Interacting Multiple Model Particle Filter Research Articles

Modified interactive multiple model particle filter for terrain referenced navigation with classification error minimisation strategy

AbstractThe authors propose an innovative solution to address challenges in terrain‐referenced navigation (TRN). The suggested solution is the interactive multiple‐model particle filter with a classification error minimisation strategy (IMM‐CPF) based on decision theory. TRN is a technique that estimates position by comparing measured terrain altitude to the digital elevation model and critically depends on obtaining accurate altitude measurements. However, these measurements can be easily contaminated to not only from sensor errors but also from vegetation effects. The TRN measurement noise model is characterised as a multi‐modal density, and it reveals an overlap between two density functions, with the mixture weight parameter varying based on surface environmental conditions. This variability can potentially degrade estimation accuracy. The proposed approach integrates truncated likelihoods into the mode estimation process to enhance mode estimation capability using a classification error minimisation strategy. The proposed strategy is based on decision theory and has been modified to be suited in the IMMPF form. The effectiveness of the proposed IMM‐CPF method is verified through simulations conducted under diverse surface conditions, demonstrating significant improvements in estimation accuracy compared to conventional algorithms. Furthermore, the significance of this method is presented in terms of computational cost and robustness.

Experimental verification of lithium-ion battery prognostics based on an interacting multiple model particle filter

A new data-driven prognostic method based on an interacting multiple model particle filter (IMMPF) is proposed for use in the determination of the remaining useful life (RUL) of lithium-ion (Li-ion) batteries and the probability distribution function (PDF) of the uncertainty associated with the RUL. An IMMPF is applied to different state equations. The battery capacity degradation model is very important in the prediction of the RUL of Li-ion batteries. The IMMPF method is applied to the estimation of the RUL of Li-ion batteries using the three improved models. Three case studies are provided to validate the proposed method. The experimental results show that the one-dimensional state equation particle filter (PF) is more suitable for estimating the trend of battery capacity in the long term. The proposed method involving interacting multiple models demonstrated a stable and high prediction accuracy, as well as the capability to narrow the uncertainty in the PDF of the RUL prediction for Li-ion batteries.

A novel T-S fuzzy particle filtering algorithm based on fuzzy C-regression clustering

In this paper, a novel Takagi-Sugeno (T-S) fuzzy model particle filtering algorithm (TSF-PF) based on fuzzy C-regression clustering is proposed for uncertainty modeling of the target dynamic model with non-Gaussian noise. In the proposed algorithm, a generic semantic framework of the T-S fuzzy model is constructed to incorporate spatial feature information of a target into the particle filter, in which the spatial feature information is characterized by several semantic fuzzy sets. Meanwhile, a fuzzy C-regression clustering method based on correntropy is proposed to adaptively identify the premise parameters of the T-S fuzzy model, which is used to adjust the weight of models, and a Kalman filter is used to identify the consequent parameters. And then an efficient importance density function is constructed by using the proposed T-S fuzzy model, which can efficiently improve the robust and diversity of the sampling particles. Furthermore, in order to improve the real-time performance of the proposed algorithm, two improved T-S fuzzy model particle filtering algorithms are presented. The simulation results show that the tracking performance of the proposed algorithms are better than that of the traditional interacting multiple model (IMM), interacting multiple model unscented Kalman filter (IMMUKF), interacting multiple model particle filter (IMMPF) and interacting multiple model Rao-Blackwellized particle filter (IMMRBPF). Particularly, the proposed algorithms can accurately track the maneuvering target when the moving direction abruptly changes or the prior information of the target dynamic model is inaccuracy.

Bayesian State Estimation for Markovian Jump Systems: Employing Recursive Steps and Pseudocodes

In this article, we review several existing Bayesian state-estimation algorithms for Markovian jump systems (MJSs) and illustrate their distinctive properties. Specifically, we analyze the jump Markov linear systems (JMLSs), for which autonomous multiple-model (AMM) algorithms, first-order generalized pseudo-Bayesian (GPB1) algorithms, secondorder generalized pseudo-Bayesian (GPB2) algorithms, interacting multiple-model (IMM) algorithms, and reweighed IMM (RIMM) algorithms are introduced. For nonlinear MJSs, we consider the sampling importance resampling (SIR) particle filter (PF) as well as the IMM PF to demonstrate how to handle nonlinearity in the framework of MJSs. For convenience, the realization codes of GPB1 and IMM algorithms and SIR PFs are provided.

A novel recursive T-S fuzzy semantic modeling approach for discrete state-space systems

In this paper, we propose a novel recursive Takagi-Sugeno (T-S) fuzzy semantic modeling approach for discrete state-space system. According to the information learning theoretic (ILT), the correntropy can capture the higher moments of the error probability distribution to deal with non-Gaussian noise. Considering the advantages of fuzzy theory and correntropy, fuzzy correntropy is constructed and a novel kernel fuzzy C-regression model clustering based on fuzzy correntropy is proposed to solve the premise parameter identification problem of the T-S fuzzy model. To the identification of the consequent part parameters of the T-S fuzzy model, a modified extended forgetting factor recursive least squares (MEFRLS) estimator is presented. Moreover, to evaluate the performance of the proposed fuzzy model, the proposed T-S fuzzy model is applied to solve the problem of maneuvering target tracking by incorporating the target feature semantic information. Finally, the experiment results show the proposed algorithm can effectively track a maneuvering target, and its performance is better than the exist algorithms, such as interacting multiple model Kalman filter (IMMKF), interacting multiple model unscented Kalman filter (IMMUKF), the interacting multiple model particle filter (IMMPF) and interacting multiple model Rao-Blackwellized particle filter the (IMMRBPF).

Reliable flight performance assessment of multirotor based on interacting multiple model particle filter and health degree

Multirotor has been applied to many military and civilian mission scenarios. From the perspective of reliability, it is difficult to ensure that multirotors do not generate hardware and software failures or performance anomalies during the flight process. These failures and anomalies may result in mission interruptions, crashes, and even threats to the lives and property of human beings. Thus, the study of flight reliability problems of multirotors is conductive to the development of the drone industry and has theoretical significance and engineering value. This paper proposes a reliable flight performance assessment method of multirotors based on an Interacting Multiple Model Particle Filter (IMMPF) algorithm and health degree as the performance indicator. First, the multirotor is modeled by the Stochastic Hybrid System (SHS) model, and the problem of reliable flight performance assessment is formulated. In order to solve the problem, the IMMPF algorithm is presented to estimate the real-time probability distribution of hybrid state of the established SHS-based multirotor model, since it can decrease estimation errors compared with the standard interacting multiple model algorithm based on extended Kalman filter. Then, the reliable flight performance is assessed with health degree based on the estimation result. Finally, a case study of a multirotor suffering from sensor anomalies is presented to validate the effectiveness of the proposed method.

Improved Interacting Multiple Model Particle Filter Algorithm

For the issue of limited filtering accuracy of interactive multiple model particle filter algorithm caused by the resampling particles don't contain the latest observation information, we made improvements on interactive multiple model particle filter algorithm in this paper based on mixed kalman particle filter algorithm. Interactive multiple model particle filter algorithm is proposed. In addition, the composed methods influence to tracking accuracy are discussed. In the new algorithm the system state estimation is generated with unscented kalman filter (UKF) first and then use the extended kalman filter (EKF) to get the proposal distribution of the particles, taking advantage of the measure information to update the particles' state. We compare and analyze the target tracking performance of the proposed algorithm of IMM-MKPF in this paper, IMM-UPF and IMM-EPF through the simulation experiment. The results show that the tracking accuracy of the proposed algorithm is superior to other two algorithms. Thus, the new method in this paper is effective. The method is of important to improve tracking accuracy further for maneuvering target tracking under the non-linear and non-Gaussian circumstances.

Interacting multiple model particle filter for prognostics of lithium-ion batteries

We propose a new data-driven prognostic method based on the interacting multiple model particle filter (IMMPF) for determining the remaining useful life (RUL) of lithium-ion (Li-ion) batteries and the probability distribution function (PDF) of the associated uncertainty. The method applies the IMMPF to different state equations. Modeling the battery capacity degradation is very important for predicting the RUL of Li-ion batteries. In this study, improvements are made on various Li-ion battery capacity models (i.e., polynomial, exponential, and Verhulst models). Further, three different one-step state transition equations are developed, and the IMMPF method is applied to estimate the RUL of Li-ion batteries with the use of the three improved models. The PDF of the predicted RUL is obtained by combining the PDFs obtained with each individual model. We conduct four case studies to validate the proposed method. The results are as follows: (1) the three improved models require fewer parameters than the original models, (2) the proposed prognostic method shows stable and high prediction accuracy, and (3) the proposed method narrows the uncertainty PDF of the predicted RUL of Li-ion batteries.

A Novel Algorithm for Crash Detection Under General Road Scenes Using Crash Probabilities and an Interactive Multiple Model Particle Filter

Driver inattention causes the majority of vehicular crashes, and these accidents produce extensive economic and social costs, as well as injuries and fatalities. Thus, the development of imminent crash detection systems is one of the most important issues in automotive safety. Various crash detection algorithms have been proposed, but the coverage of these algorithms has been limited to one or two crash scenarios. To widen the coverage of crash detection systems to include various crash modes, driver behaviors that are dependent on road scenes and vehicle dynamics should be considered. This paper proposed an algorithm for detecting an imminent collision in general road scenes. The proposed algorithm consists of crash probability data generated from Monte Carlo simulations that consider driver behavior and vehicle dynamics, a tracking algorithm that uses an interactive multiple-model particle filter, and a threat assessment algorithm that estimates crash probabilities. To reduce nuisance and false-positive alarms, the algorithm discriminated between normal and dangerous road scenes, and a point of no return was detected using three driver models that addressed different levels of driver input. The performance of the proposed algorithm was evaluated under three scenarios, and it successfully discriminated between collision and near-miss cases, and it adjusted warning times depending on the road scenes. It is expected that the proposed algorithm would have good driver acceptability based on the results of the near-miss cases. The proposed algorithm can be used as an integrated crash detection algorithm for crash warning, avoidance, and mitigation purposes while incorporating tracking information from multiple sources.

Bearing-Only Maneuvering Mobile Tracking With Nonlinear Filtering Algorithms in Wireless Sensor Networks

Mobile node localization is important to offer wireless services in vehicular communication applications. Some typical methods realize the mobile node tracking through data fusion from time of arrival (TOA) and received signal strength (RSS) measurements provided by sensor nodes or base stations (BSs). Although the TOA/RSS method is not expensive under a concern of cost, it is very sensitive to multipath signal propagation effects. As the technology of angle of arrival (AOA) antennas is showing a rapid progress, we turn to consider AOA estimation. In this paper, the nonlinear extended Kalman filter (EKF) and the particle filter (PF) along with a three-model interacting multiple model (IMM) algorithm are utilized and compared for maneuvering mobile station (MS) tracking with bearing-only measurements. A coordinated turn model is used to improve the tracking performance since the MS frequently turns in the streets. We also propose an efficient method for resampling particles to alleviate the degeneracy effect of particle propagation in the interacting multiple model particle filter (IMMPF) algorithm. Moreover, a BS sensor selection scheme is also exploited for the long-haul MS tracking case which often changes BSs in a wireless vehicular sensor network. Numerical simulations show that the three-model IMMPF algorithm outperforms the interacting multiple model extended Kalman filter algorithm and achieves a root-mean-square tracking performance which is quite close to the posterior Cramer-Rao lower bound.

Robust visual tracking based on interactive multiple model particle filter by integrating multiple cues

Visual tracking can be formulated as a state estimation problem of target representation based on observations in image sequences. To investigate the integration of rough models from multiple cue and to explore computationally efficient algorithms, this paper formulates the problem of multiple cue integration and tracking to combine Interactive Multiple Model (IMM) with particle filter (IMM_PF). Interactive Multiple Model can estimate the multiple cue state of a dynamic system with several behavioral models that switch from one to another using model likelihoods and model transition probabilities. For the problem of visual tracking, the model of IMM is adopted to three target observation models: Corrected Background Weighted Histogram (CBWH), Completed Local Ternary Patterns (CLTP) and Histogram of Oriented Gradients (HOG). The probabilities of these models are corresponding to the weights of multiple cues. IMM_PF then dynamically adjusts the weights of different features. Compared with those state-of-the-art methods in the tracking literature, this algorithm can track the object accurately in conditions of rotation, abrupt shifts, as well as clutter and partial occlusions occurring to the tracking object with good robustness, as demonstrated by experimental results.

State estimation in non-linear Markov jump systems with uncertain switching probabilities

In this article, a study of state estimation for non-linear Markov jump systems (MJSs) with uncertain transition probabilities (TPs) is investigated. In the authors’ method, the uncertainties of TPs are portrayed by intermediate stochastic variables depicted by truncated Gaussian probability density functions (TGPDFs). In order to incorporate the prior knowledge about uncertainties into the filtering process, a skew parameter is firstly inserted into TGPDF to yield skew truncated Gaussian probability density functions (STGPDFs) which contains the original one as a particular case. Then, the state estimation method is derived based on multiple model mechanism together with particle filter using confidence TPs that are obtained by normalising the expectations of STGPDFs. The proposed approach degenerates into the traditional interacting multiple model-particle filter (IMM-PF) when the standard deviations turn to zero. A meaningful example is presented to illustrate the effectiveness of the authors’ method.

Adaptive update rate for Phased Array Radar Based on IMMK-PF

Interacting Multiple Model Kalman-Particle Filter (IMMK-PF) has the advantages of particle filter and Kalman filter and good computation efficiency compared with Interacting Multiple Model Particle Filter (IMMPF). Based on IMMK-PF, an adaptive sampling target tracking algorithm for Phased Array Radar (PAR) is proposed. This algorithm first predicts Posterior Cramer-Rao Bound Matrix (PCRBM) of the target state, then updates the sample interval in accordance with change of the target dynamics by comparing the trace of the predicted PCRBM with a certain threshold. Simulation results demonstrate that this algorithm could solve the nonlinear motion and the nonlinear relationship between radar measurement and target motion state and decrease computation load.

TRACKING AIRBORNE TARGETS HIDDEN IN BLIND DOPPLER USING CURRENT STATISTICAL MODEL PARTICLE FILTER

This paper aims at finding an algorithm featuring good estimation performance and easy hardware implementation for tracking airborne target hidden in blind Doppler. Incorporating the current statistical model which is effective in dealing with the maneuvering motions that most blind Doppler issues are caused, a current statistical model particle filter (CSM-PF) is presented in this paper for tracking airborne targets hidden in blind Doppler. Simulation results demonstrate that the proposed CSM-PF shows similar performance with the interacting multiple model particle filter (IMM-PF) in terms of tracking accuracy and track continuity, but it avoids the difficulty of model selection for maneuvering targets. In addition, when hardware implementation is considered, the proposed CSM-PF has lower processing latency, fewer resource utilization and lower hardware complexity than the IMM-PF.

An unscented particle filter for ground maneuvering target tracking

In this study, an unscented particle filtering method based on an interacting multiple model (IMM) frame for a Markovian switching system is presented. The method integrates the multiple model (MM) filter with an unscented particle filter (UPF) by an interaction step at the beginning. The framework (interaction/mixing, filtering, and combination) is similar to that in a standard IMM filter, but an UPF is adopted in each model. Therefore, the filtering performance and degeneracy phenomenon of particles are improved. The filtering method addresses nonlinear and/or non-Gaussian tracking problems. Simulation results show that the method has better tracking performance compared with the standard IMM-type filter and IMM particle filter.

Using interacting multiple model particle filter to track airborne targets hidden in blind Doppler

In airborne tracking, the blind Doppler makes the target undetectable, resulting in tracking difficulties. In this paper, we studied most possible blind-Doppler cases and summed them up into two types: targets’ intentional tangential flying to radar and unintentional flying with large tangential speed. We proposed an interacting multiple model (IMM) particle filter which combines a constant velocity model and an acceleration model to handle maneuvering motions. We compared the IMM particle filter with a previous particle filter solution. Simulation results showed that the IMM particle filter outperforms the method in previous works in terms of tracking accuracy and continuity.

Exact Bayesian and particle filtering of stochastic hybrid systems

The standard way of applying particle filtering to stochastic hybrid systems is to make use of hybrid particles, where each particle consists of two components, one assuming Euclidean values, and the other assuming discrete mode values. This paper develops a novel particle filter (PF) for a discrete-time stochastic hybrid system. The novelty lies in the use of the exact Bayesian equations for the conditional mode probabilities given the observations. Therefore particles are needed for the Euclidean valued state component only. The novel particle filter is referred to as the interacting multiple model (IMM) particle filter (IMMPF) because it incorporates a filter step which is of the same form as the interaction step of the IMM algorithm. Through Monte Carlo simulations, it is shown that the IMMPF has significant advantage over the standard PF, in particular for situations where conditional switching rate or conditional mode probabilities have small values

An interacting multiple model particle filter for manoeuvring target location

A constant velocity model, a constant acceleration model and a coordinated turn model are used for manoeuvring target. However, high location precision of the target could not be obtained with any one of these models. In this paper, an interacting multiple model particle filter (IMMPF) algorithm is proposed to estimate the target location with several models. Besides similar mixing and interaction to those in a traditional interaction multiple model (IMM) estimator, a standard particle filter runs in every model and the number of particles in every model is fixed. Compared through a target location example, the proposed algorithm is better than the traditional IMM.