Kalman Filtering for Discrete Stochastic Systems with Multiplicative Noises and Random Two-Step Sensor Delays

Abstract

This paper is concerned with the optimal Kalman filtering problem for a class of discrete stochastic systems with multiplicative noises and random two-step sensor delays. Three Bernoulli distributed random variables with known conditional probabilities are introduced to characterize the phenomena of the random two-step sensor delays which may happen during the data transmission. By using the state augmentation approach and innovation analysis technique, an optimal Kalman filter is constructed for the augmented system in the sense of the minimum mean square error (MMSE). Subsequently, the optimal Kalman filtering is derived for corresponding augmented system in initial instants. Finally, a simulation example is provided to demonstrate the feasibility and effectiveness of the proposed filtering method.

Fusion Estimation from Multisensor Observations with Multiplicative Noises and Correlated Random Delays in Transmission

“…Next, we derive the recursive formulas to obtain the matrices r (ij) k , which clearly satisfy Equation (20) just by using Equation (9) and defining J (ij)…”

“…Furthermore, when the sensors send their measurements to the processing center via a communication network some additional network-induced phenomena, such as random delays or measurement losses, inevitably arise during this transmission process, which can spoil the fusion estimators performance and motivate the design of fusion estimation algorithms for systems with one (or even several) of the aforementioned uncertainties (see e.g., [12][13][14][15][16][17][18][19][20][21][22][23][24], and references therein). All the above cited papers on signal estimation with random transmission delays assume independent random delays at each sensor and mutually independent delays between the different sensors; in [25] this restriction was weakened and random delays featuring correlation at consecutive sampling times were considered, thus allowing to deal with some common practical situations (e.g., those in which two consecutive observations cannot be delayed).…”

“…For this reason, the fairly conservative assumption that the measurement noises are uncorrelated is commonly weakened in many of the aforementioned research papers on signal estimation. Namely, the optimal Kalman filtering fusion problem in systems with noise cross-correlation at consecutive sampling times is addressed, for example, in [19]; also, under different types of noise correlation, centralized and distributed fusion algorithms for systems with multiplicative noise are obtained in [11,20], and for systems where the measurements might have partial information about the signal in [7].…”

Least‐Squares Filtering Algorithm in Sensor Networks with Noise Correlation and Multiple Random Failures in Transmission

“…Also, centralized and distributed fusion algorithms are obtained in [15] for uncertain systems with correlated noises and in [5] for systems where the measurements might randomly contain only partial information about the signal. Also in [16] for systems with multiplicative noise and two-step random transmission delays, the centralized and distributed fusion estimation problems are addressed by using the state augmentation approach and, even though white noises are considered in the original model, the observation noises of the augmented system are correlated. Autocorrelated and cross-correlated noises have also been considered in systems with random parameter matrices and transmission uncertainties; some results on the fusion estimation problems in these systems can be found in [17,18], among others.…”

Networked Fusion Filtering from Outputs with Stochastic Uncertainties and Correlated Random Transmission Delays

“…These additional transmission uncertainties can spoil the fusion estimators performance and motivate the need of designing fusion estimation algorithms that take their effects into consideration. In recent years, in response to the popularity of networked stochastic systems, the fusion estimation problem from observations with random delays and packet dropouts, which may happen during the data transmission, has been one of the mainstream research topics (see, e.g., [ 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 ], and references therein). All the above papers on signal estimation with random transmission delays assume independent random delays in each sensor and mutually independent delays between the different network sensors; in [ 31 ] this restriction was weakened and random delays featuring correlation at consecutive sampling times were considered, thus allowing to deal with common practical situations (e.g., those in which two consecutive observations cannot be delayed).…”