Kalman Filtering Algorithm for Systems with Stochastic Nonlinearity Functions, Finite-Step Correlated Noises, and Missing Measurements

• Published in: Discrete dynamics in nature and society Vol. 2018; no. 2018; pp. 1 - 12
• Main Authors: Zhuo, Shufang, Huang, Hischuan, Jiang, Jibin, He, Yonghui, Wu, Yanfeng
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2018; Hindawi; John Wiley & Sons, Inc; Wiley
• Subjects: Algorithms; Analysis; Correlation analysis; Covariance matrix; Design; Discrete time systems; Economic models; Error detection; Euclidean space; Filtration; Kalman filters; Mathematical models; Mean square errors; Nonlinearity; Random variables; Sensors; Signal processing; Tracking systems
• ISSN: 1026-0226; 1607-887X
• DOI: 10.1155/2018/1516028

The locally optimal filter is designed for a class of discrete-time systems subject to stochastic nonlinearity functions, finite-step correlated noises, and missing measurements. The multiplicative noises are employed to describe the random disturbances in the system model. The phenomena of missing measurements occur in a random way and the missing probability is characterized by Bernoulli distributed random variables with known conditional probabilities. Based on the projection theory, a class of Kalman-type locally optimal filter is constructed and the filtering error covariance matrix is minimized in the sense of minimum mean square error principle. Also, by solving the recursive matrix equation, we can obtain the filter gain. Finally, two examples are provided: one is a numerical example to illustrate the feasibility and effectiveness of the proposed filtering scheme; the other is to solve the problem of target estimation for a tracking system considering networked phenomena.