Estimation of systems with statistically-constrained inputs

This paper discusses the estimation of a class of discrete-time linear stochastic systems with statistically-constrained unknown inputs (UI), which can represent an arbitrary combination of a class of un-modeled dynamics, random UI with unknown covariance matrix and deterministic UI. In filter design, an upper bound filter is explored to compute, recursively and adaptively, the upper bounds of covariance matrices of the state prediction error, innovation and state estimate error. Furthermore, the minimum upper bound filter (MUBF) is obtained via online scalar parameter convex optimization in pursuit of the minimum upper bounds. Two examples, a system with multiple piecewise UIs and a continuous stirred tank reactor (CSTR), are used to illustrate the proposed MUBF scheme and verify its performance.     

抑制高阶谐波误差的随机相移条纹分析算法

高阶谐波和随机相移误差是影响条纹分析精度的主要因素。为了同时解决这两个问题,提出了基于频域滤波的迭代相移算法。该算法采用巴特沃斯低通滤波器,从频域上滤除条纹的高阶谐波分量,再运用最小二乘迭代方法从三帧随机相移条纹图像中提取相位信息。数值模拟和实验结果表明,该算法可有效地抑制由高阶谐波和随机相移引入的波纹误差,误差PV值和RMS值分别为0.368 8 rad和0.025 3 rad,其精度高于传统的三步相移算法和Wang算法。该方法适合于高精度干涉测量和三维物体表面轮廓测量。     

基于窗口傅里叶变换剪切干涉法波前检测

提出了一种利用二维窗口傅里叶变换从径向剪切干涉条纹中准确得到波前的重建技术。首先对剪切干涉条纹做二维窗口傅里叶变换,设置阈值和频率积分范围后,进行二维窗口傅里叶逆变换,然后对包裹相位做去载频和相位展开处理得到相位差分布,最后使用波前迭代算法从相位差中复原实际波前。模拟计算表明,使用该方法最大相位复原误差为0.82%,均方根值为0.020 9 rad,实验结果验证了该方法的有效性。同时也对窗口傅里叶变换的关键参数,如窗函数的选择、窗口大小的确定以及阈值的选取等进行了简要讨论。与传统傅里叶变换法(FFT)相比,基于窗口傅里叶变换的剪切干涉波前检测法有更高的精度和稳定性,为波前检测提供一种新的处理方法。     

Conditional hitting time estimation in a nonlinear filtering model by the Brownian bridge method

We consider a model composed of a signal process X given by a classic stochastic differential equation and an observation process Y, which is supposed to be correlated to the signal process. We assume that process Y is observed from time 0 to s>0 at discrete times and aim to estimate, conditionally on these observations, the probability that the non-observed process X crosses a fixed barrier after a given time t>0. We formulate this problem as a usual nonlinear filtering problem and use optimal quantization and Monte Carlo simulations techniques to estimate the involved quantities.     

The nisio semigroup for controlled diffusions with partial observations

A one parameter semigroup of nonlinear operators on an appropriate Banach space is constructed in the spirit of Nisio for controlled diffusions with partial observations. The method is based upon considering an equivalent problem of controlling a measure-valued process representing the conditional law of the state given past observations. The latter evolves according to the usual equations of nonlinear filtering. By considering an appropriate augmentation of the class of controls, it is shown that the “minimum cost” operators associated with this control problem indeed form a semigroup of nonlinear contractions on the space of bounded continuous real-valued functions on the state space of the above measure-valued process.     

A filtering problem with a small nonlinear term

In this paper, we consider a filtering problem where the signal X _t satisfies a slightly nonlinear stochastic differential equation and we want to obtain estimates of X _t. To this end, we decompose the nonlinearity with two techniques—a deterministic one and a stochastic one—and this leads us to two sequences of estimates which can be computed by solving finite dimensional equations. We want to compare their performances: we solve this problem in most cases if we restrict ourselves to sufficiently small times t and we give conditions which permit to conclude also for larger times     

Nonlinear filtering and large deviations:a pde-control theoretic approach

We consider the asymptotic nonlinear filtering problem dx=f(x)dt + ?^1/2 dw,dy=h(x) dt + ? dv and obtain lim_?→0 ? log q ²(x,t) = -W(x,t) for unnormalized conditional densities q ²(x,t) using PDE methods. HereW(x,t) is the value function for a deterministic optimal control problem arising in Mortensen's deterministic estimation, and is the unique viscosity solution of a Hamilton-Jacobi-Bellman equation. ijab has also studied this filtering problem, and we extend his large deviation result for certain unnormalized conditional measures. The resulting variational problem corresponds to the above control problem     

The stability of stochastic partial differential equations II

We prove general results on stability (in finite time intervals) of SPDEs (stochastic partial differential equations) with unbounded coefficients, with respect to the simultaneous perturbations of the driving semimartingales, of all data, and of the underlying probability space. Hence we derive support theorems for SPDEs (with unbounded coefficients). In particular, we get theorems on supports and theorems on robustness for the nonlinear filter of diffusion processes with unbounded drift and diffusion coefficients. (The above results were proved in the case of bounded coefficients in our earlier papers [4] and [5].) Finally we treat an application in a problem of kinematic dynamo     

Optimal transmission of “television type” gaussian signals through a noiseless feedback channel

Using the methods and results of the theory of conditionally Gaussian filtering of stochastic processes and fields, an optimal scheme of “television type” signal transmission through a noiseless feedback channel is constructed under the usual power conditions, the signals being evolutionary Gaussian fields θ={θ_t(x)),tε[0,T),xεDεRⁿ . Explicit representations for optimal coding and decoding functionals, which are optimal in the sense of a special square criterion, and the expression for the error of signal reproduction are given.