experiment results show that CEER-GCF can effectively eliminate the accumulative error and optimize state estimation, which outperforms state-of-the-arts, such as unscented Kalman filter and particle filter.

This paper presents an improved approach based on the equivalent-weights particle filter (EWPF) that uses the proposal density to effectively improve the traditional particle filter. The proposed approach uses historical data to calculate statistical observations instead of the future observations used in the EWPF’s proposal density and draws on the localization scheme used in the localized PF (LPF) to construct the localized EWPF. The new approach is called the statistical observation localized EWPF (LEWPF-Sobs); it uses statistical observations that are better adapted to the requirements of real-time assimilation and the localization function is used to calculate weights to reduce the effect of missing observations on the weights. This approach not only retains the advantages of the EWPF, but also improves the assimilation quality when using sparse observations. Numerical experiments performed with the Lorenz 96 model show that the statistical observation EWPF is better than the EWPF and EAKF when the model uses standard distribution observations. Comparisons of the statistical observation localized EWPF and LPF reveal the advantages of the new method, with fewer particles giving better results. In particular, the new improved filter performs better than the traditional algorithms when the observation network contains densely spaced measurements associated with model state nonlinearities.

Particle filter is commonly used in various indoor positioning schemes, but sample impoverishment and weight degradation generally exist in particle filter. To solve this problem, this paper uses firefly algorithm to optimize particle filter. By using the global optimal value in the particle swarm to guide the remaining particles to update their positions, the particles tend to move to the high-likelihood area, which can more accurately describe the true state of the target observation. At the same time, in order to avoid particles falling into local optimum and oscillating repeatedly at the extreme point, the mathematical model of firefly algorithm is reconstructed in this paper, which is named as adaptive optimization firefly algorithm (AOFA). The experimental results show that the positioning scheme can provide the positioning accuracy with an average error of less than 0.5m. Compared with the traditional particle filter, the positioning accuracy is improved by 120%.

For nonlinear discrete-time systems where measurements can be randomly delayed by multiple sampling periods, measurements are dependent conditioned on the state trajectory, and the dependence becomes more complicated with the increase of step of random delay. A particle filtering for this system is developed, which is novel in that the likelihood is computed allowing multi step of delay and dependence of measurements. Multi step of delay is dealt with through utilizing the formula of total probability skillfully, and dependence is dealt with through estimating the filtering probability distribution of random delay. The novel particle filtering is applied to two examples to validate its effectiveness and superiority.

A standard way to move particles in a SMC sampler is to apply several steps of a MCMC (Markov chain Monte Carlo) kernel. Unfortunately, it is not clear how many steps need to be performed for optimal performance. In addition, the output of the intermediate steps are discarded and thus wasted somehow. We propose a new, waste-free SMC algorithm which uses the outputs of all these intermediate MCMC steps as particles. We establish that its output is consistent and asymptotically normal. We use the expression of the asymptotic variance to develop various insights on how to implement the algorithm in practice. We develop in particular a method to estimate, from a single run of the algorithm, the asymptotic variance of any particle estimate. We show empirically, through a range of numerical examples, that waste-free SMC tends to outperform standard SMC samplers, and especially so in situations where the mixing of the considered MCMC kernels decreases across iterations (as in tempering or rare event problems)., revised version

This paper is concerned with the problem of simultaneously tracking the direction-of-arrival (DOA) of far-field multiple moving sources/users in wireless communications using the vector-signal received by an antenna array of $N$ elements. The antenna array can be rigid (fixed array locations) or flexible (time-varying array locations), and it is used in conjunction with a “manifold extender”, a spatiotemporal state-space model and a Kalman-type tracking approach for non-stationary wireless channels. In particular, two tracking approaches are proposed. The first is based on an arrayed Extended Kalman Filter (arrayed-EKF) algorithm and the second on an arrayed Unscented Kalman Filter (arrayed-UKF) algorithm. Furthermore, if the array is rigid the spatiotemporal state-space model incorporates the DOAs and the angular velocities of the sources, while if it is flexible it also includes the array locations in the set of state-variables. The performance of the two approaches using both rigid and flexible arrays is evaluated using computer simulation studies and compared with a subspace tracking algorithm and a particle filter method under the same conditions. The results show that the arrayed-UKF and the arrayed-EKF show superior tracking performance, especially for low SNRs.

The position is one of the foremost imperative properties of an object. The Inertial Measurement Unit (IMU) development has enabled the system to continuously decrease in size, reduce power consumption, and become more and more universal. Although IMU meets the real-time needs of the localization system, it faces accumulative error and drifting problems. This paper presents an error constraint enhanced particle filter algorithm using quantum particle swarm optimization (EC-QPF), which achieves high-precision position estimation of target tracking with IMU. First, we proposed a quantum particle swarm optimization-based resampling method taking the place of the traditional weight-based resampling method in the particle filter, which avoids the particle impoverishment problem and keeps the particles’ diversity. The theoretical foundation of error constraint was raised applied to enhance the performance of the proposed particle filter. The error constraint is established utilizing the known estimated center and confidence scale to achieve particle screening based on the geometrical position of particles. Numerical experimental results show that the proposed EC-QPF has a 67% improvement instead of other modified particle filters and more efficiently eliminates the cumulative error. Furthermore, higher accuracy and stability are obtained under the exact condition, demonstrating better performance than traditional particle filter methods.

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.

A discrete quaternion filtering algorithm following high-density uncertainty matching-based deterministic sampling scheme is proposed for IMU attitude estimation. Existing quaternion filters rely on the specific distributions directly or the on-tangent-plane Gaussian distribution indirectly to model the underlying uncertainty. The key idea of this paper is to apply a Dirac mixture at few deterministic weighted samples for non-parametric interpreting the high-density uncertainty of unit quaternion manifold. In contrast to standard Monte Carlo techniques based on random sampling, the proposed approach is deterministic. Furthermore, the deterministic quaternion particles are obtained by projecting on-sphere uniform points to the unit quaternion manifold via an exponential map. The on-manifold quaternions are then exploited in a discrete Bayesian filtering procedure. We compare the new filter with the genetic algorithm embedded quaternion particle filter (GA-QPF) and the unscented quaternion estimator (USQUE) for accuracy and computation cost by using simulated and practical IMU data. The results illustrate that the proposed estimator possesses lower computational cost than the GA-QPF while providing a comparable accuracy, higher accuracy than the USQUE, as well as more effective against large initialization error.

Unslotted ALOHA protocol has been adopted as a channel access mechanism in commercial low-power wide-area networks (LPWANs), such as Sigfox and long-range (LoRa) alliance. This work examines the throughput and random access (RA) delay distribution of unslotted ALOHA systems by considering exponential random backoff (ERB) or uniform random backoff (URB) algorithm. We further characterize the operating region of the systems as unsaturated stable, bistable, and saturated regions in terms of the new packet arrival and retransmission rates. To run the system stably with the maximum throughput, we propose a Bayesian online backoff algorithm that estimates the number of backlogged devices. Its performance is compared with other algorithms, such as particle filter (PF)-based algorithm, binary exponential backoff (BEB) algorithm, and the algorithm of exploiting exact backlog size information. Through extensive simulations, it is demonstrated that the performance of the proposed algorithm is very close to the upper bound and robust to time-varying traffic condition.

The nonlinear filtering problem plays a fundamental role in multiple space-related applications. This paper offers a new filtering technique that combines Monte Carlo time propagation with a Gaussian mixture model measurement update. Differential algebra (DA) techniques are used as a tool to reduce the computational effort required by particle filters. Moreover, the use of expectation maximization (EM) optimization algorithm leads to a good approximation of the probability density functions. The performance of the new method is assessed in the nonlinear orbit determination problem, for the challenging case of low observations frequency, and in the restricted three-body dynamics.

This article addresses simultaneous localization and mapping (SLAM) via probability hypothesis density (PHD) filtering. The resulting approach, named PHD-SLAM, has demonstrated its effectiveness, especially when measurements provided by the sensors onboard the vehicle are highly contaminated by missdetections and clutter. However, since the proposal distribution (PD) of standard PHD-SLAM does not take into account most recently received measurements, a huge amount of particles are typically needed in order to achieve satisfactory performance. In this article, a new PD, which aims to approximate the vehicle pose posterior, is proposed for PHD-SLAM. The resulting algorithm, named PHD-SLAM 2.0, allows for drastically reducing the number of particles, and hence, the computational burden, while preserving the SLAM performance. The computational complexity of PHD-SLAM 2.0 is analyzed, and its performance is assessed via both simulated and real-data experiments.

Bathymetric simultaneous localization and mapping (SLAM) holds high potential for accurate navigation in long endurance autonomous underwater vehicle (AUV) missions. Due to nearly flat seabed topography, the occurrence of invalid loop closures is unavoidable in bathymetric SLAM. Thus, invalid loop closure identification is a crucial component of bathymetric SLAM, a procedure that normally requires a substantial amount of computational resources. An efficient bathymetric SLAM method considering invalid loop closures is proposed in this article, which identifies invalid loop closures via PF-Backend, a robust back end method based on particle filtering theory. Using this set-up, all beliefs of historical loop closures are estimated by a small number of particles and, for each particle, the corresponding map consistency calculated via a global graph optimizer is applied as the measurement update in the particle filter. A loop closure solidification procedure is also discussed to decrease the number of particles in the PF-Backend. The new algorithm is shown to be efficient and capable of providing accurate location and mapping results using play-back experiments.

Time series risk analysis in digitalized process operations offers a useful means to transform the unordered data information into actions and practices related to process safety. A method for easily implementing time series degradation state analysis is proposed and described in terms of the remaining useful life (RUL) counting process based on a digitization semi-empirical probabilistic model. The well logs are used to inform a case study describing underground gas storage (UGS) injection-production string degradation risk. The corrosive effect of carbon dioxide in a complex environment is also considered, which leads to the decrease of internal pressure strength (IPS) with wall thickness thinning as well as RUL. The relationship between the residual IPS and RUL of the injection-production string at different rates of wall-thinning is analyzed. Based on the Gamma process method, the key empirical parameter information with time series degradation process and the probability density functions of different degradation under corresponding conditions are obtained. Then based on the Sequential Monte Carlo algorithm, the degradation trajectory of time series with confidence belt is obtained, and the confidence interval quantization of the wall thinning rate of injection-production string under different working conditions is realized. The results show that a semi-empirical time series RUL analysis could be used to more realistically evaluate the degradation state of the injection-production string. The residual strength with the Klever-Stewart calculation model has high stability for the uncertainty characteristics of the stochastic process. The proposed model is expected to calculate and determine the RUL of string with different thinning rates of wall thickness, and then further determine the time series corrosion degradation state for risk early warning. It is thus concluded that the proposed digitization semi-empirical remaining useful life prediction model provides a highly intuitive and quantitative tool for assessing the risk of degradation at the RUL level in the injection-production string of UGS.

State estimation is one of the key requirements in robot control, which has been achieved by kinematic and dynamic models combined with motion sensors in traditional robotics. However, it is challenging to acquire accurate proprioceptive information in soft robots due to relatively high noise levels and hysteretic responses of soft actuators and sensors. In this article, we propose a method of estimating real-time states of soft robots by filtering noisy output signals and including hysteresis in the models using a Bayesian network. This approach is useful in constructing a state observer for soft robot control when both the kinematic model of the actuator and the model of the sensor are used. In our method, we regard a hysteresis function as a conditional random process model. We then introduce a dynamic Bayesian network composed of the actuator and the sensor models of the target system using distribution hysteresis mapping. Finally, we show that solving a Bayesian filtering problem is equivalent to suboptimal state estimation of the soft system. This article describes two ways for defining modeling and filtering; one is by Gaussian process regression combined with an extended Kalman filter, and the other is based on variational inference with a particle filter. While the first approach relaxes the uncertainty level in modeling to Gaussian, the second approach illustrates a general probability distribution. We experimentally validate the proposed methods through real-time state estimation of a sensor-integrated soft robotic gripper. The result shows significant improvement in state estimation compared to conventional estimation methods.

Filtering neural networks (FNNs) are popular computing frameworks for process system modeling. However, they are vulnerable to non-Gaussian noise and consequently may suffer from low filtering accuracy. To overcome the problem, in this paper, a novel model construction algorithm by combining the improved clustering kernel function smoothing technique and the particle filter neural network (ICKS-PFNN) is proposed. Specifically, ICKS-PFNN firstly presents a construction framework for particle filter neural network (PFNN), which utilizes the dynamic approximation of particles to adjust the NN’s weights and thresholds in real time. Then, the proposed model uses kernel fuzzy C-means algorithm to uncover clusters in the particles of PFNN. A novel proportional distribution sampling strategy is adopted to maintain the diversity in particle clusters, through merging the inferior and superior particles to generate new particles based on the set proportional factors, rather than directly eliminating particles. At last, the estimation of the PFNN model is achieved by utilizing a kernel function smoothing method to update the particles in each cluster. The proposed model has been tested on the real-world system for aluminium electrolysis manufacturing and compared with several closely related frameworks. The experimental results show ICKS-PFNN obtains a superb performance when compared with other baselines. ICKS-PFNN is able to tackle noise and improve the prediction accuracy when dealing with non-Gaussian systems. Successfully applying the proposed framework in aluminium electrolysis manufacturing broadens the practical impact of FNN systems.

This article presents a particle filter for pose estimation using unit dual quaternion kinematics. The eight-parameter unit dual quaternion is used for global representation of the pose, whereas the six parameters of the dual modified Rodrigues parameters (MRPs) are used for local pose representation in the state-space model. The dual MRPs enable estimates of the mean and the covariance to be calculated from the particles without violating the algebraic constraint of the unit dual quaternion. For verification of the filter and comparison with state of the art, we consider pose measurements available in the form of unit dual quaternions. Angular velocity and specific force measurements from a body-mounted inertial measurement unit are also considered in the filtering. We show through simulations that the suggested particle filter has comparable accuracy with a previously proposed unscented Kalman filter based on unit dual quaternions. We also consider a practical application where the pose of an arbitrary rigid object is estimated using a sequence of point clouds from a 3-D camera. A model point cloud of the object is displaced with the unit dual quaternion associated with each particle, and a fitting score is calculated between the displaced model point cloud and the measured point cloud from the 3-D camera. The likelihoods of the fitting scores are calculated from an exponential distribution and are used to update the weights of the particles. The system was verified in an experiment where the motion of a swinging payload hanging from a crane was estimated using a 3-D camera.

This article regards the dependency structure of wind power and load time series at each moment as the conditional probability of a high-dimensional discrete stochastic process. A dynamic Bayesian network (DBN) model is proposed to calculate the joint probability distribution of high-dimensional stochastic processes, which can completely describe the potential dependency structure of wind power and load at each time. The DBN model is based on a data-driven approach, using Bayesian information criteria (BICs) as the scoring function, and using a greedy search algorithm to determine the initial network and transmission network DBN structure. Maximum likelihood estimation (MLE) is used to estimate the parameters of the initial network and the transmission network. The DBN model is established from these two networks, and the joint probability distribution of the stochastic process is obtained. Sequential Monte Carlo (SMC) sampling is performed on the DBN model to generate the dependent simulation sequence of wind power and load. Using probability density, mean value, maximum output fluctuation, and autocorrelation and cross-correlation functions as evaluation indicators, the statistical characteristics of the historical sequence, simulation sequence based on the DBN model, and simulation sequence based on the hidden Markov model (HMM) are comprehensively compared and analyzed to verify the effectiveness of the DBN model.

Rapid search and localization for nuclear sources can be an important aspect in preventing human harm from illicit material in dirty bombs or from contamination. In the case of a single mobile radiation detector, there are numerous challenges to overcome such as weak source intensity, multiple sources, background radiation, and the presence of obstructions, i.e., a non-convex environment. In this work, we investigate the sequential decision making capability of deep reinforcement learning in the nuclear source search context. A novel neural network architecture (RAD-A2C) based on the advantage actor critic (A2C) framework and a particle filter gated recurrent unit for localization is proposed. Performance is studied in a randomized 20×20 m convex and non-convex simulation environment across a range of signal-to-noise ratio (SNR)s for a single detector and single source. RAD-A2C performance is compared to both an information-driven controller that uses a bootstrap particle filter and to a gradient search (GS) algorithm. We find that the RAD-A2C has comparable performance to the information-driven controller across SNR in a convex environment. The RAD-A2C far outperforms the GS algorithm in the non-convex environment with greater than 95% median completion rate for up to seven obstructions.

Approximate Bayesian Computation ( abc ) is a statistical learning technique to calibrate and select models by comparing observed data to simulated data. This technique bypasses the use of the likelihood and requires only the ability to generate synthetic data from the models of interest. We apply abc to fit and compare insurance loss models using aggregated data. A state-of-the-art abc implementation in Python is proposed. It uses sequential Monte Carlo to sample from the posterior distribution and the Wasserstein distance to compare the observed and synthetic data.

This work revisits particle filtering RFID localization methods, solely based on phase measurements. The reader is installed on a low-cost robotic platform, which performs autonomously (and independently from the RFID reader) open source simultaneous localization and mapping (SLAM). In contrast to prior art, the proposed methods introduce a weight metric for each particle-measurement pair, based on geometry arguments, robust to phase measurement noise (e.g., due to multipath). In addition, the methods include the unknown constant phase offset as a parameter to be estimated. No reference tags are employed, no assumption on the tags’ topology is assumed and special attention is paid for reduced execution time. It is found that the proposed phase-based localization methods offer robust performance in the presence of multipath, even when the tag phase measurements are variable in number and sporadic. The methods can easily accommodate a variable number of reader antennas. Mean absolute 3D localization error in the order of 24 cm for RFID tags in a library was shown, even though the system did not exploit excessive bandwidth or any reference tags. As a collateral dividend, the proposed methods also offer a concrete way to classify the environment as multipath-rich or not.

Secure power system operation relies on accurate steady-state and dynamic system models. It is thus crucial to carefully validate the models in power systems, in particular the generator models. The phasor measurement unit (PMU) technologies provide a low-cost option for generator model validation and parameter calibration without interfering with their operation. In this paper, an empirical parameter sensitivity Gramian based approach is developed to identify the critical parameters from a nonlinear system perspective. We further propose a synchrophasor measurement based generator parameter calibration method by adaptive Approximate Bayesian Computation with a sequential Monte Carlo sampler (A-ABC-SMC) that avoids directly dealing with likelihood functions. We propose adaptive threshold sequence scheme and perturbation kernel function in A-ABC-SMC in order to improve the computational efficiency. The effectiveness of the proposed method is validated for a hydro generator against multiple system events. The simulation results show that the proposed approach can accurately and efficiently estimate the full probabilistic posterior distributions of the generator parameters even when there are gross errors in the parameters’ prior distributions.

Network protocols are applied to reduce the amount of data which are transmitted simultaneously over the network. In this article, round-robin protocol (RRP) and try-once-discard protocol (TODP) are studied for state estimation over network where information of different sensor nodes are fused. Using these protocols, at each time sample, only one sensor node can send its information over the network and consequently the required bandwidth is significantly reduced. Particle filters (PF) are able to estimate states of generally any nonlinear and non-Gaussian systems. Therefore, in this article, the development of particle filtering in networked systems under RRP and TODP protocols is studied. Toward this goal, two sequential importance sampling resampling algorithms under RRP and TODP are proposed where their corresponding marginal posterior pdfs are approximated by sequentially computations of weights. For the case of RRP, likelihoods of previous measurements are included in the weight computations while for TODP case, only the latest likelihood appears. Moreover, the approximated marginal posterior pdfs under RRP and TODP are compared with the normal posterior pdf using Kullback–Leibler divergence measure. This measure computes the difference between two probability distributions. Finally, the efficiency of the proposed method is demonstrated for a networked interconnected four-tank system.

In this work, an efficient direction of arrival (DOA) tracking method for coherently distributed sources is proposed. The central DOA and angle spread are estimated by the proposed method with a particle filter at each snapshot. The spectrum calculated by the distributed source parameter estimator (DSPE) is used as a pseudo-likelihood function for particle updating, which enables the particle filter to process sensor signals directly without estimating the source amplitude. The proposed method is compared with the total least square estimating signal parameter via rotational invariance technique and the fast implementation of a power iteration subspace updating (FAPI-TLS-ESPRIT). The proposed method is verified by Monte Carlo simulations, and simulation results show that the proposed method can achieve an excellent DOA tracking performance and outperforms the FAPI-TLS-ESPRIT method. In addition, the proposed method can simultaneously estimate the central DOA and angle spread.

This paper deals with fault detection and diagnosis scheme for stochastic non-linear systems using particle filter. To address the problem of fault detection of helicopters in the presence of senso...

Multi-modal likelihood function of Present-Value model makes traditional estimation approach sensitive to initial values. In this article, we apply Sequential Monte Carlo (SMC) approach in the esti...

To solve the problem of the direction of arrival (DOA) maneuvering in acoustic vector sensor (AVS) array, we propose an interactive multi-model Multi-target Multi-Bernoulli (IMM-MeMBer) two-dimensional (2-D) DOA tracking algorithm. The idea of the IMM algorithm is employed to interactively estimate the predicted sampled particles at the expense of calculating the likelihood function of the predicted particles by pseudo-spectrum of multi-signal classification (MUSIC). The proposed method fully considers various possibilities of target motion, which makes the target state estimation more effective. Moreover, the de-noising and exponential weighting of MUSIC pseudo-spectrum improve the likelihood function of particles, thus enhancing the weight of particles in high likelihood region and making these particles more effective in the subsequent resampling process. Simulation results show that the IMM-MeMBer algorithm has better performance than projection approximation subspace tracking of deflation MUSIC (PASTD-MUSIC), MeMBer, particle filter (PF), and random finite set PF (RFS-PF) in the DOA tracking of maneuvering sources.

This article proposes a novel sparse kernel ridge regression assisted particle filter (SKRR-PF) based remaining useful life (RUL) estimation method to address the reliability of the cascode gallium nitride field-effect transistors in emerging power electronics systems. The proposed method will overcome three main challenges in this area: first, a large variation in the RUL estimation under the severe noise uncertainty; second, sample degeneracy and sample impoverishment; and third, the low capability of tracing the dynamic and abrupt change in the fault precursor trajectory. The state-of-the-art RUL estimation methods require a significant number of samples to address such issues, including particle degeneracy and sample impoverishment. Also, the state-of-the-art methods mostly fail to apply under a system's dynamic condition changes over a switch's lifetime. The proposed method will significantly enhance the estimation accuracy by introducing SKRR in resampling the posterior probability density function estimation, especially under the dynamically varying system's health condition due to the harsh industrial operation. Thus, the proposed method will offer fast tracing the sudden change in the RDS, ON trajectory, leading to a significant accurate RUL estimation. The performance of the proposed method has been rigorously validated through the purposely designed power cycling testbed.

Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning' algorithms have been developed to estimate the scaled cumulant generating function, based on importance sampling via cloning of rare event trajectories. So far, attempts to study the convergence properties of these algorithms in continuous time have only led to partial results for particular cases. Adapting previous results from the literature of particle filters and sequential Monte Carlo methods, we establish a first comprehensive and fully rigorous approach to bound systematic and random errors of cloning algorithms in continuous time. To this end we develop a method to compare different algorithms for particular classes of observables, based on the martingale characterization of stochastic processes. Our results apply to a large class of jump processes on compact state space, and do not involve any time discretization in contrast to previous approaches. This provides a robust and rigorous framework that can also be used to evaluate and improve the efficiency of algorithms., 42 pages

For lithium-ion batteries used in the electric vehicles, accurate prediction of capacity and remaining useful life online is extremely important. However, most of the research works focus on the prediction accuracy but neglect the complexity of the test environment, which makes many methods show poor robustness in application. To solve the problem, in this article, we first introduce the simultaneous input and state estimation algorithm into the online prediction of state-of-charge and capacity, and combine the Gauss–Hermite extended particle filter to predict the remaining useful life. By setting different gradients of state noises in experiments, the proposed algorithm demonstrates the best accuracy and robustness in comparison with other algorithms. Through the two-factor authentication in simulations, the maximum error of capacity estimation is 35 mAh. For the prediction of remaining useful life, the minimum relative error of the proposed method is 0.4%. Therefore, the high accuracy and strong robustness of the proposed algorithm are verified.

Infrared target tracking plays an important role in both civil and military fields. The main challenges in designing a robust and high-precision tracker for infrared sequences include overlap, occlusion, and appearance change. To this end, this paper proposes an infrared target tracker based on the proximal robust principal component analysis method. Firstly, the observation matrix is decomposed into a sparse occlusion matrix and a low-rank target matrix, and the constraint optimization is carried out with an approaching proximal norm which is better than l1-norm. Then, the Alternating Direction Method of Multipliers (ADMM) is employed to solve this convex optimization problem by estimating the variables alternately. Finally, the framework of particle filter with model update strategy is exploited to locate the target. Through a series of experiments on real infrared target sequences, the effectiveness and robustness of our algorithm are proved.

Gravity-matching algorithm is a key to the gravity-aided inertial navigation system (INS). The traditional particle filter-based matching algorithm with a gravity sample vector is efficient. However, the range of particle filter and the probability model of the actual location are not specified in the algorithm. An improved particle filter-based matching algorithm with a gravity sample vector is proposed. Because of the high short-term accuracy of INS, the error range of INS in a short period is analyzed in a polar coordinate system in this algorithm. First, the attitude error angle model of INS is established. Relative angle error is proposed to calculate latitudes and longitudes of particles in the fan area at any position. Then a particle filter embedded in a particle filter is proposed to calculate the error range of the real position and establish the probability model of this position. Finally, in order to reduce the matching error, the relative displacements of the positions of the particles and the upper matching positions are added to the weights of the particles. Simulation results show that the proposed method has higher accuracy and better robustness.

A clustering similarity particle filter based on state trajectory consistency is presented for the mathematical modeling, performance estimation, and smart sensing of nonlinear systems. Starting from an information fusion model based on the consistency principle of the spatial state trajectory, the predicted observation information of the current particle filter (original trajectory) and future multistage Gaussian particle filter (modified trajectory) are selected as the state trajectories of the sampling particles. Clustering similarity methods are used to measure the state trajectories of the sampling particles and the actual system (reference trajectory). The importance weight of a first-order Markov model is updated with the measurement results. By integrating the targeted compensation scheme of the latest measurement information into the sequential importance sampling process, the adverse effects of the particle degradation phenomenon are effectively reduced. The convergence theorems of the improved particle filter are proposed and proved. The improved filter is applied to practical cases of nonlinear process estimation, economic statistical prediction, and battery health assessment, and the simulation results show that the improved particle filter is superior to traditional filters in estimation accuracy, efficiency, and robustness.

This work proposes an Eigen-based type-2 fuzzy algorithm for analysis of power signal disturbances. The power quality disturbances are random and non-linear by nature so the role of a particle filter is to estimate various parameters such as amplitude and phase. Particle filtering is now the most popular for tracking and signal processing. It has gained popularity in the signal processing by virtue of its ability to deal with non-linear and non-Gaussian systems.Our approach is to define an orthogonal matrix, for multiple power quality events then to evaluate Eigen values of estimated parameters. These Eigen values play an important role in detection of power quality events the estimated parameters and Eigen values applied as input to type-2 fuzzy for classification of power quality events. Finally robustness of algorithm in terms of improved accuracy and correctness with actual industrial data set of power quality events is compared under three different SNR conditions of 30, 20 and 10 dB with support vector machine, neural network based techniques and type-1 fuzzy logic based classification methods. High accuracy and less computation time make this algorithm robust and a suitable choice for non-linear and non-stationary power quality events analysis.

Trajectory data collected from probe vehicles become increasingly important for urban traffic operation and management. However, current data tend to be sparse in time and space due to technical constraints or privacy concerns, which fail to provide a complete picture of traffic flow. This study proposes a particle filter (PF) based approach to reconstruct the vehicle trajectory for signalized arterial using sparse probe data. First, the arterial intersection is divided into multiple road cells and the estimation of cell travel time is formulated as a quadratic programming problem. Then, PF is applied to reconstruct the incomplete vehicle trajectory between consecutive updates. Specifically, to calculate and update the weight of initial particles, three measurability criteria are designed for importance sampling considering the structure of signalized arterial and the feature of vehicular updates, i.e., travel time adjustment accuracy, arterial link speed limit and travel time adjustment possibility. Last, NGSIM trajectory data are extracted at intervals to construct the sparse data, which are used to verify the effectiveness of the proposed method. The results show that reconstructed trajectories match closely with ground truth both at the single intersection and along the arterial with multiple intersections.

Parallel/Distributed particle filters have been widely used in the estimation of states of dynamic systems by using multiple processing units (PUs). In parallel/distributed particle filters, the centralized resampling needs a central unit (CU) to serve as a hub to execute the global resampling. The centralized scheme is the main obstacle for the improved performance due to its global nature. To reduce the communication cost, the decentralized resampling was proposed, which only conducted the resampling on each PU. Although the decentralized resampling can improve the performance, it suffers from the low accuracy due to the local nature. Therefore, we propose a novel hybrid resampling algorithm to dynamically adjust the intervals between the centralized resampling steps and the decentralized resampling steps based on the measured system convergence. We formulate the proposed algorithm and prove it to be uniformly convergent. Since the proposed algorithm is a generalization of various versions of the hybrid resampling, its proof provides the solid theoretical foundation for their wide adoptions in parallel/distributed particle filters. In the experiments, we evaluate and compare different resampling algorithms including the centralized resampling algorithm, the decentralized resampling algorithm, and different types of existing hybrid resampling algorithms to show the effectiveness and the improved performance of the proposed hybrid resampling algorithm.

Bayesian model selection enables comparison and ranking of conceptual subsurface models described by spatial prior models, according to the support provided by available geophysical data. Deep generative neural networks can efficiently encode such complex spatial priors, thereby, allowing for a strong model dimensionality reduction that comes at the price of enhanced non-linearity. In this setting, we explore a recent adaptive sequential Monte Carlo (ASMC) approach that builds on Annealed Importance Sampling (AIS); a method that provides both the posterior probability density function (PDF) and the evidence (a central quantity for Bayesian model selection) through a particle approximation. Both techniques are well suited to parallel computation and rely on importance sampling over a sequence of intermediate distributions, linking the prior and the posterior PDF. Each subsequent distribution is approximated by updating the particle weights and states, compared with the previous approximation, using a small pre-defined number of Markov chain Monte Carlo (MCMC) proposal steps. Compared with AIS, the ASMC method adaptively tunes the tempering between neighboring distributions and performs resampling of particles when the variance of the particle weights becomes too large. We evaluate ASMC using two different conceptual models and associated synthetic cross-hole ground penetrating radar (GPR) tomography data. For the most challenging test case, we find that the ASMC method is faster and more reliable in locating the posterior PDF than state-of-the-art adaptive MCMC. The evidence estimates are found to be robust with respect to the choice of ASMC algorithmic variables and much less sensitive to the model proposal type than MCMC.[...], Comment: Geophysical Journal International (2021)

Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior distributions. For this purpose, Monte Carlo (MC) methods, such as Markov Chain Monte Carlo and importance sampling algorithms, are often employed. In this work, we introduce the theory and practice of a Compressed MC (C-MC) scheme to compress the statistical information contained in a set of random samples. In its basic version, C-MC is strictly related to the stratification technique, a well-known method used for variance reduction purposes. Deterministic C-MC schemes are also presented, which provide very good performance. The compression problem is strictly related to the moment matching approach applied in different filtering techniques, usually called as Gaussian quadrature rules or sigma-point methods. C-MC can be employed in a distributed Bayesian inference framework when cheap and fast communications with a central processor are required. Furthermore, C-MC is useful within particle filtering and adaptive IS algorithms, as shown by three novel schemes introduced in this work. Six numerical results confirm the benefits of the introduced schemes, outperforming the corresponding benchmark methods. A related code is also provided. (The code is provided at http://www.lucamartino.altervista.org/CMC_CODE_pub_EX1.zip )

Bearings-only filtering (BOF) is important in many practical applications. It is also a challenging nonlinear filtering problem due to limited information contained in highly nonlinear measurements. Researchers have proposed various nonlinear filters for BOF problems. We propose a new approach to nonlinear filtering using pseudomeasurement construction based uncorrelated conversion for BOF. This approach can more effectively utilize the measurement information than the original linear minimum mean square error estimator. The constructed pseudomeasurement is uncorrelated with the original measurement. Based on the recently proposed uncorrelated conversion based filter (UCF), we propose a UCF using pseudorange construction (UCF-PRC) for the BOF problem. An improved filter, the optimized UCF-PRC, is also proposed to minimize the mean square error. The effectiveness of the new filters is demonstrated by simulation results. Specifically, compared with the particle filter, the UCF-PRC has better estimation accuracy with nearly the same computational cost.

We present a novel dual quaternion filter for recursive estimation of rigid body motions. Based on the sequential Monte Carlo scheme, particles are deployed on the manifold of unit dual quaternions. This allows non-parametric modeling of arbitrary distributions underlying on the SE(3) group. The proposal distribution for importance sampling is estimated particle-wise by a novel dual quaternion unscented Kalman filter (DQ-UKF). It is adapted to the manifold geometric structure and drives the prior particles towards high-likelihood regions on the manifold. The resultant unscented dual quaternion particle filter (U-DQPF) incorporates the most recently observed evidence, raising the particle efficiency considerably for nonlinear pose estimation tasks. Compared with ordinary particle filters and other parametric model-based dual quaternion filtering schemes, the proposed U-DQPF shows superior performance in nonlinear SE(3) estimation.

This paper develops Rao-Blackwellized particle filter with asynchronous dependence between system noise and measurement noise. It is pointed out that this dependence affects both the particle filter update step for the nonlinear sub-system and the Kalman filter update step for the conditionally linear sub-system in Rao-Blackwellized particle filter. A de-correlation method is suggested to deal with such influence. The optimal importance density function for sampling the nonlinear sub-state is found out, and a suboptimal one for approximating the optimal importance density function is proposed. The proposed methods are applied to target tracking to testify their effectiveness and superiority.