A particle filter-based framework for real-time state estimation of a non-linear hyperbolic PDE system describing transient flows in CO2 pipelines

In this study, we combined the Maximum Likelihood Estimator from our previous works with a Sequential Importance Resampling (SIR) particle filter to estimate the states of the stochastic Gompertz tumor growth model. We also implemented a parallel version in CUDA for the SIR filter in order to reduce its execution time. Extensive simulations with synthetic data were run to examine whether the SIR filter can provide more accurate state estimates in respect to the Normalized Mean Squared Deviation criterion compared to those provided by the deterministic Gompertz model. Moreover, we monitored and compared the execution time of the SIR's parallel and sequential implementations for different numbers of particles. The results showed that the SIR filter can estimate the system's states very accurately, even at the early tumor growth stages. Additionally, the parallel implementation that ran on the GPU was way more efficient than the implementation that ran on the CPU. By combining the Maximum Likelihood Estimator (MLE) with an SIR filter, we were able to obtain very accurate estimates of the tumors' volume. Furthermore, the execution time for the SIR filter was significantly decreased by taking advantage of the GPUs ability to perform a very large number of computations in parallel.

The remaining useful life (RUL) estimation is an important metric that helps in condition-based maintenance. Damage data obtained from the diagnostics techniques are often noisy, and the RUL estimated from the data is less reliable. Estimating the probabilistic RUL by quantifying the uncertainty in the predictive model parameters using the noisy data increases confidence in the predicted values. In this work, Bayesian inference is used to inversely quantify the uncertainty in the model parameters of the predictive damage model in adhesively bonded joints, and quantified parameter uncertainty is represented by a probability distribution function (PDF). It is difficult to obtain a closed-form solution for the RUL from the PDF of model parameters due to the nonlinearity of the damage models. Instead, statistical simulations are used to generate the model parameter samples from the PDF, and the RUL is estimated from the samples. In the statistical simulations, the predictive damage model is evaluated for each parameter sample. Using a physics-based model as the predictive model increases computational time, which makes the statistical techniques to be computationally expensive. It is essential to reduce the computational time to estimate the RUL in a feasible time. In this work, real-time probabilistic RUL estimation is demonstrated in adhesively bonded joints using the Sequential Monte Carlo (SMC) sampling method and cloud-based computations. The SMC sampling method is an alternative to traditional Markov Chain Monte Carlo (MCMC) methods, which enables generating statistical parameter samples in parallel. The parallel computational capabilities of the SMC methods are exploited by running the SMC simulation on multiple cloud calls. This approach is demonstrated by estimating fatigue RUL in the adhesively bonded joint. The accuracy of probabilistic RUL estimated by SMC is validated by comparing it with RUL estimated by the MCMC and the experimental values. The SMC simulation is run on the cloud and the computational speedup of the SMC is demonstrated.

We consider the application of the sequential Monte Carlo (SMC) methodology to the problem of blind symbol detection in a wireless orthogonal frequency-division multiplexing (OFDM) system over a frequency-selective fading channel. Bayesian inference of the unknown data symbols in the presence of an unknown multipath fading channel is made only from the observations over one OFDM symbol duration. A novel blind SMC detector built on the techniques of importance sampling and resampling is developed for differentially encoded OFDM systems. The performance of different schemes of delayed-weight estimation methods is studied. Furthermore, being soft-input and soft-output in nature, the proposed SMC detector is employed as the first-stage demodulator in a turbo receiver for a coded OFDM system. Such a turbo receiver successively improves the receiver performance by iteratively exchanging the so-called extrinsic information with the maximum a posteriori (MAP) outer channel decoder. Finally, the performance of the proposed sequential Monte Carlo receiver is demonstrated through computer simulations.

We consider the application of the sequential Monte Carlo (SMC) methodology to the problem of blind symbol detection in a wireless orthogonal frequency-division multiplexing (OFDM) system over a frequency-selective fading channel. A novel blind SMC detector, built on the techniques of importance sampling and resampling, is developed for differentially encoded OFDM systems. The performance of different schemes of delayed-weight estimation methods is studied.

In this paper, the problem of direction of arrival (DOA) tracking based on the co-prime array is studied. Owing to low signal-to-noise ratio (SNR) in underwater environment, making estimating DOA of a moving source become a challenging problem. In this work, a framework of particle filter (PF) with sequential importance resampling (SIR) is developed to address this problem. The involved particles are generated from the uniform motion model, and then weighted by their measurement likelihood function. By vectorizing the autocorrelation matrix of the output data from the co-prime array, a virtual uniform linear array with extended array aperture can be obtained. Applying spatial smoothing technique to the au-correlation matrix of the virtual uniform linear array, the MUSIC pseudo-spectrum can be formulated and then used as the likelihood function. Due to the enlarged array aperture and the super resolution property of MUSIC, the involved particles can be updated more appropriately. Simulation studies are presented to verify the validity of the proposed method.

Feedback particle filter (FPF) is a numerical algorithm to approximate the solution of the nonlinear filtering problem in continuous-time settings. In any numerical implementation of the FPF algorithm, the main challenge is to numerically approximate the so-called gain function. A numerical algorithm for gain function approximation is the subject of this paper. The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian $\Delta_\rho$. The numerical problem is to approximate this solution using only finitely many particles sampled from the probability distribution $\rho$. A diffusion map-based algorithm was proposed by the authors in prior works [A. Taghvaei and P. G. Mehta, Gain function approximation in the feedback particle filter, in 2016 IEEE 55th Conference on Decision and Control (CDC), IEEE, 2016, pp. 5446--5452], [A. Taghvaei, P. G. Mehta, and S. P. Meyn, Error estimates for the kernel gain function approximation in the feedback particle filter, in American Control Conference (ACC), IEEE, 2017, pp. 4576--4582] to solve this problem. The algorithm is named as such because it involves, as an intermediate step, a diffusion map approximation of the exact semigroup $e^{\Delta_\rho}$. The original contribution of this paper is to carry out a rigorous error analysis of the diffusion map-based algorithm. The error is shown to include two components: bias and variance. The bias results from the diffusion map approximation of the exact semigroup. The variance arises because of finite sample size. Scalings and upper bounds are derived for bias and variance. These bounds are then illustrated with numerical experiments that serve to emphasize the effects of problem dimension and sample size. The proposed algorithm is applied to two filtering examples and comparisons provided with the sequential importance resampling (SIR) particle filter.

This paper describes two Doppler only indoor passive Wi-Fi tracking methods based on high Doppler resolution passive radar. Two filters are investigated in this paper, the extended Kalman filter and the sequential importance resampling (SIR) particle filter. Experimental results for these two tracking filters are presented using results from software defined passive Wi-Fi radar using a standard 802.11 access point as an illuminator. The experimental results show that the SIR particle filter performs well using Wi-Fi signals for indoor tracking with a high degree of accuracy. Proposals for simplifying the SIR particle and application to multiple target tracking are also discussed.

Bayesian statistical data assimilation for ecosystem models using Markov Chain Monte Carlo

Accurate state estimation is essential for autonomous driving in global navigation satellite system (GNSS)-denied environments. Particle filters, particularly sequential importance resampling (SIR), are widely used for sensor fusion but suffer from weight degeneracy and particle impoverishment during resampling. To address this, we propose Particle Transformer, a deep learning-based resampling framework combining weighted multi-head attention for particle importance modeling and a variational autoencoder (VAE) for diversity preservation. An adaptive strategy based on effective sample size (ESS) further balances accuracy and efficiency. Experiments on the KITTI odometry dataset show 3.0 % lower absolute trajectory error (ATE) and 21.2 % lower relative pose error (RPE) compared to systematic resampling, while maintaining maximum diversity with only 6.4 ms per frame.

Adaptive resampling-based particle filtering for tool life prediction

Particle filtering with adaptive resampling scheme for modal frequency identification and dispersion curves estimation in ocean acoustics

This paper analyzes and compares two error correction algorithms in context of traffic control applications. They are the Sequential Importance Sampling (SIS) and the Sequential Importance Resampling (SIR). Performances of both algorithms are analyzed and conclusions are drawn. Moreover, experimental results prove that algorithms' parameters have a great impact on their performances.

In this paper, we present an easy-hardware-implementation multiple model particle filter (MMPF) for maneuvering target tracking. In the proposed filter, the sampling importance resampling (SIR) filter typically used for nonlinear and/or non-Gaussian application is extended to incorporating multiple models that are composed of a constant velocity (CV) model and a "current" statistical (CS) model, and the Independent Metropolis Hasting (IMH) sampler is utilized for the resampling unit in each model. Compared with the bootstrap MMPF, the proposed MMPF requires no knowledge of models and model transition probabilities for different maneuvering motions, and keeps a constant number of particles per model at all times. This allows a regular pipelined hardware structure and can be implemented in hardware easily. Furthermore, using the IMH sampler for the resampling unit avoids the bottleneck introduced by the traditional systematic resampler and reduces the latency of the whole implementation. Simulation results indicate that the proposed filter has approximately equal tracking performance with the bootstrap MMPF. Hardware architecture of the IMH sampler and its corresponding sample unit are presented, and a parallel architecture consisting of CV model processing element (PE), CS model PE and a central unit (CU) is described. The proposed architecture is evaluated on a Xilinx Virtex-II Pro FPGA platform for a maneuvering target tracking application and the results show many advantages of the proposed MMPF over existing approaches in terms of efficiency, lower latency, and easy hardware implementation.

A note on auxiliary particle filters

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