Observation Of Unbiased Estimation Of Linear Systems With Time-delay And Unknown Input

Recently,the measurement-delay systems with unknown inputs are used in many practical applications,such as data transmission systems,manufacturing systems,traffic control systems and so on.Due to the interference of the external environment,the limitation of the computing resources and the communication bandwidth,the observed data usually contains measurement-delay and unknown inputs.In addition,packet loss may occur on the transmission link.The existence of time delay,unknown inputs and the packet loss will reduce the accuracy of estimator,accordingly,reduce the accuracy of control actions.Apart from these,they are the source of potential instability.Therefore,the estimation problem of the measurement-delay systems with unknown inputs has been paid much attention by scholars.The early work for the systems with time delay has been investigated by the approaches of the system augmentation and the partial difference Riccati equation,but these two methods have high computational complexity.In general,it is often assumed that the noise is Gaussian when modeling a system,but since the external environment is not ideal,there may be interference with unknown statistics.In addition,due to the limitation of the bandwidth resources and the interference of the external environment,the observed data may also experience packet loss,and the packet loss leads to incomplete observation data,thereby they can reduce the accuracy of the estimation.For the above problems,the main works of this paper are list as follows:(1)For the estimation problems of the systems with time-delay and unknown inputs,we first use the reorganized innovation annalysis method to git rid of time-delay.Then,based on the unbiasedness,we obtain system's constraints.Finally,by using the Lagrangian multiplier and the principle of minimum variance estimation,we obtain the unbiased estimator for the systems with time-delay and unknown inputs.(2)For the estimation problems of the systems with time-delay?unknown inputs and package loss,firstly,in order to reasonably describe the package loss,we use the diagonal matrix.Then,based on the reorgnaized innovation method?the unbiasedness and the principle of minimum variance estimation,we obtain the system's estimator.(3)In order to prove the effectiveness of the estimator proposed above,we give some numerical examples by using MATLAB.