The Sliced Gaussian Mixture Filter for Efficient Nonlinear Estimation

This paper addresses the efficient state estimation for mixed linear/nonlinear dynamic systems with noisy measurements. Based on a novel density representation - sliced Gaussian mixture density - the decomposition into a (conditionally) linear and nonlinear estimation problem is derived. The systematic approximation procedure minimizing a certain distance measure allows the derivation of (close to) optimal and deterministic estimation results. This leads to high-quality representations of the measurement-conditioned density of the states and, hence, to an overall more efficient estimation process. The performance of the proposed estimator is compared to state-of-the-art estimators, like the well-known marginalized particle filter

Simultaneous State and Parameter Estimation of Distributed-Parameter Physical Systems based on Sliced Gaussian Mixture Filter

This paper presents a method for the simultaneous state and parameter estimation of finite-dimensional models of distributed systems monitored by a sensor network. In the first step, the distributed system is spatially and temporally decomposed leading to a linear finite-dimensional model in state space form. The main challenge is that the simultaneous state and parameter estimation of such systems leads to a high-dimensional nonlinear problem. Thanks to the linear substructure contained in the resulting finite-dimensional model, the development of an overall more efficient estimation process is possible. Therefore, in the second step, we propose the application of a novel density representation - sliced Gaussian mixture density - in order to decompose the estimation problem into a (conditionally) linear and a nonlinear problem. The systematic approximation procedure minimizing a certain distance measure allows the derivation of (close to) optimal and deterministic results. The proposed estimation process provides novel prospects in sensor network applications. The performance is demonstrated by means of simulation results

Bayesian Estimation with Uncertain Parameters of Probability Density Functions

In this paper, we address the problem of processing imprecisely known probability density func- tions by means of Bayesian estimation. The imprecise knowledge about probability density functions is given as stochastic uncertainty about their parameters. The proposed processing of this special density in a Bayesian estimator is accomplished by reinterpretation of the Fil- ter and prediction equations. Here, the parameters are treated as a higher order state, which can be processed by Bayesian estimation techniques. For state estima- tion, this avoids the need to select specific values for unknown parameters and, thus, allows the processing of all potential parameters at once. The proposed approach further allows the use of imprecisely known model equa- tions for measurement and state prediction by the same principle

Distributed detection, localization, and estimation in time-critical wireless sensor networks

In this thesis the problem of distributed detection, localization, and estimation (DDLE) of a stationary target in a fusion center (FC) based wireless sensor network (WSN) is considered. The communication process is subject to time-critical operation, restricted power and bandwidth (BW) resources operating over a shared communication channel Buffering from Rayleigh fading and phase noise. A novel algorithm is proposed to solve the DDLE problem consisting of two dependent stages: distributed detection and distributed estimation. The WSN performs distributed detection first and based on the global detection decision the distributed estimation stage is performed. The communication between the SNs and the FC occurs over a shared channel via a slotted Aloha MAC protocol to conserve BW. In distributed detection, hard decision fusion is adopted, using the counting rule (CR), and sensor censoring in order to save power and BW. The effect of Rayleigh fading on distributed detection is also considered and accounted for by using distributed diversity combining techniques where the diversity combining is among the sensor nodes (SNs) in lieu of having the processing done at the FC. Two distributed techniques are proposed: the distributed maximum ratio combining (dMRC) and the distributed Equal Gain Combining (dEGC). Both techniques show superior detection performance when compared to conventional diversity combining procedures that take place at the FC. In distributed estimation, the segmented distributed localization and estimation (SDLE) framework is proposed. The SDLE enables efficient power and BW processing. The SOLE hinges on the idea of introducing intermediate parameters that are estimated locally by the SNs and transmitted to the FC instead of the actual measurements. This concept decouples the main problem into a simpler set of local estimation problems solved at the SNs and a global estimation problem solved at the FC. Two algorithms are proposed for solving the local problem: a nonlinear least squares (NLS) algorithm using the variable projection (VP) method and a simpler gird search (GS) method. Also, Four algorithms are proposed to solve the global problem: NLS, GS, hyperspherical intersection method (HSI), and robust hyperspherical intersection (RHSI) method. Thus, the SDLE can be solved through local and global algorithm combinations. Five combinations are tied: NLS2 (NLS-NLS), NLS-HSI, NLS-RHSI, GS2, and GS-N LS. It turns out that the last algorithm combination delivers the best localization and estimation performance. In fact , the target can be localized with less than one meter error. The SNs send their local estimates to the FC over a shared channel using the slotted-Aloha MAC protocol, which suits WSNs since it requires only one channel. However, Aloha is known for its relatively high medium access or contention delay given the medium access probability is poorly chosen. This fact significantly hinders the time-critical operation of the system. Hence, multi-packet reception (MPR) is used with slotted Aloha protocol, in which several channels are used for contention. The contention delay is analyzed for slotted Aloha with and without MPR. More specifically, the mean and variance have been analytically computed and the contention delay distribution is approximated. Having theoretical expressions for the contention delay statistics enables optimizing both the medium access probability and the number of MPR channels in order to strike a trade-off between delay performance and complexity

Learning Dynamic Systems for Intention Recognition in Human-Robot-Cooperation

This thesis is concerned with intention recognition for a humanoid robot and investigates how the challenges of uncertain and incomplete observations, a high degree of detail of the used models, and real-time inference may be addressed by modeling the human rationale as hybrid, dynamic Bayesian networks and performing inference with these models. The key focus lies on the automatic identification of the employed nonlinear stochastic dependencies and the situation-specific inference

Nonlinear Gaussian Filtering : Theory, Algorithms, and Applications

By restricting to Gaussian distributions, the optimal Bayesian filtering problem can be transformed into an algebraically simple form, which allows for computationally efficient algorithms. Three problem settings are discussed in this thesis: (1) filtering with Gaussians only, (2) Gaussian mixture filtering for strong nonlinearities, (3) Gaussian process filtering for purely data-driven scenarios. For each setting, efficient algorithms are derived and applied to real-world problems

Nonlinear state and parameter estimation of spatially distributed systems

In this thesis two probabilistic model-based estimators are introduced that allow the reconstruction and identification of space-time continuous physical systems. The Sliced Gaussian Mixture Filter (SGMF) exploits linear substructures in mixed linear/nonlinear systems, and thus is well-suited for identifying various model parameters. The Covariance Bounds Filter (CBF) allows the efficient estimation of widely distributed systems in a decentralized fashion