The extended Kalman filter (EKF) is a popular state estimation method for nonlinear dynamical models. The model error covariance matrix is often seen as a tuning parameter in EKF, which is often simply postulated by the user. In this paper, we study the filter likelihood technique for estimating the parameters of the model error covariance matrix. The approach is based on computing the likeliho...

A group of mobile robots can localize cooperatively, using relative position and absolute orientation measurements, fused through an extended Kalman filter (ekf). The topology of the graph of relative measurements is known to affect the steady state value of the position error covariance matrix. Classes of sensor graphs are identified, for which tight bounds for the trace of the covariance matr...

this paper presents an approach for solving a nonlinear stochastic differential equations (nsdes) using a new basis functions (nbfs). these functions and their operational matrices areused for representing matrix form of the nbfs. with using this method in combination with the collocation method, the nsdes are reduced a stochastic nonlinear system of equations and unknowns. then, the error anal...

The task of matrix completion involves estimating the entries of a matrix, M ∈ Rm×n, when a subset, Ω ⊂ {(i, j) : 1 ≤ i ≤ m, 1 ≤ j ≤ n} of the entries are observed. A particular set of low rank models for this task approximate the matrix as a product of two low rank matrices, M̂ = UV T , where U ∈ Rm×k and V ∈ Rn×k and k min{m,n}. A popular algorithm of choice in practice for recovering M from t...

We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising it; and a priori bounds on the error of each entry, individually. In the noiseless case our algorithm is exact. For rank-one matrices, the new algorithm is fas...

We consider the decoding of convolutional codes using an error trellis constructed based on a submatrix of a given check matrix. In the proposed method, the syndromesubsequence computed using the remaining submatrix is utilized as auxiliary information for decoding. Then the ML error path is correctly decoded using the degenerate error trellis. We also show that the decoding complexity of the p...

Several authors have recently considered a parallel method for solving sparse triangular systems with many right-hand sides. The method employs a partition into sparse factors of the product form of the inverse of the coefficient matrix. It is shown here that while the method can be unstable, stability is guaranteed if a certain scalar that depends on the matrix and the partition is small and t...

Neutral stability limits for wake flow behind a flat plate is studied using spectral method. First, Orr-Sommerfeld equation was changed to matrix form, covering the whole domain of solution. Next, each term of matrix was expanded using Chebyshev expansion series, a series very much equivalent to the Fourier cosine series. A group of functions and conditions are applied to start and end points i...

In this research paper, we use a normalized graph cut measure as a thresholding principle to separate an object from the background based on the standard S membership function. The implementation of the proposed algorithm known as fuzzy normalized graph cut method. This proposed algorithm compared with the fuzzy entropy method [25], Kittler [11], Rosin [21], Sauvola [23] and Wolf [33] method. M...