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 ...

Over the last 20-30 years, the extended Kalman filter (EKF) has become the algorithm of choice in numerous nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system as well estimating parameters for nonlinear system identification (e.g., learning the weights of a neural network). The EKF applies the standard linear Kalman filter met...

Consider the following state space model (signal and observation model). Y t = H t X t + W t , W t ∼ N (0, R) (1) X t = F t X t−1 + U t , U t ∼ N (0, Q) (2)

The state-covariance of a linear filter is characterized by a certain algebraic commutativity property with the state matrix of the filter, and also imposes a generalized interpolation constraint on the power spectrum of the input process. This algebraic property and the relationship between state-covariance and the power spectrum of the input allow the use of matrix pencils and analytic interp...

The Probability Hypothesis Density (PHD) filter is a multipletarget filter for recursively estimating the number of targets and their state vectors from sets of observations. The filter is able to operate in environments with false alarms and missed detections. Two distinct algorithmic implementations of this technique have been developed. The first of which, called the Particle PHD filter, req...

Inferior vena cava (IVC) filters have become essential components in deep vein thrombosis treatment, and are particularly critical for preventing pulmonary embolisms in anticoagulation-resistant patients. Filter efficacy relies on maintaining IVC patency, or openness, by preventing filter-induced thrombosis following clot capture. A computational fluid dynamics (CFD) model has been developed to...

This paper develops a unified approach to the transient analysis of adaptive filters with error nonlinearities. In addition to deriving earlier results in a unified manner, the approach also leads to new performance results without restricting the regression data to being Gaussian or white. The framework is based on energy-conservation arguments and avoids the need for explicit recursions for t...

We propose a combination method for a diffusion affine projection algorithm. There are two steps to estimate unknown optimal weight in Adapt-then-combine strategy of diffusion adaptive filtering. In an adaptation step, variable step-size affine projection algorithm works to get an improvement of convergence rate and small steady-state error. In a diffusion step, the proposed combination method ...

A robust filter is designed for uncertain discrete time models. The filter is based on a regularized solution and guarantees minimum state error variance. Simulation results confirm its superior performance over other robust filter designs. keywords: regularization, least-squares, robust filter, regularization parameter, parametric uncertainty.