A Two-Step Approach for Offset and Position Estimation from Pseudo-Ranges Applied to Multilateration Tracking

In multilateration tracking, an object, e.g., an airplane, emits a known reference signal, which is received by several base stations (sensors) located at known positions. The receiving times of the signal at the sensors correspond to the times of arrival (TOA) plus an unknown offset, because the emission time is unknown. Usually, for estimating the position of the object, the receiving times are converted to a larger number of time differences of arrival (TDOA) in order to eliminate the unknown offset. To avoid this conversion, the proposed approach directly uses the receiving times. This is achieved by 1. determining the optimal offset from the redundant measurements in closed form and 2. by considering a modified measurement equation. As a result, position estimation can be performed by optimal stochastic linearization

Probabilistische modellbasierte Signalverarbeitung zur instantanen Lageschätzung

In dieser Arbeit werden Modelle und Verfahren für die instantane Verarbeitung von Messsignalen im Bereich der Lageschätzung vorgestellt. Dabei wird eine durchgängige mathematische Systembeschreibung gewählt, um die auftretenden Unsicherheiten, welche durch die Messungen und durch die Modellierung auftreten, zu berücksichtigen. Bei der Lageschätzung werden die Translation und die Rotation eines Objekts bezüglich eines Koordinatensystems bestimmt

Gaussian Filtering using State Decomposition Methods

State estimation for nonlinear systems generally requires approximations of the system or the probability densities, as the occurring prediction and filtering equations cannot be solved in closed form. For instance, Linear Regression Kalman Filters like the Unscented Kalman Filter or the considered Gaussian Filter propagate a small set of sample points through the system to approximate the posterior mean and covariance matrix. To reduce the number of sample points, special structures of the system and measurement equation can be taken into account. In this paper, two principles of system decomposition are considered and applied to the Gaussian Filter. One principle exploits that only a part of the state vector is directly observed by the measurement. The second principle separates the system equations into linear and nonlinear parts in order to merely approximate the nonlinear part of the state. The benefits of both decompositions are demonstrated on a real-world example

The Sliced Gaussian Mixture Filter with Adaptive State Decomposition Depending on Linearization Error

In this paper, a novel nonlinear/non-linear model decomposition for the Sliced Gaussian Mixture Filter is presented. Based on the level of nonlinearity of the model, the overall estimation problem is decomposed into a severely nonlinear and a slightly nonlinear part, which are processed by different estimation techniques. To further improve the efficiency of the estimator, an adaptive state decomposition algorithm is introduced that allows decomposition according to the linearization error for nonlinear system and measurement models. Simulations show that this approach has orders of magnitude less complexity compared to other state of the art estimators, while maintaining comparable estimation errors

Decentralized State Estimation of Distributed Phenomena based on Covariance Bounds

This paper addresses the problem of decentralized state estimation of distributed physical phenomena observed by a sensor network. The centralized approaches are not scalable for large sensor networks, because all information has to be transmitted to a powerful central processing node requiring an extensive amount of communication bandwidth and a lot of processing power. Thus, for a decentralized reconstruction of distributed phenomena, we propose a novel methodology consisting of three steps: (a) conversion of the distributed phenomenon into a lumped-parameter system description, (b) decomposition of the resulting system in order to map the description to the actual sensor network, and (c) decomposition of the density representation leading to a decentralized estimation approach. The main problem of a decentralized approach is that due to the propagation of local information through the network, unknown correlations are caused. This fact needs to be considered during the reconstruction process in order to get correct and consistent estimation results. For that reason, we employ a robust estimator (based on Covariance Bounds) for the local reconstruction update on each sensor node. By this means, the individual sensor nodes are able to estimate the local state of the distributed phenomenon using local estimates obtained and communicated by adjacent nodes only. The information about their correlations is not stored in the sensor network

Wireless Acoustic Tracking for Extended Range Telepresence

Telepresence systems enable a user to experience virtual or distant environments by providing sensory feedback. Appropriate devices include head mounted displays (HMD) for visual perception, headphones for auditory response, or even haptic displays for tactile sensation and force feedback. While most common designs use dedicated input devices like joysticks or a space mouse, the approach followed in the present work takes the user\u27s position and viewing direction as an input, as he walks freely in his local surroundings. This is achieved by using acoustic tracking, where the user\u27s pose (position and orientation) is estimated on the basis of ranges measured between a set of wall-fastened loudspeakers and a microphone array fixed on the user\u27s HMD. To allow for natural user motion, a wearable, fully wireless telepresence system is introduced. The increase in comfort compared to wired solutions is obvious, as the user\u27s awareness of distracting cables is taken away during walking. Also the lightweight design and small dimensions contribute to ergonomics, as the whole assembly fits well into a small backpack

(Semi-)Analytic Gaussian Mixture Filter

In nonlinear filtering, special types of Gaussian mixture filters are a straightforward extension of Gaussian filters, where linearizing the system model is performed individually for each Gaussian component. In this paper, two novel types of linearization are combined with Gaussian mixture filters. The first linearization is called analytic stochastic linearization, where the linearization is performed analytically and exactly, i.e., without Taylor-series expansion or approximate sample-based density representation. In cases where a full analytical linearization is not possible, the second approach decomposes the nonlinear system into a set of nonlinear subsystems that are conditionally integrable in closed form. These approaches are more accurate than fully applying classical linearization

Semi-Analytic Stochastic Linearization for Range-Based Pose Tracking

In range-based pose tracking, the translation and rotation of an object with respect to a global coordinate system has to be estimated. The ranges are measured between the target and the global frame. In this paper, an intelligent decomposition is introduced in order to reduce the computational effort for pose tracking. Usually, decomposition procedures only exploit conditionally linear models. In this paper, this principle is generalized to conditionally integrable substructures and applied to pose tracking. Due to a modified measurement equation, parts of the problem can even be solved analytically

Semi-Analytic Gaussian Assumed Density Filter

For Gaussian Assumed Density Filtering based on moment matching, a framework for the efficient calculation of posterior moments is proposed that exploits the structure of the given nonlinear system. The key idea is a careful discretization of some dimensions of the state space only in order to decompose the system into a set of nonlinear subsystems that are conditionally integrable in closed form. This approach is more efficient than full discretization approaches. In addition, the new decomposition is far more general than known Rao-Blackwellization approaches relying on conditionally linear subsystems. As a result, the new framework is applicable to a much larger class of nonlinear systems

Efficient Multilateration Tracking with Concurrent Offset Estimation using Stochastic Filtering Techniques

Multilateration systems operate by deter- mining distances between a signal transmitter and a number of receivers. In aerial surveillance, radio sig- nals 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 dif- ference of arrival (TDOA) measurements, calculated by subtracting receiving times of one receiver from another. As TDOAs require intersecting hyperboloids, which is considered a hard task, this paper follows a different ap- proach, using raw receiving times. Thus, estimating the signal\u27s emission time is required, captured as a com- mon offset within an augmented version of the system state. This way, the multilateration problem is reduced to intersecting cones. Estimation of the aircraft\u27s posi- tion based on a nonlinear measurement model and an underlying linear system model is achieved using a lin- ear regression Kalman filter [1, 2]. A decomposed com- putation of the filter step is introduced, allowing a more efficient calculation