In this paper different filtering techniques for nonlinear state estimation are explored and compared. We distinguish between approaches that approximate the nonlinear function (extended Kalman filter) and other approaches approximating the distribution of measurements and state (unscented Kalman filter and sequential Monte Carlo filter). The paper is showing both, the algorithms and simulated ...

One case is the problem of acoustic echo cancellation, where the digital filter employed has to identify as close as possible the acoustic echo path that is found to be highly nonlinear. In this situation a better system identification can be achieved by a nonlinear filter. The problem is to find a nonlinear filter structure able to realize a good approximation of the echo path without any sign...

In recent years, the Takagi–Sugeno (T–S) fuzzy model has been commonly used for the approximation of nonlinear systems. Using the T-S fuzzy model, nonlinear systems can be converted into linear time-varying systems, which can reduce approximation errors compared with the conventional Taylor approximation. In this paper, we propose a new nonlinear filter with a finite impulse response (FIR) stru...

In this paper, a nonlinear and/or nonnormal filter is proposed using rejection sampling. Generating random draws of the state-vector directly from the filtering density, the filtering estimate is simply obtained as the arithmetic average of the random draws. In the proposed filter, the random draws are recursively generated at each time. The Monte Carlo experiments indicate that the proposed no...

The particle filter (PF) has emerged as a powerful tool for solving nonlinear and/or non-Gaussian filtering problems. When some of the states enter the model linearly, this can be exploited by using particles only for the “nonlinear” states and employing conditional Kalman filters for the “linear” states; this leads to the Rao-Blackwellised particle filter (RBPF). However, it is well known that...

In this letter we assert that we have reconstructed the nonlinear filter function of LILI-128 stream cipher on IBM notebook PC using MATLAB. Our reconstruction need approximately 13 12 2 ~ 2 bits and the attack consumes 5825.016 sec (using tic and toc sentences of MATLAB) or 5825.016/3600=1.6181hours. We got the expression of the nonlinear filter function of Lili-128 which has 46 items from lin...

In INS (Inertial Navigation System) /GPS (Global Positioning System) integration, nonlinear models should be properly handled. The most popular and commonly used method is the Extended Kalman Filter (EKF) which approximates the nonlinear state and measurement equations using the first order Taylor series expansion. On the other hand, recently, some nonlinear filtering methods such as Gaussian S...

Preface These lecture notes are concerned with state estimation problem of linear and particularly nonlinear discrete and continuous-discrete stochastic systems. State estimation has a great variety of applications including The general solution of the state estimation problem is based on the Bayesian recursive relations and the Fokker-Planck equation which generate conditional probability dens...

Robust nonlinear integrated navigation of GPS and low cost MEMS is a hot topic of research these days. A robust filter is required to cope up with the problem of unpredictable discontinuities and colored noises associated with low cost sensors. H∞ filter is previously used in Extended Kalman filter and Unscented Kalman filter frame. Unscented Kalman filter has a problem of Cholesky matrix facto...

Discrete-time signal processing (DSP) tools have been used to analyze numerous optical filter configurations in order to optimize their linear response. In this paper, we propose a DSP approach to design nonlinear optical devices by treating the desired nonlinear response in the weak perturbation limit as a discrete-time filter. Optimized discrete-time filters can be designed and then mapped on...