Stochastic gradient algorithm for a dual-rate Box-Jenkins model based on auxiliary model and FIR model简

Based on the work in Ding and Ding （2008）, we develop a modifi ed stochastic gradient （SG） parameter estimation algorithm for a dual-rate Box-Jenkins model by using an auxiliary model. We simplify the complex dual-rate Box-Jenkins model to two fi nite impulse response （FIR） models, present an auxiliary model to estimate the missing outputs and the unknown noise variables, and compute all the unknown parameters of the system with colored noises. Simulation results indicate that the proposed method is effective.     

基于辅助模型的多新息广义增广随机梯度算法

将辅助模型辨识思想与多新息辨识理论相结合,利用系统可测信忠建立一个辅助模型.分别用辅助模型输出和噪声估计值代替辨识模型信忠向量中未知真实输出变量和不可测噪声项,并引入新忠长度扩展标量新息为新息向量,提出了Box-lenkins模型的辅助模型多新忠广义增广随机梯度辨识方法.所提出方法重复使用系统数据,能够改善参数估计精度,加快算法的收敛速度.     

Combined parameter and output estimation of dual-rate systems using an auxiliary model

For a dual-rate sampled-data system, an auxiliary model based identification algorithm for combined parameter and output estimation is proposed. The basic idea is to use an auxiliary model to estimate the unknown noise-free output (true output) of the system, and directly to identify the parameters of the underlying fast single-rate model from the dual-rate input-output data. It is shown that the parameter estimation error consistently converges to zero under generalized or weak persistent excitation conditions and unbounded noise variance, and that the output estimates uniformly converge to the true outputs. An example is included.     

Two-stage multi-innovation stochastic gradient algorithm for multivariate output-error ARMA systems based on the auxiliary model

ABSTRACT

This paper investigates the parameter estimation problem for multivariate output-error systems perturbed by autoregressive moving average noises. Since the identification model has two different kinds of parameters, a vector and a matrix, the gradient algorithm cannot be used directly. Therefore, we decompose the original system model into two sub-models and proceed the identification problem by the collaboration between the two sub-models. By employing the gradient search and determining the optimal step-sizes, we present an auxiliary model based two-stage projection algorithm. However, in order to alleviate the sensitivity to the noise, we reselect the step-sizes and derive the auxiliary model based two-stage stochastic gradient (AM-2S-SG) algorithm. Based on the AM-2S-SG algorithm, an auxiliary model based two-stage multi-innovation stochastic gradient algorithm is proposed to generate more accurate estimates. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed algorithms.     

An efficient hierarchical identification method for general dual-rate sampled-data systems

For the lifted input–output representation of general dual-rate sampled-data systems, this paper presents a decomposition based recursive least squares (D-LS) identification algorithm using the hierarchical identification principle. Compared with the recursive least squares (RLS) algorithm, the proposed D-LS algorithm does not require computing the covariance matrices with large sizes and matrix inverses in each recursion step, and thus has a higher computational efficiency than the RLS algorithm. The performance analysis of the D-LS algorithm indicates that the parameter estimates can converge to their true values. A simulation example is given to confirm the convergence results.     

基于随机梯度的双率系统自校正控制方法

针对输入更新频率是输出刷新频率整数倍的未知参数双率系统,设计一个损失输出估计器计算采样间输出,再根据随机梯度算法设计参数估计器并得到系统模型的估计参数,基于最小方差控制原则设计出双率系统的自适应控制器。通过与基于最小二乘方法辨识系统参数的自适应控制算法进行比较,可以看出该算法的计算量较小,尤其是在输入数据更新频率与输出数据刷新频率相差较大时,计算量的差距更加明显。最后用仿真例子说明了该算法的有效性。     

Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique

This paper considers the identification problems of Hammerstein finite impulse response moving average (FIR-MA) systems using the maximum likelihood principle and stochastic gradient method based on the key term separation technique. In order to improve the convergence rate, a maximum likelihood multi-innovation stochastic gradient algorithm is presented. The simulation results show that the proposed algorithms can effectively estimate the parameters of the Hammerstein FIR-MA systems.     

反馈非线性系统随机梯度辨识算法及其收敛性

反馈非线性受控自回归系统是由前向通道的受控自回归模型和反馈通道的静态非线性构成, 这类系统经过参数化后得到双线性参数辨识模型. 本文通过对辨识模型中双线性参数乘积项进行分解, 基于梯度搜索原理, 提 出了反馈非线性系统的随机梯度辨识算法. 为了改善随机梯度算法的收敛速度, 引入遗忘因子, 文章给出了遗忘因子随机梯度算法, 利用随机过程理论, 建立了随机梯度算法的参数估计收敛定理, 证明了算法的收敛性. 最后, 通过数值仿真验证了算法的有效性.     

Least squares based iterative identification for a class of multirate systems

This paper studies modeling and identification problems for multi-input multirate systems with colored noises. The state-space models are derived for the systems with different input updating periods and furthermore the corresponding transfer functions are obtained. To solve the difficulty of identification models with unmeasurable noises terms, the least squares based iterative algorithm is presented by replacing the unmeasurable variables with their iterative estimates. Finally, the simulation results indicate that the proposed iterative algorithm has advantages over the recursive algorithms.     

基于内部结构MPOMDP模型的策略梯度学习算法

为了提高MPOMDP模型的知识表示能力和推理效率,提出一种基于Agent内部结构的MPOMDP模型。该模型能表示Agent的内部结构及其时间演化,并通过将系统联合概率分布表示成每个Agent内部变量集的局部因式形式,以提高模型的推理效率。将GPI-POMDP算法扩展到基于内部结构的MPOMDP模型中,给出基于内部状态的多Agent策略梯度算法（MIS-GPOMDP）,来求解基于内部结构的MPOMDP。实验结果表明MIS-GPOMDP算法具有较高的推理效率,且算法是收敛的。     

Modelling and asset allocation for financial markets based on a stochastic volatility microstructure model

On the basis of the market microstructure theory, a continuous time microstructure model is proposed for describing the dynamics of financial markets with stochastic volatility property. From the microstructure model, one may obtain the estimates of two state variables, which represent the market excess demand and liquidity respectively but cannot be directly observed. Based on the indirectly obtained excess demand information instead of the prediction of price, a simple asset dynamic allocation approach is investigated. The local linearization method, nonlinear Kalman filter and maximum likelihood method-based estimation approach for the microstructure model proposed is presented. Case studies on the financial markets modelling and the estimated model-based asset dynamic allocation control for the JPY/USD (Japanese Yen/US Dollar) exchange rate and Japan TOPIX (Tokyo stock Price IndeX) show a satisfactory modelling precision and dynamic allocation performance.     

基于不同加权因子的随机多模型自适应控制

针对一类噪声方差未知的随机系统,基于不同加权因子设计多个参数辨识器辨识模型参数,在此基础上,构成多模型自适应控制器.在每个采样时刻基于指标切换函数选择最佳辨识模型.并将基于此最佳模型设计的控制器切换为当前控制器.同时,证明了多个模型控制器之间相互切换时整个闭环系统是全局收敛的.仿真结果表明,同单一自适应模型控制器相比,这种基于多个不同加权因子的多模型自适应控制器在模型参数发生跳变时可很好地改善被控对象的控制品质.     

Two‐stage auxiliary model gradient‐based iterative algorithm for the input nonlinear controlled autoregressive system with variable‐gain nonlinearity

This article focuses on the parameter estimation problem of the input nonlinear system where an input variable‐gain nonlinear block is followed by a linear controlled autoregressive subsystem. The variable‐gain nonlinearity is described analytical by using an appropriate switching function. According to the gradient search technique and the auxiliary model identification idea, an auxiliary model‐based stochastic gradient algorithm with a forgetting factor is presented. For the sake of improving the parameter estimation accuracy, an auxiliary model gradient‐based iterative algorithm is proposed by utilizing the iterative identification theory. To further optimize the performance of the algorithm, we decompose the identification model of the system into two submodels and derive a two‐stage auxiliary model gradient‐based iterative (2S‐AM‐GI) algorithm by using the hierarchical identification principle. The simulation results confirm the effectiveness of the proposed algorithms and show that the 2S‐AM‐GI algorithm has higher identification efficiency compared with the other two algorithms.     

基于辅助模型和数据滤波的伪线性回归系统参数估计方法

针对伪线性输出误差回归系统的辨识模型新息信息向量存在不可测变量的问题,首先通过构造一个辅助模型,用辅助模型的输出代替未知中间变量,推导得到的基于辅助模型的递推最小二乘参数估计算法计算量较大,但算法的辨识效果不佳。进一步采用估计的噪声模型对系统观测数据进行滤波,使用滤波后的数据进行参数估计,从而推导提出了基于数据滤波的递推最小二乘参数估计算法。仿真结果表明,所提算法能够有效估计伪线性回归线性输出误差系统的参数。     

基于跳数梯度的传感器网络节点距离测量

针对无线传感器网络节点距离测量精度问题,提出了一种基于平滑跳数梯度的间接测距方法DV-SHG(DV-hop with Smoothing Hop Gradient)。DV-SHG应用节点的邻居节点信息对跳数值和平均每跳距离进行修正以提高测距精度。理论分析及仿真结果表明,与DV-GNN(DV-hop with the Number of Gradient Neighbors)算法相比,在相同的计算和通信开销下,DV-SHG算法能获得较高的测距精度,在节点密集分布的无线传感器网络中具有很好的测距效果。     

Extended stochastic gradient identification algorithms for Hammerstein–Wiener ARMAX systems

An extended stochastic gradient algorithm is developed to estimate the parameters of Hammerstein–Wiener ARMAX models. The basic idea is to replace the unmeasurable noise terms in the information vector of the pseudo-linear regression identification model with the corresponding noise estimates which are computed by the obtained parameter estimates. The obtained parameter estimates of the identification model include the product terms of the parameters of the original systems. Two methods of separating the parameter estimates of the original parameters from the product terms are discussed: the average method and the singular value decomposition method. To improve the identification accuracy, an extended stochastic gradient algorithm with a forgetting factor is presented. The simulation results indicate that the parameter estimation errors become small by introducing the forgetting factor.     

粒子群优化算法在FIR数字滤波器设计中的应用

介绍了基于粒子群优化算法的FIR数字滤波器的设计方法,并用该方法设计了一个高通滤波器。与用Parks-McClellan算法设计的高通滤波器进行了对比,发现基于粒子群优化算法的FIR滤波器的通带波动更小,阻带衰减更大。将用这两种算法设计的滤波器作用于混频信号,得出的结果也证明了基于粒子群优化算法的FIR滤波器的有效性。     

一种基于灰度的梯度边界检测优化算法*

为降低基于梯度的边界检测算法的复杂度,常使用两种梯度近似算法。但这些梯度近似值受边界方向的影响较大,降低了边界检测的性能。提出了通用梯度近似算法的数学模型和两种优化准则,进而推导出两种梯度近似的优化算法。分析表明：与常用算法相比,优化算法在各向同性的性能方面提高4.4倍,在梯度幅度的逼近度提高57倍。同时,给出了优化算法的简单快捷的实现方法。     

Analysis and application of a novel fast algorithm for 2-D ARMA model parameter estimation

In this paper, we analyze a novel algorithm for 2-D ARMA model parameter estimation in the presence of noise and then develop a fast and efficient blind image restoration algorithm. We show that the novel algorithm can minimize a quadratic convex optimization problem and has a lower computational complexity than the conventional algorithms. As a result, the novel algorithm involves no convergence and local minimum issue. Moreover, the proposed blind image restoration algorithm can overcome the local minimization problem. Computed results confirm that the novel algorithm can more quickly obtain more accurate estimates than the conventional algorithms in the presence of noise.     

Decomposition‐based multiinnovation gradient identification algorithms for a special bilinear system based on its input‐output representation

This article considers the parameter estimation for a special bilinear system with colored noise. Its input‐output representation is derived by eliminating the state variables in the bilinear system. Based on the input‐output representation of the bilinear system, a multiinnovation generalized extended stochastic gradient (MI‐GESG) algorithm is proposed by using the multiinnovation identification theory. Furthermore, a decomposition‐based multiinnovation (ie, hierarchical multiinnovation) generalized extended stochastic gradient identification (H‐MI‐GESG) algorithm is derived to enhance the parameter estimation accuracy by using the hierarchical identification principle, and a GESG algorithm is presented for comparison. Compared with the existing identification algorithms for the bilinear system, the proposed MI‐GESG and H‐MI‐GESG algorithms can generate more accurate parameter estimation. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms.