Nonlinear Stochastic Filtering and Estimation

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Author Index
A B C D E F G H I
J K L M N O P Q R
S T U V W X Y Z

Approximate Nonlinear Filtering and Its Applications for GPS

Authors:

Babak Azimi-Sadjadi, Perinkulam S. Krishnaprasad,

Volume: 1, Page 1579 Paper number 2096

Abstract:

In this paper we address the problem of nonlinear filtering in the presence of integer uncertainty. This setup is specially important for the case of differential GPS with carrier phase measurements. In simulation results we show that Particle Filtering is capable of resolving integer ambiguity in the given nonlinear setup. Motivated by these results we introduce a new Particle Filtering algorithm that can reduce the computational complexity for a certain class of problems. In this class, it is assumed that the conditional density of the state of the system given the observations is close to a known exponential family of densities.

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Stability and Approximation of Nonlinear Filters in the Hilbert Metric, and Application to Particle Filters

Authors:

François LeGland, Nadia Oudjane,

Volume: 1, Page 1585 Paper number 1833

Abstract:

In this paper, the stability of the optimal filter w.r.t. its initial condition and w.r.t. the model, is studied in a general HMM using the Hilbert projective metric. These stability results are then used to prove the uniform convergence of the interacting particle filter to the optimal filter, as the number of particles goes to infinity.

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Inversion of Nonlinear Stochastic Models for Parameter Estimation

Authors:

Ola Markusson, Haakan Hjalmarsson,

Volume: 1, Page 1591 Paper number 1338

Abstract:

Prediction error and maximum likelihood estimation of nonlinear stochastic models requires inversion of the model, a step which may require substantial efforts, either in terms of manual calculations or through the use of software capable of symbolic computations. In this paper we show that model inversion can be easily implemented in numerical software such as, e.g., Simulink and MatrixX, by means of a feedback connection based on the model. We derive sufficient conditions for the existence of a stable causal inverse as well as sufficient conditions for the initial transient to decay. These conditions are given in terms of properties for a linear time-varying system associated with the nonlinear model. The method is illustrated on a numerical example.

CD001338.PDF (From Author)

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Robust Kalman Filter Design for Hybrid Systems with Norm-Bounded Unknown Nonlinearities

Authors:

Peng Shi, Mehmet Karan, C. Yalcin Kaya,

Volume: 1, Page 1597 Paper number 1792

Abstract:

This paper considers the filtering problem for a class of linear hybrid systems with nonlinear uncertainties and Markovian jump parameters. The unknown nonlinearities in the system are time-varying and norm-bounded. First, we show the equivalence of the norm bounded linear and nonlinear uncertainty sets. Then, instead of the original hybrid linear system with nonlinear uncertainties, we consider the same system with linear uncertainties. By using a Riccati equation approach for this new system, a robust filter is designed using two sets of coupled Riccati-like equations such that the estimation error is guaranteed to have an upper bound.

CD001792.PDF (From Author) CD001792.PDF (Scanned)

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Efficiency of an Approximate Filter for a Particular Class of Nonlinear Diffusions with Observations Corrupted by Small Noise

Authors:

Paula Milheiro-Oliveira, Jean Picard,

Volume: 1, Page 1599 Paper number 1130

Abstract:

The asymptotic behaviour of a nonlinear continuous time approximate filter when the variance of the observation noise tends to 0 is investigated. We consider a particular class of signals modeled by a two-dimensional quasi-linear diffusion from which only one of the components is noisy, and we assume that a one-dimensional linear function of the signal, depending only of the unnoisy component, is observed in a low noise channel. Under some detectability assumptions the unobserved signal can be restored by means of an approximate nonlinear filter. We establish that the filtering error converges to 0 and we give an upper bound for the convergence rate. The efficiency of the approximate filter is compared with the efficiency of the optimal filter and the order of magnitude of the error between the two filters, as the observation noise vanishes, is obtained. A more general case is briefly presented.

CD001130.PDF (From Author)

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