逼近积分点数下限的五阶容积卡尔曼滤波定轨算法

为了在保持滤波定轨精度不变的条件下提高定轨计算的实时性,提出一种新的逼近积分点个数下限的五阶容积卡尔曼滤波定轨算法.首先,采用一种数值容积准则对非线性函数的高斯加权积分进行近似,该准则所需的积分点个数仅比五阶代数精度容积准则积分点个数的理论下限多一个积分点,并在贝叶斯滤波算法框架下推导出本文算法的更新步骤.然后,给出实时定轨所需的状态方程和量测方程,在状态方程中考虑了J2项引力摄动和大气阻力摄动,在量测方程中利用坐标系转换推导了轨道状态与测量元素之间的非线性关系.仿真实验结果表明,本文所提算法在定轨精度方面与已有的五阶滤波算法相当,但所需的积分点个数最少,计算实时性最高,从而验证了本文算法的有效性.     

Control of epileptiform spikes based on nonlinear unscented Kalman filter

A new control strategy based on nonlinear unscented Kalman filter(UKF) is proposed for a neural mass model that serves as a model for simulating real epileptiform stereo-electroencephalographic (SEEG) signals. The UKF is used as an observer to estimate the state from the noisy measurement because it has been proved to be effective for state estimation of nonlinear systems. A UKF controller is constructed via the estimated state and is illustrated to be effective for epileptiform spikes suppression of aforementioned model by numerical simulations.     

基于Huber的高阶容积卡尔曼跟踪算法

为改善高阶容积卡尔曼滤波算法的滤波精度和鲁棒性, 提出了一种新的基于Huber的高阶容积卡尔曼滤波算法. 在采用统计线性回归模型近似非线性量测模型的基础上, 利用Huber M 估计算法实现状态的量测更新. 进一步结合高阶球面-径向容积准则的状态预测模块构成基于 Huber的高阶容积卡尔曼跟踪算法. 重点分析了Huber代价函数的调节因子对算法跟踪性能的影响. 通过对纯方位目标跟踪和再入飞行器跟踪两个实例验证了所提算法的跟踪性能优于传统高阶容积卡尔曼滤波算法.     

Variational Bayesian-Based Improved Maximum Mixture Correntropy Kalman Filter for Non-Gaussian Noise

The maximum correntropy Kalman filter (MCKF) is an effective algorithm that was proposed to solve the non-Gaussian filtering problem for linear systems. Compared with the original Kalman filter (KF), the MCKF is a sub-optimal filter with Gaussian correntropy objective function, which has been demonstrated to have excellent robustness to non-Gaussian noise. However, the performance of MCKF is affected by its kernel bandwidth parameter, and a constant kernel bandwidth may lead to severe accuracy degradation in non-stationary noises. In order to solve this problem, the mixture correntropy method is further explored in this work, and an improved maximum mixture correntropy KF (IMMCKF) is proposed. By derivation, the random variables that obey Beta-Bernoulli distribution are taken as intermediate parameters, and a new hierarchical Gaussian state-space model was established. Finally, the unknown mixing probability and state estimation vector at each moment are inferred via a variational Bayesian approach, which provides an effective solution to improve the applicability of MCKFs in non-stationary noises. Performance evaluations demonstrate that the proposed filter significantly improves the existing MCKFs in non-stationary noises.     

Design of Nonlinear Autoregressive Exogenous Model Based Intelligence Computing for Efficient State Estimation of Underwater Passive Target

In this study, an intelligent computing paradigm built on a nonlinear autoregressive exogenous (NARX) feedback neural network model with the strength of deep learning is presented for accurate state estimation of an underwater passive target. In underwater scenarios, real-time motion parameters of passive objects are usually extracted with nonlinear filtering techniques. In filtering algorithms, nonlinear passive measurements are associated with linear kinetics of the target, governing by state space methodology. To improve tracking accuracy, effective feature estimation and minimizing position error of dynamic passive objects, the strength of NARX based supervised learning is exploited. Dynamic artificial neural networks, which contain tapped delay lines, are suitable for predicting the future state of the underwater passive object. Neural networks-based intelligence computing is effectively applied for estimating the real-time actual state of a passive moving object, which follows a semi-curved path. Performance analysis of NARX based neural networks is evaluated for six different scenarios of standard deviation of white Gaussian measurement noise by following bearings only tracking phenomena. Root mean square error between estimated and real position of the passive target in rectangular coordinates is computed for evaluating the worth of the proposed NARX feedback neural network scheme. The Monte Carlo simulations are conducted and the results certify the capability of the intelligence computing over conventional nonlinear filtering algorithms such as spherical radial cubature Kalman filter and unscented Kalman filter for given state estimation model.     

Tracking noisy limit cycle oscillation with nonlinear filters

For engineering systems, the dynamic state estimates provide valuable information for the detection and prediction of failure due to noise and vibration. From this perspective, nonlinear filtering techniques are applied to the problem of state estimation of dynamical systems undergoing noisy limit cycle oscillation. Specifically, the extended Kalman filter, ensemble Kalman filter and particle filter are used to track the limit cycle oscillations of a Duffing oscillator using noisy observational data. The noisy limit cycle oscillations feature highly non-Gaussian trends. The efficiency and limitations of the extended Kalman filter, ensemble Kalman filter and particle filter in tracking limit cycle oscillations are examined with respect to the model and measurement noise and sparsity of measurement data. For the limit cycle oscillations considered here, it is demonstrated that the ensemble Kalman filter and particle filter outperform the extended Kalman filter in the presence of sparse observational data or strong measurement noise. For moderate measurement noise and frequent measurement data, the ensemble Kalman filter and particle filter perform equally well in comparison to the extended Kalman filter.     

INPUT FORCES ESTIMATION OF BEAM STRUCTURES BY AN INVERSE METHOD

An on-line recursive inverse method to estimate the input forces of beam structures is presented. The inverse method is based on the Kalman filter and a recursive least-squares algorithm. The filter models the system dynamics in a linear set of state equations. The state equations of the beam structures were constructed using the finite element method. The practicability and accuracy of the estimation method were examined with numerical simulations from which the input forces of a cantilever beam with a lumped mass on the free end were estimated from the output responses. In the numerical experiments, the cantilever beam was subjected to five types of input forces, i.e., sinusoidal, triangular impulse, rectangular impulse, a series of impulses and random. The simulation results show that the inverse method has an excellent performance to estimate the input forces of beam structural systems from the noisy measurements.     

小波网络辅助卡尔曼滤波的捷联惯导传递对准

初始对准精度是捷联惯导系统的主要误差来源之一。针对舰载机捷联惯导的传递对准模型准确建模困难,且测量噪声和过程噪声随舰船动态而变化,这样就会降低滤波的精度,卡尔曼滤波有一定的局限性,提出了将小波神经网络辅助卡尔曼滤波器用于惯导系统的传递对准。把能直接影响卡尔曼滤波估计误差的参数作为网络的输入,进过样本训练后,把网络的输出与经过卡尔曼滤波得到的结果相加,实现了捷联惯导的传递对准的滤波功能。这种新算法在实际应用中的非线性情况下优于传统卡尔曼滤波方法。仿真结果表明了其实用性和有效性。     

Nonparametric identification of nonlinear dynamic systems using a synchronisation-based method

The present study proposes an identification method for highly nonlinear mechanical systems that does not require a priori knowledge of the underlying nonlinearities to reconstruct arbitrary restoring force surfaces between degrees of freedom. This approach is based on the master–slave synchronisation between a dynamic model of the system as the slave and the real system as the master using measurements of the latter. As the model synchronises to the measurements, it becomes an observer of the real system. The optimal observer algorithm in a least-squares sense is given by the Kalman filter. Using the well-known state augmentation technique, the Kalman filter can be turned into a dual state and parameter estimator to identify parameters of a priori characterised nonlinearities. The paper proposes an extension of this technique towards nonparametric identification. A general system model is introduced by describing the restoring forces as bilateral spring-dampers with time-variant coefficients, which are estimated as augmented states. The estimation procedure is followed by an a posteriori statistical analysis to reconstruct noise-free restoring force characteristics using the estimated states and their estimated variances. Observability is provided using only one measured mechanical quantity per degree of freedom, which makes this approach less demanding in the number of necessary measurement signals compared with truly nonparametric solutions, which typically require displacement, velocity and acceleration signals. Additionally, due to the statistical rigour of the procedure, it successfully addresses signals corrupted by significant measurement noise. In the present paper, the method is described in detail, which is followed by numerical examples of one degree of freedom (1DoF) and 2DoF mechanical systems with strong nonlinearities of vibro-impact type to demonstrate the effectiveness of the proposed technique.     

A novel hard decision decoding scheme based on genetic algorithm and neural network

A novel hard decision decoding scheme based on a hybrid intelligent algorithm combining genetic algorithm and neural network, named as genetic neural-network decoding (GND), is proposed. GND offsets the reliability loss caused by channel transmission error and hard decision quantization by making full use of the genetic algorithm's optimization capacity and neural network's pattern classification function to optimize the hard decision outputs of received matched filter and restore a more likelihood codeword as the input of hard decision decoder. As can be seen from the theoretical analysis and computer simulation, GND scheme is close to the traditional soft decision decoding in error correction performance, while its complexity, compared with the traditional soft decision decoding, is greatly reduced because its decoding process does not need to use the channel statistical information.     

基于混合粒子滤波的水下小目标跟踪

针对水下小目标粒子滤波估计过程中“粒子贫化”引起的估计性能下降,提出了混合粒子滤波算法。该算法在常规粒子滤波算法基础上,在每一步迭代估计过程中进行量测的再次随机采样,以丰富随机粒子多样性,缓解水下小目标状态估计过程中的“粒子贫化”的影响。对算法进行了仿真分析,并将该方法用于水下小目标探测实验的数据处理,结果表明,相比于常规的粒子滤波算法,所提出的混合粒子滤波得到了误差更小且稳定的状态估计结果,有效地改善水下小目标跟踪的精度和稳健性。     

光度曲线反演空间目标形状的发展现状

光度曲线反演空间目标形状和姿态等参数为空间目标监视与识别提供了新的技术途径。首先分析了基于光度曲线反演空间目标信息的必要性,之后通过关注和跟踪国内外最新发展情况,全面总结了目前进行形状反演的3种主流方法的研究现状及优缺点,对3种反演方法进行了比较分析,指出基于非线性滤波技术的形状反演方法是未来的主要发展方向,并分析了3种非线性滤波技术的优缺点。最后针对反演存在的问题,指出了基于改进的实时性更好的粒子滤波算法,融合多种传感器信息反演几何形状和表面材料更为复杂的空间目标是下一步研究发展的主要方向。     

基于粒子滤波的一种改进的资料同化方法

针对在粒子数较少时传统的集合卡尔曼滤波和粒子滤波方法不能有效表征后验概率密度函数(PDF)的问题, 提出了一种改进的粒子滤波方法. 主要思想是在预测步之后引入更新步, 并且将观测时刻与非观测时刻的同化分析进行区别处理. 对典型的低维和高维混沌系统的仿真结果表明:改进粒子滤波方法是一种非常有效的估计非线性非高斯随机系统状态的方法.     

基于时频差的正交容积卡尔曼滤波跟踪算法

针对基于时频差测量的无源跟踪中面临的非线性估计问题, 提出一种正交容积卡尔曼滤波跟踪算法. 该算法在容积卡尔曼滤波算法的基础上, 通过引入特定正交矩阵改进容积采样方法, 在高维状态估计下减小因采样产生的误差, 在没有增加计算量的前提下, 有效提高收敛速度及跟踪精度. 仿真结果表明, 在基于到达时差和到达频差的联合无源跟踪问题中, 与扩展卡尔曼滤波及容积卡尔曼滤波算法相比, 本文所提算法在跟踪性能上有明显提升.     

Chaotic secure communication based on strong tracking filtering

A scheme for implementing secure communication based on chaotic maps and strong tracking filter (STF) is presented, and a modified STF algorithm with message estimation is developed for the special requirement of chaotic secure communication. At the emitter, the message symbol is modulated by chaotic mapping and is output through a nonlinear function. At the receiver, the driving signal is received and the message symbol is recovered dynamically by the STF with estimation of message symbol. Simulation results of Holmes map demonstrate that when message symbols are binary codes, STF can effectively recover the codes of the message from the noisy chaotic signals. Compared with the extended Kalman filter (EKF), STF has a lower bit error rate.     

Error Covariance Matrix Estimation of Noisy and Dynamically Coupled Time Series

We estimate the covariance matrix of the errors in several dynamically coupled time series corrupted by measurement errors. We say that several scalar time series are dynamically coupled if they record the values of measurements of the state variables of the same smooth dynamical system. The estimation of the covariance matrix of the errors is made using a noise reduction algorithm that efficiently exploits the information contained jointly in the dynamically coupled noisy time series. The method is particularly powerful for short length time series with high uncertainties.     

Experimental realization of optimal noise estimation for a general Pauli channel

We present the experimental realization of the optimal estimation protocol for a Pauli noisy channel. The method is based on the generation of 2-qubit Bell states and the introduction of quantum noise in a controlled way on one of the state subsystems. The efficiency of the optimal estimation, achieved by a Bell measurement, is shown to outperform quantum process tomography.     

State Estimation of an Underwater Markov Chain Maneuvering Target Using Intelligent Computing

In this study, an application of deep learning-based neural computing is proposed for efficient real-time state estimation of the Markov chain underwater maneuvering object. The designed intelligent strategy is exploiting the strength of nonlinear autoregressive with an exogenous input (NARX) network model, which has the capability for estimating the dynamics of the systems that follow the discrete-time Markov chain. Nonlinear Bayesian filtering techniques are often applied for underwater maneuvering state estimation applications by following state-space methodology. The robustness and precision of NARX neural network are efficiently investigated for accurate state prediction of the passive Markov chain highly maneuvering underwater target. A continuous coordinated turning trajectory of an underwater maneuvering object is modeled for analyzing the performance of the neural computing paradigm. State estimation modeling is developed in the context of bearings only tracking technology in which the efficiency of the NARX neural network is investigated for ideal and complex ocean environments. Real-time position and velocity of maneuvering object are computed for five different cases by varying standard deviations of white Gaussian measured noise. Sufficient Monte Carlo simulation results validate the competence of NARX neural computing over conventional generalized pseudo-Bayesian filtering algorithms like an interacting multiple model extended Kalman filter and an interacting multiple model unscented Kalman filter.     

利用粒子滤波从雷达回波实时跟踪反演大气波导

粒子滤波(particle filter,PF)是利用蒙特卡洛仿真方法处理递推估计问题的非线性滤波算法,这种方法不受模型线性和高斯假设的约束,是处理非线性非高斯动态系统状态估计的有效算法,适用于雷达回波反演大气波导(RFC)这类非线性非高斯问题.文中分别介绍了PF的基本思想和具体算法实现步骤,最后导出PF反演算法的迭代求解格式.数值试验结果表明,与扩展卡尔曼滤波(extended kalman filter,EKF)和不敏卡尔曼滤波(unscented kalman filter,UKF)相比,PF更适用于RFC这类高度非线性反演问题,可有效提高反演结果的稳定性和精度.     

基于粒子滤波状态估计的滚动轴承故障识别方法

提出了一种基于粒子滤波状态估计的滚动轴承故障识别方法,该方法主要包括故障模型建立和故障识别两个步骤。在故障模型建立部分,首先依据滚动轴承不同故障状态下的振动信号,建立对应的自回归模型,作为故障模型;在故障识别部分,将正常状态下对应的模型,转化为状态空间模型,设计粒子滤波器,然后对不同的故障状态进行估计,提取其残差的相关特征,并结合模型参数特征应用BP神经网络识别算法进行故障识别。最后以美国凯斯西储大学的滚动轴承振动数据为例,验证了该方法的有效性。