A note on auxiliary particle filters

We propose a novel blocked version of the continuous-time bouncy particle sampler of Bouchard-Côté et al. (J Am Stat Assoc 113(522):855–867, 2018) which is applicable to any differentiable probability density. This alternative implementation is motivated by blocked Gibbs sampling for state-space models (Singh et al. in Biometrika 104(4):953–969, 2017) and leads to significant improvement in terms of effective sample size per second, and furthermore, allows for significant parallelization of the resulting algorithm. The new algorithms are particularly efficient for latent state inference in high-dimensional state-space models, where blocking in both space and time is necessary to avoid degeneracy of MCMC. The efficiency of our blocked bouncy particle sampler, in comparison with both the standard implementation of the bouncy particle sampler and the particle Gibbs algorithm of Andrieu et al. (J R Stat Soc Ser B Stat Methodol 72(3):269–342, 2010), is illustrated numerically for both simulated data and a challenging real-world financial dataset.

Nonlinear state-space models are ubiquitous in modeling real-world dynamical systems. Sequential Monte Carlo (SMC) techniques, also known as particle methods, are a well-known class of parameter estimation methods for this general class of state-space models. Existing SMC-based techniques rely on excessive sampling of the parameter space, which makes their computation intractable for large systems or tall data sets. Bayesian optimization techniques have been used for fast inference in state-space models with intractable likelihoods. These techniques aim to find the maximum of the likelihood function by sequential sampling of the parameter space through a single SMC approximator. Various SMC approximators with different fidelities and computational costs are often available for sample-based likelihood approximation. In this paper, we propose a multi-fidelity Bayesian optimization algorithm for the inference of general nonlinear state-space models (MFBO-SSM), which enables simultaneous sequential selection of parameters and approximators. The accuracy and speed of the algorithm are demonstrated by numerical experiments using synthetic gene expression data from a gene regulatory network model and real data from the VIX stock price index.

Electronic interference poses a significant challenge to Unmanned Aerial Vehicle (UAV) tracking systems, compromising navigation accuracy and operational safety in critical applications such as surveillance, disaster response, and infrastructure inspection. This study introduces a novel application of the Auxiliary Particle Filter (APF) for robust UAV tracking under interference conditions, focusing on fixed-reference scenarios. The APF incorporates adaptive proposal distributions and robust weight updates to effectively mitigate interference-induced measurement errors. Through comprehensive simulation that evaluates performance under varying interference and sensor degradation scenarios, the APF demonstrates superior accuracy, achieving a mean Root Mean Square Error (RMSE) of 4.82 meters with low variability (m). This significantly outperforms traditional filters, including the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). Notably, the APF maintains stable performance even under severe interference conditions, where conventional approaches exhibit substantial degradation. Statistical validation confirms these improvements across all test scenarios (p < 0.001). The detailed implementation guidelines provided in this study enable adoption across diverse operational contexts. These findings establish the APF as a robust and reliable solution for interference-prone environments and lay the groundwork for its adaptation to more dynamic tracking scenarios in autonomous UAV operations.

This paper proposes a novel particle filter, namely, the auxiliary iterated extended Kalman particle filter (AIEKPF). To generate the importance density, based on the auxiliary particle filtering (APF) technique the proposed filter uses the iterated extended Kalman filter (IEKF) to integrate the latest measurements into state transition density. This new filter can match the posterior density well, because of the robustness of the APF and the importance density generated by the IEKF. The performance of the presented particle filter is evaluated by two different estimation problems with the noise of Gaussian distribution and Gamma distribution, respectively. The experimental results illustrate that the AIEKPF is superior to the extended Kalman filter and some existing particle filters, such as the standard particle filter (PF), the extended Kalman particle filter, the unscented Kalman particle filter (UKPF) and the auxiliary extended Kalman particle filter, where the number of particles is relatively small, such as 200 and 1,000. However, with an increase of particles, the superiority of the proposed method may decline compared with the PF and APF as showed in the experiments. Also, the AIEKPF has less running time than the UKPF under the same conditions, and from the viewpoint of the average effective sample sizes, it is clear that the AIEKPF has the slightest degeneracy in all filters presented in the experiments.

Varying rotate speed can cause changes in a measured gearbox vibration signal. There is a need to develop a technique to provide accurate state indicator of gearbox under fluctuating rotate speed conditions. This paper presents an approach for gearbox fault detection under varying rotate speed condition based on auxiliary particle filter. Firstly, the model of vibration part which sensitive to the alternating rotate speed condition was established based on the relation of cosine signal three points sampling values. Then this part vibration signal was estimated based on auxiliary particle filter. Based on these the residual signal was obtained which lower sensitiveness to the alternating rotate rate condition. Thus the gearbox fault was detected by the residual signal statistic quantity kurtosis and amplitude of Fourier transform. Finally, the different work condition vibration signals of the laboratory gearbox under varying rotate speed condition were detected and signal processing was studied with those signals as examples. The results show that the proposed method is feasible and effective.

The particle filter has attracted considerable attention in visual tracking due to its relaxation of the linear and Gaussian restrictions in the state space model. It is thus more flexible than the Kalman filter. However, the conventional particle filter uses system transition as the proposal distribution, leading to poor sampling efficiency and poor performance in visual tracking. It is not a trivial task to design satisfactory proposal distributions for the particle filter. In this paper, we introduce an improved particle filtering framework into visual tracking, which combines the unscented Kalman filter and the auxiliary particle filter. The efficient unscented auxiliary particle filter (UAPF) uses the unscented transformation to predict one-step ahead likelihood and produces more reasonable proposal distributions, thus reducing the number of particles required and substantially improving the tracking performance. Experiments on real video sequences demonstrate that the UAPF is computationally efficient and outperforms the conventional particle filter and the auxiliary particle filter.KeywordsParticle FilterImportance SamplingObservation ModelVisual TrackingUnscented Kalman FilterThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The application of the auxiliary particle filter to the robot localization problem is considered. The auxiliary particle filter (APF) is an enhancement of the generic particle filter. However, APF suffers from the impoverishment problem and needs a large number of particles to represent the system posterior probability density function. An evolutionary computing method, the genetic algorithm is introduced into APF to remove early convergence yet improves the quality of potential solutions. Experiment results show that the evolutionary APF algorithm needs fewer particles and is more precise and robust for mobile robot localization in dynamic environment.KeywordsMobile RobotParticle FilterGenetic AlgoRobot LocalizationAverage Localization ErrorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We propose the robust 2D localization applies an Auxiliary Particle Filter (APF) to Monte Carlo Localization (MCL). Urban environments have fewer landmarks than two-dimensional (2D) indoor maps for efficiently finding a unique location. Localization using MCL have the problem that few landmarks pose divergence of the particles of MCL. We use APF for MCL, because APF continues resampling until convergence particle occurs in one localization step. Another problem with 2D urban mapping is that of data association posed by three-dimensional (3D) surfaces. Pitching and rolling may, for example, adversely affect 2D scan-data metrics due to 3D surfaces, causing mismatching data association in 2D maps. We therefore use a Laplacian filter for 2D grid maps. Experimental results show that our localization method is more highly stable in urban environments than MCL.

Efficient matrix approach for classical inference in state space models

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

We introduce a new sequential methodology to calibrate the fixed parameters and trace the stochastic dynamical variables of a state-space system. The proposed framework is based on the nested hybrid filters (NHF) of [1], that combine two layers of filters, one inside the other, to compute the joint posterior probability distribution of the static parameters and the state variables. In particular, we explore the use of deterministic sampling techniques in the first layer of the algorithm, instead of Monte Carlo methods, which reduces computational cost and so makes the algorithms potentially better-suited for high-dimensional state and parameter spaces. We present numerical results for a stochastic Lorenz 63 model.

In this research, a non-infrastructure-based and low-cost indoor navigation method is proposed through the integration of smartphone built-in microelectromechanical systems (MEMS) sensors and indoor map information using an auxiliary particle filter (APF). A cascade structure Kalman particle filter algorithm is designed to reduce the computational burden and improve the estimation speed of the APF by decreasing its update frequency and the number of particles used in this research. In the lower filter (Kalman filter), zero velocity update and non-holonomic constraints are used to correct the error of the inertial navigation-derived solutions. The innovation of the design lies in the combination of upper filter (particle filter) map-matching and map-aiding methods to further constrain the navigation solutions. This proposed navigation method simplifies indoor positioning and makes it accessible to individual and group users, while guaranteeing the system’s accuracy. The availability and accuracy of the proposed algorithm are tested and validated through experiments in various practical scenarios.

Particle flow filters have been recently developed as an alternative approach for nonlinear filtering. The particles approximating the prior are migrated using differential equations to be distributed according to the posterior. Computationally tractable exact solutions only exist for linear Gaussian models. For other scenarios, approximations are required and it is not fully understood how these approximations impact the movement of the particles and the subsequent propagation of error in the filter. An alternative approach is to use the particle flow methods to perform the importance sampling step within a particle filtering framework. Existing methods along these lines involve either intensive calculation or the construction of a transport map, which can be challenging. In this paper, we propose to use existing particle flow methods in an auxiliary particle filter. The flows are used to sample auxiliary variables; and these allow us to identify importance sampling distributions that are well-matched to the posteriors. Simulations results indicate that the auxiliary particle filters we develop have accuracy and computational complexity similar to that of the underlying particle flow filters.

This paper provides a solution for the multiple changepoint detection problems in financial time series prediction without knowing the number and location of changepoints. The proposed approach is a Sequential Monte Carlo (SMC) method for estimating GARCH based volatility models which are subject to an unknown number of changepoints. Recent Auxiliary Particle Filtering (APF) techniques are used to calculate the posterior densities and forecasts in real-time. This approach also automatically deals with the common path dependence problem of these type volatility models. We studied on simulated volatility data using GARCH model and have shown that the proposed approach works well with the generated data. For the non-linearity multiple changepoint detection problem, APF is investigated over the simulated volatility to model the switching regimes. In this study, a full structural changepoint specification is defined in which all parameters of the conditional variance of GARCH are subject to change respectively.

In the application of particle filter algorithm for target tracking in wireless sensor networks, an Auxiliary particle filter (APF) and Gaussian particle filter (GPF) are discussed to solve the particle degradation problem of Particle Filter (PF). By introducing an auxiliary variable and two rounds weighted processes, APF makes the particle weights stable and relaxes particle degradation. GPF uses a Gaussian density function to approximately estimate posterior probability distribution. It doesn’t require re-sampling, and there is no particle degradation. Therefore, three algorithm are applied to single-target tracking in wireless sensor networks. Finally, the comparison of three algorithm’s performance in target tracking is presented and the simulation results are also given. From these results we can see that APF has better accuracy than PF algorithm and GPF has better accuracy and real-time performance than PF algorithm.