Joint state and parameter estimation in particle filtering and stochastic optimization

In this paper, an adaptive estimation algorithm is proposed for non-linear dynamic systems with unknown static parameters based on combination of particle filtering and Simultaneous Perturbation Stochastic Approxi- mation （SPSA） technique. The estimations of parameters are obtained by maximum-likelihood estimation and sampling within particle filtering framework, and the SPSA is used for stochastic optimization and to approximate the gradient of the cost function. The proposed algorithm achieves combined estimation of dynamic state and static parameters of nonlinear systems. Simulation result demonstrates the feasibilitv and efficiency of the proposed algorithm     

Particle filters for state and parameter estimation in batch processes

In process engineering, on-line state and parameter estimation is a key component in the modelling of batch processes. However, when state and/or measurement functions are highly non-linear and the posterior probability of the state is non-Gaussian, conventional filters, such as the extended Kalman filter, do not provide satisfactory results. This paper proposes an alternative approach whereby particle filters based on the sequential Monte Carlo method are used for the estimation task. Particle filters are initially described prior to discussing some implementation issues, including degeneracy, the selection of the importance density and the number of particles. A kernel smoothing approach is introduced for the robust estimation of unknown and time-varying model parameters. The effectiveness of particle filters is demonstrated through application to a benchmark batch polymerization process and the results are compared with the extended Kalman filter.     

Combining particle MCMC with Rao-Blackwellized Monte Carlo data association for parameter estimation in multiple target tracking

We consider state and parameter estimation in multiple target tracking problems with data association uncertainties and unknown number of targets. We show how the problem can be recast into a conditionally linear Gaussian state-space model with unknown parameters and present an algorithm for computationally efficient inference on the resulting model. The proposed algorithm is based on combining the Rao-Blackwellized Monte Carlo data association algorithm with particle Markov chain Monte Carlo algorithms to jointly estimate both parameters and data associations. Both particle marginal Metropolis–Hastings and particle Gibbs variants of particle MCMC are considered. We demonstrate the performance of the method both using simulated data and in a real-data case study of using multiple target tracking to estimate the brown bear population in Finland.     

Joint state and multi-innovation parameter estimation for time-delay linear systems and its convergence based on the Kalman filtering

This paper studies the joint state and parameter estimation problem for a linear state space system with time-delay. A multi-innovation gradient algorithm is developed based on the Kalman filtering principle. To improve the convergence rate, a filtering based multi-innovation gradient algorithm is proposed by using the filtering technique. The analysis indicates that the parameter estimates given by the proposed algorithms converge to their true values under the persistent excitation conditions. A simulation example is given to confirm that the proposed algorithms are effective.     

Geometric particle swarm optimization for robust visual ego-motion estimation via particle filtering

Conventional particle filtering-based visual ego-motion estimation or visual odometry often suffers from large local linearization errors in the case of abrupt camera motion. The main contribution of this paper is to present a novel particle filtering-based visual ego-motion estimation algorithm that is especially robust to the abrupt camera motion. The robustness to the abrupt camera motion is achieved by multi-layered importance sampling via particle swarm optimization (PSO), which iteratively moves particles to higher likelihood region without local linearization of the measurement equation. Furthermore, we make the proposed visual ego-motion estimation algorithm in real-time by reformulating the conventional vector space PSO algorithm in consideration of the geometry of the special Euclidean group SE(3), which is a Lie group representing the space of 3-D camera poses. The performance of our proposed algorithm is experimentally evaluated and compared with the local linearization and unscented particle filter-based visual ego-motion estimation algorithms on both simulated and real data sets.     

粒子滤波进展与展望

粒子滤波器是基于序贯M onte Carlo仿真方法的非线性滤波算法,本文对粒子滤波器的研究现状和研究进展做了综述,详细论述了粒子滤波原理、收敛性、应用及进展.首先在Bayes框架内分析了序贯重要性采样原理,重要性分布函数的选择,以及重采样方法,总结了粒子滤波器发展过程中的各种改进策略和新变种,讨论了粒子滤波器在各个领域的应用及进展,最后介绍了粒子方法的新发展,新动态,并对未来发展方向做了进一步的展望.     

Joint state and parameter robust estimation of stochastic nonlinear systems

Successful implementation of many control strategies is mainly based on accurate knowledge of the system and its parameters. Besides the stochastic nature of the systems, nonlinearity is one more feature that may be found in almost all physical systems. The application of extended Kalman filter for the joint state and parameter estimation of stochastic nonlinear systems is well known and widely spread. It is a known fact that in measurements, there are inconsistent observations with the largest part of population of observations (outliers). The presence of outliers can significantly reduce the efficiency of linear estimation algorithms derived on the assumptions that observations have Gaussian distributions. Hence, synthesis of robust algorithms is very important. Because of increased practical value in robust filtering as well as the rate of convergence, the modified extended Masreliez–Martin filter presents the natural frame for realization of the joint state and parameter estimator of nonlinear stochastic systems. The strong consistency is proved using the methodology of an associated ODE system. The behaviour of the new approach to joint estimation of states and unknown parameters of nonlinear systems in the case when measurements have non‐Gaussian distributions is illustrated by intensive simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

Box particle filtering for nonlinear state estimation using interval analysis

In recent years particle filters have been applied to a variety of state estimation problems. A particle filter is a sequential Monte Carlo Bayesian estimator of the posterior density of the state using weighted particles. The efficiency and accuracy of the filter depend mostly on the number of particles used in the estimation and on the propagation function used to re-allocate weights to these particles at each iteration. If the imprecision, i.e. bias and noise, in the available information is high, the number of particles needs to be very large in order to obtain good performances. This may give rise to complexity problems for a real-time implementation. This kind of imprecision can easily be represented by interval data if the maximum error is known. Handling interval data is a new approach successfully applied to different real applications. In this paper, we propose an extension of the particle filter algorithm able to handle interval data and using interval analysis and constraint satisfaction techniques. In standard particle filtering, particles are punctual states associated with weights whose likelihoods are defined by a statistical model of the observation error. In the box particle filter, particles are boxes associated with weights whose likelihood is defined by a bounded model of the observation error. Experiments using actual data for global localization of a vehicle show the usefulness and the efficiency of the proposed approach.     

Adaptive divided difference filtering for simultaneous state and parameter estimation

A novel adaptive version of the divided difference filter (DDF) applicable to non-linear systems with a linear output equation is presented in this work. In order to make the filter robust to modeling errors, upper bounds on the state covariance matrix are derived. The parameters of this upper bound are then estimated using a combination of offline tuning and online optimization with a linear matrix inequality (LMI) constraint, which ensures that the predicted output error covariance is larger than the observed output error covariance. The resulting sub-optimal, high-gain filter is applied to the problem of joint state and parameter estimation. Simulation results demonstrate the superior performance of the proposed filter as compared to the standard DDF.     

An adaptive surrogate modeling-based sampling strategy for parameter optimization and distribution estimation (ASMO-PODE)

Parameter distribution estimation has long been a hot issue for the uncertainty quantification of environmental models. Traditional approaches such as MCMC (Markov Chain Monte Carlo) are prohibitive to be applied to large complex dynamic models because of the high computational cost of computing resources. To reduce the number of model evaluations required, we proposed an adaptive surrogate modeling-based sampling strategy for parameter distribution estimation, named ASMO-PODE (Adaptive Surrogate Modeling-based Optimization – Parameter Optimization and Distribution Estimation). The ASMO-PODE can provide an estimation of the parameter distribution using as little as one percent of the model evaluations required by a regular MCMC approach. The effectiveness and efficiency of the ASMO-PODE approach have been evaluated with 2 test problems and one land surface model, the Common Land Model. The results demonstrated that the ASMO-PODE method is an economic way for parameter optimization and distribution estimation.     

An adaptive optimization scheme with satisfactory transient performance

Adaptive optimization (AO) schemes based on stochastic approximation principles such as the Random Directions Kiefer-Wolfowitz (RDKW), the Simultaneous Perturbation Stochastic Approximation (SPSA) and the Adaptive Fine-Tuning (AFT) algorithms possess the serious disadvantage of not guaranteeing satisfactory transient behavior due to their requirement for using random or random-like perturbations of the parameter vector. The use of random or random-like perturbations may lead to particularly large values of the objective function, which may result to severe poor performance or stability problems when these methods are applied to closed-loop controller optimization applications. In this paper, we introduce and analyze a new algorithm for alleviating this problem. Mathematical analysis establishes satisfactory transient performance and convergence of the proposed scheme under a general set of assumptions. Application of the proposed scheme to the adaptive optimization of a large-scale, complex control system demonstrates the efficiency of the proposed scheme.     

Freeway traffic estimation within particle filtering framework

This paper formulates the problem of real-time estimation of traffic state in freeway networks by means of the particle filtering framework. A particle filter (PF) is developed based on a recently proposed speed-extended cell-transmission model of freeway traffic. The freeway is considered as a network of components representing different freeway stretches called segments. The evolution of the traffic in a segment is modelled as a dynamic stochastic system, influenced by states of neighbour segments. Measurements are received only at boundaries between some segments and averaged within possibly irregular time intervals. This limits the measurement update in the PF to only these time instants when a new measurement arrives, while in between measurement updates any simulation model can be used to describe the evolution of the particles. The PF performance is validated and evaluated using synthetic and real traffic data from a Belgian freeway. An unscented Kalman filter is also presented. A comparison of the PF with the unscented Kalman filter is performed with respect to accuracy and complexity.     

采用粒子群算法的空时二维参数估计

针对传统的空时二维参数估计计算复杂、鲁棒性及通用性差、收敛速度慢等缺点,根据空时具有等效性,以空域和时域处理算法可以相互转化为基础,推导出合适的适应度函数,运用改进的粒子群算法同时搜索信号的到达角和频率,用K means聚类算法对搜索结果进行分类,利用粒子群算法计算简单、全局收敛、可并行性等特点提高算法的搜索能力。计算机仿真表明,与传统的方法相比该算法具有较好的统计和收敛性能。     

Approximate nonlinear filtering and its application in navigation

In this paper, we introduce for the first time particle filtering for an exponential family of densities. We prove that under certain conditions the approximated conditional density of the state converges to the true conditional density. In the realistic setting where the conditional density does not lie in an exponential family but stays close to it, we show that under certain assumptions the error of the estimate given by an approximate nonlinear filter (which we call the projection particle filter), is bounded. We use projection particle filtering in state estimation for a combination of inertial navigation system (INS) and global positioning system (GPS), referred to as integrated INS/GPS. We illustrate via numerical experiments that projection particle filtering outperforms regular particle filtering in navigation performance, and extended Kalman filter as well when satellite loss-of-lock occurs.     

Partially‐observable stochastic hybrid systems (poshss) state estimation and optimal control

This paper discusses the state estimation and optimal control problem of a class of partially‐observable stochastic hybrid systems (POSHS). The POSHS has interacting continuous and discrete dynamics with uncertainties. The continuous dynamics are given by a Markov‐jump linear system and the discrete dynamics are defined by a Markov chain whose transition probabilities are dependent on the continuous state via guard conditions. The only information available to the controller are noisy measurements of the continuous state. To solve the optimal control problem, a separable control scheme is applied: the controller estimates the continuous and discrete states of the POSHS using noisy measurements and computes the optimal control input from the state estimates. Since computing both optimal state estimates and optimal control inputs are intractable, this paper proposes computationally efficient algorithms to solve this problem numerically. The proposed hybrid estimation algorithm is able to handle state‐dependent Markov transitions and compute Gaussian‐ mixture distributions as the state estimates. With the computed state estimates, a reinforcement learning algorithm defined on a function space is proposed. This approach is based on Monte Carlo sampling and integration on a function space containing all the probability distributions of the hybrid state estimates. Finally, the proposed algorithm is tested via numerical simulations.     

Joint estimation of state and noise parameters in a linear dynamic system with impulsive measurement noise: Application to OFDM systems

Interference mitigation is one of the main challenges in wireless communication, especially in ad hoc networks. In such context, the Multiple Access Interference (MAI) is known to be of an impulsive nature. Therefore, the conventional Gaussian assumption is inadequate to model this type of interference. Nevertheless, it can be accurately modeled by stable distributions. In fact, it was shown in literature that the α-stable distribution is a useful tool to model impulsive data. In this paper, we tackle the problem of noise compensation in ad hoc networks. More precisely, this issue is addressed within an Orthogonal Frequency Division Multiplexing (OFDM) transmission link assuming a symmetric α-stable model for the signal distortion due to MAI. Based on Bayesian estimation, the proposed approach estimates the transmitted OFDM symbols in the time domain using the Sequential Monte Carlo (SMC) methods. Unlike existing schemes, we consider the more realistic case where the impulsive noise parameters are assumed to be unknown at the receiver. Consequently, our approach deals also with the difficult task of noise parameters estimation which can be very useful for other purposes such as target tracking in wireless sensor networks or channel estimation. Simulations results, provided in terms of Mean Square Error (MSE) and Bit Error Rate (BER), illustrate the efficiency and the robustness of this scheme.     

Compressive sampling optimization for user signal parameter estimation in massive MIMO systems

As the most promising technology in wireless communications, massive multiple-input multiple-output (MIMO) faces a significant challenge in practical implementation because of the high complexity and cost involved in deploying a separate front-end circuit for each antenna. In this paper, we apply the compressive sampling technique to reduce the number of required front-end circuits in the analog domain and the computational complexity in the digital domain. Unlike the commonly adopted random projections, we exploit the a priori probability distribution of the user positions to optimize the compressive sampling strategy, so as to maximize the mutual information between the compressed measurements and the direction-of-arrival (DOA) of user signals. With the optimized compressive sampling strategy, we further propose a compressive sampling Capon spatial spectrum estimator for DOA estimation. In addition, the user signal power is estimated by solving a compressed measurement covariance matrix fitting problem. Furthermore, the user signal waveforms are estimated from a robust adaptive beamformer through the reconstruction of an interference-plus-noise compressed covariance matrix. Simulation results clearly demonstrate the performance advantages of the proposed techniques for user signal parameter estimation as compared to existing techniques.     

粒子滤波算法研究进展与展望

粒子滤波是一种通过非参数化的Monte Carlo模拟方法实现递推贝叶斯估计的算法。本文对粒子滤波的发展和研究现状进行了阐述,详细介绍和分析了粒子滤波的基本原理、存在的几个关键问题及解决方法,总结归纳出11种主要改进粒子滤波器,同时论述了粒子滤波应用领域。最后对未来发展提出了展望。