Quantitative measures of observability for stochastic systems

Subaşı, Yüksel
The observability measure based on the mutual information between the last state and the measurement sequence originally proposed by Mohler and Hwang (1988) is analyzed in detail and improved further for linear time invariant discrete-time Gaussian stochastic systems by extending the definition to the observability measure of a state sequence. By using the new observability measure it is shown that the unobservable states of the deterministic system have no effect on this measure and any observable part with no measurement uncertainty makes it infinite. Other distance measures i.e., Bhattacharyya and Hellinger distances are also investigated to be used as observability measures. The relationships between the observability measures and the covariance matrices of Kalman filter and the state sequence conditioned on the measurement sequence are derived. Steady state characteristics of the observability measure based on the last state is examined. The observability measures of a subspace of the state space, an individual state, the modes of the system are investigated. One of the results obtained in this part is that the deterministically unobservable states may have nonzero observability measures. The observability measures based on the mutual information are represented recursively and calculated for nonlinear stochastic systems. Then the measures are applied to a nonlinear stochastic system by using the particle filter methods. The arguments given for the LTI case are also observed for nonlinear stochastic systems. The second moment approximation deviates from the actual values when the nonlinearity in the system increases.


Quantitative measure of observability for linear stochastic systems
Subasi, Yuksel; Demirekler, Mübeccel (Elsevier BV, 2014-06-01)
In this study we define a new observability measure for stochastic systems: the mutual information between the state sequence and the corresponding measurement sequence for a given time horizon. Although the definition is given for a general system representation, the paper focuses on the linear time invariant Gaussian case. Some basic analytical results are derived for this special case. The measure is extended to the observability of a subspace of the state space, specifically an individual state and/or t...
Geometric measures of entanglement
UYANIK, KIVANÇ; Turgut, Sadi (American Physical Society (APS), 2010-03-01)
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.
Fuzzy neural network learning method for time series analysis using multivariate autoregression
Sisman, NA; Alpaslan, Ferda Nur (1998-11-13)
This paper describes how temporal fuzzy neural network model proposed in [4] can be applied to time series analysis when a multivariate autoregressive model is constructed. The fuzzy multivariate autoregression procedure is described first, then the temporal fuzzy neural network model using this procedure is presented.
Galois structure of modular forms of even weight
Gurel, E. (Elsevier BV, 2009-10-01)
We calculate the equivariant Euler characteristics of powers of the canonical sheaf on certain modular curves over Z which have a tame action of a finite abelian group. As a consequence, we obtain information on the Galois module structure of modular forms of even weight having Fourier coefficients in certain ideals of rings of cyclotomic algebraic integers. (c) 2009 Elsevier Inc. All rights reserved.
Linearization and optimization of robot dynamics via inertial parameter design
Soylu, Reşit (1996-08-01)
In this article, the concept of linearity number (LN) is introduced to measure the ''linearity'' of the equations of motion of a serial manipulator. This number is computable in closed-form and is an average quantitative index of the degree of linearity of the robot over a specified region in the joint space. The definition is flexible, allowing the user to create custom-made definitions according to his or her specific needs. Using the concept of LN and the developed computer package CADLOR, one can design...
Citation Formats
Y. Subaşı, “Quantitative measures of observability for stochastic systems,” Ph.D. - Doctoral Program, Middle East Technical University, 2012.