Fritsche, Carsten
Orguner, Umut
Gustafsson, Fredrik
Parametric Cramer-Rao lower bounds (CRLBs) are given for discrete-time systems with non-zero process noise. Recursive expressions for the conditional bias and mean-square-error (MSE) (given a specific state sequence) are obtained for Kalman filter estimating the states of a linear Gaussian system. It is discussed that Kalman filter is conditionally biased with a non-zero process noise realization in the given state sequence. Recursive parametric CRLBs are obtained for biased estimators for linear state estimators of linear Gaussian systems. Simulation studies are conducted where it is shown that Kalman filter is not an efficient estimator in a conditional sense.


Continuous-time nonlinear estimation filters using UKF-aided gaussian sum representations
Gökçe, Murat; Kuzuoğlu, Mustafa; Department of Electrical and Electronics Engineering (2014)
A nonlinear filtering method is developed for continuous-time nonlinear systems with observations/measurements carried out in discrete-time by means of UKFaided Gaussian sum representations. The time evolution of the probability density function (pdf) of the state variables (or the a priori pdf) is approximated by solving the Fokker-Planck equation numerically using Euler’s method. At every Euler step, the values of the a priori pdf are evaluated at deterministic sample points. These values are used with Ga...
Recent results on Bayesian Cramér-Rao bounds for jump Markov systems
Fritsche, Carsten; Orguner, Umut; Svensson, Lennart; Gustafsson, Fredrik (2016-07-08)
In this paper, recent results on the evaluation of the Bayesian Cramer-Rao bound for jump Markov systems are presented. In particular, previous work is extended to jump Markov systems where the discrete mode variable enters into both the process and measurement equation, as well as where it enters exclusively into the measurement equation. Recursive approximations are derived with finite memory requirements as well as algorithms for checking the validity of these approximations are established. The tightnes...
On plateaued functions, linear structures and permutation polynomials
Mesnager, Sihem; Kaytancı, Kübra; Özbudak, Ferruh (2019-01-01)
We obtain concrete upper bounds on the algebraic immunity of a class of highly nonlinear plateaued functions without linear structures than the one was given recently in 2017, Cusick. Moreover, we extend Cusick’s class to a much bigger explicit class and we show that our class has better algebraic immunity by an explicit example. We also give a new notion of linear translator, which includes the Frobenius linear translator given in 2018, Cepak, Pasalic and Muratović-Ribić as a special case. We find some app...
Investigation of decoupling techniques for linear and nonlinear systems
Kalaycıoğlu, Taner; Özgüven, Hasan Nevzat; Department of Mechanical Engineering (2018)
Structural coupling methods are widely used in predicting dynamics of coupled systems. In this study, the reverse problem, i.e. predicting the dynamic behavior of a particular subsystem from the knowledge of the dynamics of the overall system and of all the other subsystems, is studied. This problem arises when a substructure cannot be measured separately, but only when coupled to neighboring substructures. The dynamic decoupling problem of coupled linear structures is well investigated in literature. Howev...
Nonlinear system identification and nonlinear experimental modal analysis by using response controlled stepped sine testing
Karaağaçlı, Taylan; Özgüven, Hasan Nevzat; Department of Mechanical Engineering (2020-12-24)
In this work, two novel nonlinear system identification methods are proposed in both the modal and spatial domains, respectively, based on response-controlled stepped-sine testing (RCT) where the displacement amplitude of the excitation point is kept constant throughout the frequency sweep. The proposed nonlinear modal identification method, which is also a nonlinear experimental modal analysis technique, applies to systems with several nonlinearities at different (and even unknown) locations (e.g. joint no...
Citation Formats
C. Fritsche, U. Orguner, and F. Gustafsson, “ON PARAMETRIC LOWER BOUNDS FOR DISCRETE-TIME FILTERING,” 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/53898.