Estimability of the linear effects in state space models with an unknown initial condition

In the case of state space models with an unknown initial condition, the diffuse Kalman smoother can be used to obtain smoothed state estimates. When the full initial state is not estimable because the available data are insufficient, some linear combinations of the states can still be estimable. This brief note provides a simple method to determine whether a linear combination of a state is estimable.     

随机系统的可估计性──信息理论方法

本文在信息理论的框架下研究了随机系统的可估计性问题，对于线性高斯系统导出了其可估计性判据，并讨论了可估计性与相应确定性中观测性之间的关系。     

Self‐alignment and calibration of a MEMS IMU: Improving observability and estimability by rotary motions of IMU

The stationary self‐alignment and calibration (SSAC) for a low‐cost MEMS IMU is quite challenging due to the poor observability of an inertial system under static condition and the significant sensor errors of MEMS inertial sensors. This research proposes to employ IMU rotations to improve the system observability and estimability regarding the SSAC of a low‐cost MEMS IMU. IMU rotations about the X, Y, and Z axes are employed in this paper. The analytic estimation algorithm for each error state is derived and the observability of the system with IMU rotation is analyzed. As the observability analysis will not provide clues about how well an error state can be estimated, the estimability analysis is also conducted based on the eigenvalues and eigenvectors from the covariance matrix in the Kalman filter. Tests are conducted with a tri‐axial turntable to verify the improvements on system observability and estimability brought by IMU rotations. Of both theoretical analysis and results indicated with proper IMU rotations, only azimuth error still remains unobservable, and the IMU rotation also significantly improves the estimability of all error states, including the unobservable azimuth.     

Mathematical modelling of chemical processes—obtaining the best model predictions and parameter estimates using identifiability and estimability procedures

Chemical engineers who develop fundamental models often have difficulties estimating all model parameters due to problems with parameter identifiability and estimability. These two concepts are reviewed, as are techniques for assessing identifiability and estimability. When some parameters are not estimable from the data, modellers must decide whether to conduct new experiments, change the model structure, or to estimate only a subset of the parameters and leave the others at fixed values. Estimating a reduced number of parameters can lead to better model predictions with lower mean squared error (MSE). MSE‐based techniques for parameter subset selection are discussed and compared. © 2011 Canadian Society for Chemical Engineering     

通讯约束下的线性系统状态降维与估计

本文面向状态估计, 考察了通讯功率受限时线性动态系统状态的降维问题. 为了满足平行信道传输数据的维数限制和通讯功率约束, 采取降低状态维数的方法, 通过传输信号的新息, 提高传输效率, 利用有限的通信资源, 使得接收端的状态估计达到最优. 本文采用差分脉冲编码调制系统(DPCM), 基于最小误差熵估计准则和Kalman估计算法, 得出了最优的状态降维矩阵的设计方法, 并且对随机系统的可估计性以及对相应确定性系统的能观性进行了分析. 分析和仿真结果表明, 这种设计方法在传输信号满足通讯功率限制的条件下可以使接收端的状态估计性能达到最优.     

测角无源定位与跟踪的观测器自适应运动分析

本文采用定位的位置误差GDOP(Geometrical Dilution of Precision)作为优化对象,具体分析二维无源定位的可估计性优化问题,通过边估计边优化观测器运动的方法,以期在定位的各个时刻能得到最优的定位精度.本文还证明了在GDOP标准下,跟踪问题中的观测器运动寻优方法与其对应的定位问题相同.从而解决了在测角无源定位与跟踪中为了提高定位精度观测器如何进行自适应运动的问题.     

Estimability and stochastic observability of quantised linear systems

The estimability and stochastic observability of quantised discrete-time linear dynamic systems are discussed from information theoretic viewpoint. Algebraic conditions of estimability and stochastic observability for quantised linear Gaussian systems, i.e., certain Gramians having full rank, are proposed based on the measure of mutual information. The obtained conditions of estimability and observability are consistent with the intuition and provide us with valuable hints on quantiser design. It is shown analytically that the Gramians of quantised systems converge to that of unquantised systems when the quantisation intervals turn to zero, and a well-designed quantiser can preserve the estimability and stochastic observability of the original system even if it is as coarse as one bit. Furthermore, the relation between estimability and stochastic observability is established for quantised stochastically autonomous systems. The analytical results are verified by illustrative simulations.     

Kinetic parameter estimation of HDPE slurry process from molecular weight distribution: Estimability analysis and multistep methodology

This study addresses kinetic parameter estimation for a high‐density polyethylene (HDPE) slurry process based on fitting molecular weight distributions (MWDs). From the process model, we conduct an estimability analysis by assessing the relative sensitivity between output variables and kinetic parameters as well as confidence intervals. This determines which parameters can be estimated. Conversely, a major challenge remains with the solution of an ill‐conditioned parameter estimation problem with MWD as the output variable. To overcome the convergence difficulties with the associated problem, we develop a novel multistep methodology where we first obtain MWD parameters by matching to data and then estimate kinetic parameters by matching to the regressed MWD parameters. Computational results and eigenvalue analysis show this multistep methodology separates an ill‐conditioned problem into two well‐conditioned subproblems. Moreover, we consider simulation‐based and industrial HDPE case studies. These results demonstrate the applicability, potential, and efficiency of this solution procedure. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3442–3459, 2014     

Observability of the ambient conditions in model‐based estimation for wind farm control: A focus on static models

Wind farm control (WFC) algorithms rely on an estimate of the ambient wind speed, wind direction, and turbulence intensity in the determination of the optimal control setpoints. However, the measurements available in a commercial wind farm do not always carry sufficient information to estimate these atmospheric quantities. In this paper, a novel measure (“observability”) is introduced that quantifies how well the ambient conditions can be estimated with the measurements at hand through a model inversion approach. The usefulness of this measure is shown through several case studies. While the turbine power signals and the inter‐turbine wake interactions provide information on the wind direction, the case studies presented in this article show that there is a strong need for wind direction measurements for WFC to sufficiently cover observability for any ambient condition. Further, generally, more wake interaction leads to a higher observability. Also, the mathematical framework presented in this article supports the straightforward notion that turbine power measurements provide no additional information compared with local wind speed measurements, implying that power measurements are superfluous. Irregular farm layouts result in a higher observability due to the increase in unique wake interaction. The findings in this paper may be used in WFC to predict which ambient quantities can (theoretically) be estimated. The authors envision that this will assist in the estimation of the ambient conditions in WFC algorithms and can lead to an improvement in the performance of WFC algorithms over the complete envelope of wind farm operation.