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While nonlinear filtering for circular quantities is closely related to nonlinear filtering on linear domains, the underlying manifold enables the development of novel filters that take advantage of the boundedness of the domain. Previously, we introduced Fourier filters that approximate the density or its square root using Fourier series. For these filters, we proposed filter steps for arbitrary...
We propose a novel progressive Gaussian filter for nonlinear stochastic systems. A Gaussian approximation of the posterior is computed without an explicit assumption of a linear relation between the system state and the measurement. This allows for better quality of the estimation compared to Kalman filters for nonlinear problems like the EKF or UKF. In this work, we use the progressive filter framework,...
Recursive filtering with multimodal likelihoods and transition densities on periodic manifolds is, despite the compact domain, still an open problem. We propose a novel filter for the circular case that performs well compared to other state-of-the-art filters adopted from linear domains. The filter uses a limited number of Fourier coefficients of the square root of the density. This representation...
Circular estimation problems arise in many applications and can be addressed with the help of circular distributions. In particular, the wrapped normal and von Mises distributions are widely used in the context of circular problems. To facilitate the development of nonlinear filters, a deterministic sample-based approximation of these distributions with a so-called wrapped Dirac mixture distribution...
A new Gaussian filter for estimating the state of nonlinear systems is derived that relies on two main ingredients: i) the progressive inclusion of the measurement information and ii) a tight coupling between a Gaussian density and its deterministic Dirac mixture approximation. No second Gaussian assumption for the joint density of state and measurement is required, so that the performance is much...
Since the advent of Monte-Carlo particle filtering, particle representations of densities have become increasingly popular due to their flexibility and implicit adaptive resolution. In this paper, an algorithm for the multiplication of a systematic Dirac mixture (DM) approximation with a continuous likelihood function is presented, which applies a progressive correction scheme, in order to avoid the...
In this paper, the estimation of conditional densities of continuous random variables from noisy samples is considered. The conditional densities are modeled as heteroscedastic Gaussian mixture densities allowing for closed-form solution of Bayesian inference with full densities. The key idea is a regularization based on the curvature of the conditional density function's surface. The main contributions...
Multilateration systems operate by determining distances between a signal transmitter and a number of receivers. In aerial surveillance, radio signals are emitted as Secondary Surveillance Radar (SSR) by the aircraft, representing the signal transmitter. A number of base stations (sensors) receive the signals at different times. Most common approaches use time difference of arrival (TDOA) measurements,...
A non-parametric conditional density estimation algorithm for nonlinear stochastic dynamic systems is proposed. The contributions are a novel support vector regression for estimating conditional densities, modeled by Gaussian mixture densities, and an algorithm based on cross-validation for automatically determining hyper-parameters for the regression. The conditional densities are employed with a...
Indoor WLAN positioning should be modeled as a nonlinear and non-Gaussian dynamic system due to the complex indoor environment, radio propagation and motion behaviour. The aim of this paper is to analyze different filtering strategies for real life indoor WLAN positioning systems. The performance criteria for the comparison are the mean of localization errors and computational complexity. Three nonlinear...
A deterministic procedure for optimal approximation of arbitrary probability density functions by means of Dirac mixtures with equal weights is proposed. The optimality of this approximation is guaranteed by minimizing the distance of the approximation from the true density. For this purpose a distance measure is required, which is in general not well defined for Dirac mixtures. Hence, a key contribution...
This paper is concerned with the absolute localization of mobile robots, which are equipped with an onboard device performing angular measurements on the location of known but mutually indistinguishable landmarks. Novel algorithms are proposed, 1. for efficient posture initialization based on a simple linear solution scheme, and 2. for purposes of recursive posture estimation. Derived within a set-theoretic...
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