Robust state estimator design for uncertain linear systems using optimization techniques

The estimation of state variables of dynamic systems in noisy environments has been an active research field in recent decades. In this way, Kalman filtering approach may not be robust in the presence of modeling uncertainties. So, several methods have been proposed to design robust estimators for the systems with uncertain parameters. In this paper, an optimized filter is proposed for this problem considering an uncertain discrete-time linear system. After converting the subject to an optimization problem, three algorithms are used for optimizing the state estimator parameters: particle swarm optimization (PSO) algorithm, modified genetic algorithm (MGA) and learning automata (LA). Experimental results show that, in comparison with the standard Kalman filter and some related researches, using the proposed optimization methods results in robust performance in the presence of uncertainties. However, MGA-based estimation method shows better performance in the range of uncertain parameter than other optimization methods.     

A Novel Adaptive Kalman Filter Based on Credibility Measure

It is quite often that the theoretic model used in the Kalman filtering may not be sufficiently accurate for practical applications, due to the fact that the covariances of noises are not exactly known. Our previous work reveals that in such scenario the filter calculated mean square errors(FMSE) and the true mean square errors(TMSE) become inconsistent, while FMSE and TMSE are consistent in the Kalman filter with accurate models. This can lead to low credibility of state estimation regardless o...     

An algorithmic approach to adaptive state filtering using recurrentneural networks

Practical algorithms are presented for adaptive state filtering in nonlinear dynamic systems when the state equations are unknown. The state equations are constructively approximated using neural networks. The algorithms presented are based on the two-step prediction-update approach of the Kalman filter. The proposed algorithms make minimal assumptions regarding the underlying nonlinear dynamics and their noise statistics. Non-adaptive and adaptive state filtering algorithms are presented with both off-line and online learning stages. The algorithms are implemented using feedforward and recurrent neural network and comparisons are presented. Furthermore, extended Kalman filters (EKFs) are developed and compared to the filter algorithms proposed. For one of the case studies, the EKF converges but results in higher state estimation errors that the equivalent neural filters. For another, more complex case study with unknown system dynamics and noise statistics, the developed EKFs do not converge. The off-line trained neural state filters converge quite rapidly and exhibit acceptable performance. Online training further enhances the estimation accuracy of the developed adaptive filters, effectively decoupling the eventual filter accuracy from the accuracy of the process model.     

改进粒子群算法优化扩展卡尔曼滤波器电机转速估计

针对感应电机扩展卡尔曼滤波器转速估计中难以取得卡尔曼滤波器系统噪声矩阵和测量噪声矩阵最优值的问题, 提出了一种基于改进粒子群算法优化的扩展卡尔曼滤波器转速估计方法。算法通过融合遗传算法和粒子群算法的优点, 采用可调整的算法模型对粒子群算法进行改进, 将改进的粒子群算法对扩展卡尔曼滤波器中的系统噪声矩阵和测量噪声矩阵进行优化处理, 将优化后的卡尔曼滤波器应用于感应电机转速估计。仿真实验表明, 与试探法、标准粒子群算法及遗传算法比较, 改进粒子群算法优化的扩展卡尔曼滤波器能够有效提高转速估计的精度, 从而提高无速度传感器矢量控制系统的控制性能。     

Adaptive Gaussian filters for nonlinear state estimation with one-step randomly delayed measurements

This paper proposes new algorithms of adaptive Gaussian filters for nonlinear state estimation with maximum one-step randomly delayed measurements. The unknown random delay is modeled as a Bernoulli random variable with the latency probability known a priori. However, a contingent situation has been considered in this work when the measurement noise statistics remain partially unknown. Due to unavailability of the complete knowledge of measurement noise statistics, the unknown measurement noise covariance matrix is estimated along with states following: (i) variational Bayesian approach, (ii) maximum likelihood estimation. The adaptation algorithms are mathematically derived following both of the above approaches. Subsequently, a general framework for adaptive Gaussian filter is presented with which variants of adaptive nonlinear filters can be formulated using different rules of numerical approximation for Gaussian integrals. This paper presents a few of such filters, viz., adaptive cubature Kalman filter, adaptive cubature quadrature Kalman filter with their higher degree variants, adaptive unscented Kalman filter, and adaptive Gauss–Hermite filter, and demonstrates the comparative performance analysis with the help of a nontrivial Bearing only tracking problem in simulation. Additionally, the paper carries out relative performance comparison between maximum likelihood estimation and variational Bayesian approaches for adaptation using Monte Carlo simulation. The proposed algorithms are also validated with the help of an off-line harmonics estimation problem with real data.     

基于AKPSO算法的加速度计快速标定方法

针对粒子群优化（ PSO）算法在加速度计标定优化后期出现的早熟、陷入局部最优的不足,以及KalmanPSO（ KPSO）算法在设计与应用过程中存在的缺陷,提出了基于自适应 Kalman 滤波的改进 PSO （ AKPSO）算法,并将其成功应用于加速度计快速标定。利用粒子群状态空间Markov链模型,建立了粒子群系统状态方程和观测方程;采用指数加权的自适应衰减记忆Kalman滤波来对粒子的位置进行估计。加速度计标定仿真结果表明：所提出的算法在收敛速度、收敛精度方面都要优于PSO,KPSO算法,有效地提高了加速度计的标定精度。     

On the choice of importance distributions for unconstrained and constrained state estimation using particle filter

Recursive state estimation of constrained nonlinear dynamical system has attracted the attention of many researchers in recent years. For nonlinear/non-Gaussian state estimation problems, particle filters have been widely used (Arulampalam et al. [1]). As pointed out by Daum [2], particle filters require a proposal distribution and the choice of proposal distribution is the key design issue. In this paper, a novel approach for generating the proposal distribution based on a constrained Extended Kalman filter (C-EKF), Constrained Unscented Kalman filter (C-UKF) and constrained Ensemble Kalman filter (C-EnkF) has been proposed. The efficacy of the proposed state estimation algorithms using a particle filter is illustrated via a successful implementation on a simulated gas-phase reactor, involving constraints on estimated state variables and another example problem, which involves constraints on the process noise (Rao et al. [10]). We also propose a state estimation scheme for estimating state variables in an autonomous hybrid system using particle filter with Unscented Kalman filter as a proposal and unconstrained Ensemble Kalman filter (EnKF) as a proposal. The efficacy of the proposed state estimation scheme for an autonomous hybrid system is demonstrated by conducting simulation studies on a three-tank hybrid system. The simulation studies underline the crucial role played by the choice of proposal distribution in formulation of particle filters.     

A DE and PSO based hybrid algorithm for dynamic optimization problems

Many real world optimization problems are dynamic in which the fitness landscape is time dependent and the optima change over time. Such problems challenge traditional optimization algorithms. For such problems, optimization algorithms not only have to find the global optimum but also need to closely track its trajectory. In this paper, a new hybrid algorithm integrating a differential evolution (DE) and a particle swarm optimization (PSO) is proposed for dynamic optimization problems. Multi-population strategy is adopted to enhance the diversity and try to keep each subpopulation on a different peak in the fitness landscape. A hybrid operator combining DE and PSO is designed, in which each individual is sequentially carried out DE and PSO operations. An exclusion scheme is proposed that integrates the distance based exclusion scheme with the hill-valley function to track the adjacent peaks. The algorithm is applied to the set of benchmark functions used in CEC 2009 competition for dynamic environment. Experimental results show that it is more effective in terms of overall performance than other comparative algorithms.     

具有适应性突变和惯性权重的粒子群优化(PSO)算法及其在动态系统参数估计中的应用

An important problem in engineering is the unknown parameters estimation in nonlinear systems. In this paper, a novel adaptive particle swarm optimization (APSO) method is proposed to solve this problem. This work considers two new aspects, namely an adaptive mutation mechanism and a dynamic inertia weight into the conventional particle swarm optimization (PSO) method. These mechanisms are employed to enhance global search ability and to increase accuracy. First, three well-known benchmark functions namely Griewank, Rosenbrock and Rastrigrin are utilized to test the ability of a search algorithm for identifying the global optimum. The performance of the proposed APSO is compared with advanced algorithms such as a nonlinearly decreasing weight PSO (NDWPSO) and a real-coded genetic algorithm (GA), in terms of parameter accuracy and convergence speed. It is confirmed that the proposed APSO is more successful than other aforementioned algorithms. Finally, the feasibility of this algorithm is demonstrated through estimating the parameters of two kinds of highly nonlinear systems as the case studies.     

Novel hybrid optimization algorithm using PSO and MADS for the trajectory estimation of a four track wheel skid-steered mobile robot

Several optimization algorithms, such as the particle swarm optimization (PSO), genetic algorithm (GA), and ant colony optimization, have previously been applied in order to reliably obtain more accurate trajectory estimation for mobile robot. However, these optimization algorithms can get easily trapped in local optima when solving a complex system, which has many local optima and many input variables. This paper proposes a novel hybrid optimization algorithm-based tuning of the extended Kalman filter, which involves the PSO and mesh adaptive direct search algorithms, prior to operation. As demonstrated by our experimental results, the advantages of the novel hybrid optimization algorithm resolve the limitations of other algorithms in the trajectory estimation of a four track wheel skid-steered mobile robot (4-TW SSMR).     

A two-stage quantum-behaved particle swarm optimization with skipping search rule and weight to solve continuous optimization problem

Quantum-behaved particle swarm optimization (QPSO) is a recently developed heuristic method by particle swarm optimization (PSO) algorithm based on quantum mechanics, which outperforms the search ability of original PSO. But as many other PSOs, it is easy to fall into the local optima for the complex optimization problems. Therefore, we propose a two-stage quantum-behaved particle swarm optimization with a skipping search rule and a mean attractor with weight. The first stage uses quantum mechanism, and the second stage uses the particle swarm evolution method. It is shown that the improved QPSO has better performance, because of discarding the worst particles and enhancing the diversity of the population. The proposed algorithm (called ‘TSQPSO’) is tested on several benchmark functions and some real-world optimization problems and then compared with the PSO, SFLA, RQPSO and WQPSO and many other heuristic algorithms. The experiment results show that our algorithm has better performance than others.     

AN OPTIMAL DESIGN OF IIR DIGITAL FILTER USING PARTICLE SWARM OPTIMIZATION

In this article, a novel approach for infinite-impulse response (IIR) digital filters using particle swarm optimization (PSO) is presented. IIR filter is essentially a digital filter with recursive responses. Because the error surface of digital IIR filters is generally nonlinear and multimodal, so global optimization techniques are required in order to avoid local minima. This study is based on a heuristic way to design IIR filters. PSO is a powerful global optimization algorithm introduced in combinatorial optimization problems. This study finds the optimum coefficients of the IIR digital filter through PSO. It is found that the calculated values are more optimal than the FDA tool and GA available for the design of the filter in MATLAB. Design of low-pass and high-pass IIR digital filters is proposed in order to provide an estimate of the transition band. The simulation results of the employed examples show an improvement on the transition band. The stability of designed filters is described by the position of Pole-Zeros.     

Digital FIR filter design using fitness based hybrid adaptive differential evolution with particle swarm optimization

This paper presents an efficient way of designing linear phase finite impulse response (FIR) low pass and high pass filters using a novel algorithm ADEPSO. ADEPSO is hybrid of fitness based adaptive differential evolution (ADE) and particle swarm optimization (PSO). DE is a simple and robust evolutionary algorithm but sometimes causes instability problem; PSO is also a simple, population based robust evolutionary algorithm but has the problem of sub-optimality. ADEPSO has overcome the above individual disadvantages faced by both the algorithms and is used for the design of linear phase low pass and high pass FIR filters. The simulation results show that the ADEPSO outperforms PSO, ADE, and DE in combination with PSO not only in magnitude response but also in the convergence speed and thus proves itself to be a promising candidate for designing the FIR filters.     

改进粒子群优化算法在TDOA定位中的应用

针对TDOA定位估计中的非线性最优化问题,提出了一种基于改进粒子群优化的TDOA定位算法。该算法在自适应粒子群优化算法的基础上,引入禁忌搜索策略,有效地解决了粒子群优化算法容易陷入局部最优的问题,使算法快速收敛到全局最优解。仿真结果表明:该算法性能稳定,定位精度高。     

基于差分文化算法的FIR数字滤波器设计

有限脉冲响应（FIR）数字滤波器的设计实质可看作是多参数优化问题。为高效实现FIR数字滤波器,将滤波器的设计转化为滤波器参数优化问题,然后提出差分文化粒子群（DC）算法在参数空间进行并行搜索以获得滤波器设计的最优参数值。提出的差分文化算法结合文化原理差分演进原理,是一种可用于实数优化的多维搜索算法。计算机仿真实验表明在设计FIR数字滤波器设计时,差分文化算法的收敛速度和性能都优于粒子群,量子粒子群以及自适应量子粒子群优化等算法,证明了该方法的有效性和优越性。     

QPSO算法优化的非线性观测器设计方法研究

具有量子行为的粒子群优化算法(Quantum-behavedParticleSwarmOptimization,简称QPSO)是继粒子群优化算法(ParticleSwarmOptimization,简称PSO)后,最新提出的一种新型、高效的进化算法。论文在研究基于PSO算法的非线性观测器基础上,提出了一种基于QPSO算法的非线性观测设计方法。以vanderPol系统为例进行了仿真实验,其基本思想是将非线性连续时间系统的状态估计问题转换为非线性函数的在线优化问题,然后利用PSO或QPSO算法获得系统状态的最优估计。仿真结果显示了基于QPSO算法的非观测器比基于PSO算法的非线性观测器的性能更优越。     

A novel real-time adaptive suboptimal recursive state estimation scheme for nonlinear discrete dynamic systems with non-Gaussian noise

A real-time state filtering and prediction scheme which is adaptive, recursive, and suboptimal is proposed for discrete time nonlinear dynamic systems with either Gaussian or non-Gaussian noise. The proposed scheme (PR) estimates states adaptively whenever both the observation is available and there exists a non-zero and finite number of real state roots of the observation model, otherwise the PR estimates states non-adaptively. The PR state transition and observation functions are as general as the state transition and observation functions for particle filters. The PR is based upon discrete noise approximation, state quantization, and a suboptimal implementation of multiple hypothesis testing. The PR first detects state estimate divergence points along the time axis, and then state estimate divergences are prevented by introducing new admissible state quantization levels; whereas the extended Kalman filter (EKF), sampling importance resampling (SIR) particle filter (bootstrap filter), and auxiliary sampling importance resampling (ASIR) particle filter produce diverging state estimates from actual state values for many dynamic models. The PR uses state transition functions in order to calculate transition probabilities from gates to gates. If these transition probabilities are somehow available, then state transition functions are not needed for state estimation with the PR; whereas state transition functions are necessary for state estimation with both particle filters and the EKF. The PR is very suitable for state estimation with either constraints imposed on state estimates or missing observations. The PR is more general than grid-based estimation approaches. Monte Carlo simulations have shown the effectiveness of the PR, that is, the PR performance is better than the performances of the EKF, SIR, and ASIR particle filters for many nonlinear models with white Gaussian noise, four examples of which are presented in the paper.     

Swarm-based intelligent optimization approach for layout problem

Layout problem is a kind of NP-Complete problem. It is concerned more and more in recent years and arises in a variety of application fields such as the layout design of spacecraft modules, plant equipment, platforms of marine drilling well, shipping, vehicle and robots. The algorithms based on swarm intelligence are considered powerful tools for solving this kind of problems. While usually swarm intelligence algorithms also have several disadvantages, including premature and slow convergence. Aiming at solving engineering complex layout problems satisfactorily, a new improved swarm-based intelligent optimization algorithm is presented on the basis of parallel genetic algorithms. In proposed approach, chaos initialization and multi-subpopulation evolution strategy based on improved adaptive crossover and mutation are adopted. The proposed interpolating rank-based selection with pressure is adaptive with evolution process. That is to say, it can avoid early premature as well as benefit speeding up convergence of later period effectively. And more importantly, proposed PSO update operators based on different versions PSO are introduced into presented algorithm. It can take full advantage of the outstanding convergence characteristic of particle swarm optimization (PSO) and improve the global performance of the proposed algorithm. An example originated from layout of printed circuit boards (PCB) and plant equipment shows the feasibility and effectiveness of presented algorithm.     

嵌入层叠混沌策略的随机粒子群算法

鉴于求解复杂问题时粒子群优化算法易出现早熟收敛的问题,通过引入轨迹扰动因子,提出随机粒子群进化迭代方程.该方程在统计行为中保证粒子向特定的收敛中心逼近,但对“旧址”的依赖性呈现出随机特性,从而使粒子群的快速跳转和迁移成为可能,避免过早落入局部陷阱.同时该进化方程还利用层叠混沌策略和对称极值扰动策略进一步增强算法的局部收敛性和全局搜索性.实验表明,由上述进化方程和改进策略构成的随机混沌粒子群算法具有鲁棒性较强、收敛速度较快和精度较高等优势,性能优于其他同源粒子群算法.