Kalman filtering: theory and practice
Kalman filtering: theory and practice
On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Wide area traffic: the failure of Poisson modeling
IEEE/ACM Transactions on Networking (TON)
Signal processing with fractals: a wavelet-based approach
Signal processing with fractals: a wavelet-based approach
IEEE/ACM Transactions on Networking (TON)
On the relationship between file sizes, transport protocols, and self-similar network traffic
ICNP '96 Proceedings of the 1996 International Conference on Network Protocols (ICNP '96)
The Karhunen-Loève Transform of Discrete MVL Functions
ISMVL '05 Proceedings of the 35th International Symposium on Multiple-Valued Logic
Estimation and equalization of fading channels with random coefficients
ICASSP '96 Proceedings of the Acoustics, Speech, and Signal Processing, 1996. on Conference Proceedings., 1996 IEEE International Conference - Volume 02
Signal modeling and parameter estimation for 1/f processes using scale stationary models
ICASSP '96 Proceedings of the Acoustics, Speech, and Signal Processing, 1996. on Conference Proceedings., 1996 IEEE International Conference - Volume 05
IEEE Transactions on Signal Processing
A class of second-order stationary self-similar processes for 1/fphenomena
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
On the use of fractional Brownian motion in the theory of connectionless networks
IEEE Journal on Selected Areas in Communications
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In this paper, we develop a state space representation and Kalman filtering method for self-similar processes. Key components of our development are the concept of multivariate self-similarity and the mathematical framework of scale stationarity. We define multivariate self-similarity as joint self-similarity, in which the self-similarity is governed by a matrix valued parameter H. Such a generalization suits the nature of Multi-Input Multi-Output (MIMO) systems, since each channel is likely to be governed by a different self-similarity parameter. The system and measurement models for the proposed Kalman filter are defined as tx˙(t) = tHAt-Hx(t) + tHBu(t) and y(t) = Cx(t) + Dv(t), respectively. Here, the derivative operator tx˙(t) indicates that the memory of the process is stored in time scales, unlike the memory stored in time shifts for stationary processes. We exploit this fact in developing an insightful interpretation of the Riccati equation and the Kalman gain matrix, which lead to an efficient numerical implementation of the proposed Kalman filter via exponential sampling. Additionally, we include a discussion of network traffic modeling and communications applications of the proposed Kalman filter. This study demonstrates that the scale stationarity framework leads to mathematically tractable and physically intuitive formulation of Kalman filtering for self-similar processes.