Frederik Beutler

Closed-form range-based posture estimation based on decoupling translation and orientation

For estimating the posture, i.e., position and orientation, of an extended target based on range measurements, a new closed-form solution is proposed; it is based on decoupling position and orientation. For decoupling, any procedure for range-based localization of point targets, i.e., for mere position estimation, can be used. The new solution is suboptimal, but nevertheless provides good accuracy and is very practical from an application point of view.

An experimental evaluation of position estimation methods for person localization in wireless sensor networks

In this paper, the localization of persons by means of aWireless Sensor Network (WSN) is considered. Persons carry on-body sensor nodes and move within a WSN. The location of each person is calculated on this node and communicated through the network to a central data sink for visualization. Applications of such a system could be found in mass casualty events, firefighter scenarios, hospitals or retirement homes for example. For the location estimation on the sensor node, three derivatives of the Kalman filter and a closed-form solution (CFS) are applied, compared, and evaluated in a real-world scenario. A prototype 65-node ZigBeeWSN is implemented and data are collected in in- and outdoor environments with differently positioned on-body nodes. The described estimators are then evaluated off-line on the experimentally collected data. The goal of this paper is to present a comprehensive real-world evaluation of methods for person localization in a WSN based on received signal strength (RSS) range measurements. It is concluded that person localization in in- and outdoor environments is possible under the considered conditions with the considered filters. The compared methods allow for sufficiently accurate localization results and are robust against inaccurate range measurements.

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.

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.

Optimal stochastic linearization for range-based localization

In range-based localization, the trajectory of a mobile object is estimated based on noisy range measurements between the object and known landmarks. In order to deal with this uncertain information, a Bayesian state estimator is presented, which exploits optimal stochastic linearization. Compared to standard state estimators like the Extended or Unscented Kalman Filter, where a point-based Gaussian approximation is used, the proposed approach considers the entire Gaussian density for linearization. By employing the common assumption that the state and measurements are jointly Gaussian, the linearization can be calculated in closed form and thus analytic expressions for the range-based localization problem can be derived.

The Probabilistic Instantaneous Matching Algorithm

A new Bayesian filtering technique for estimating signal parameters directly from discrete-time sequences is introduced. The so called probabilistic instantaneous matching algorithm recursively updates the probability density function of the parameters for every received sample and, thus, provides a high update rate up to the sampling rate with high accuracy. In order to do so, one of the signal sequences is used as part of a time-variant nonlinear measurement equation. Furthermore, the time-variant nature of the parameters is explicitly considered via a system equation, which describes the evolution of the parameters over time. An important feature of the probabilistic instantaneous matching algorithm is that it provides a probability density function over the parameter space instead of a single point estimate. This probability density function can be used in further processing steps, e.g. a range based localization algorithm in the case of time-of-arrival estimation

Instantaneous pose estimation using rotation vectors

An algorithm for estimating the pose, i.e., translation and rotation, of an extended target object is introduced. Compared to conventional methods, where pose estimation is performed on the basis of time-of-flight (TOF) measurements between external sources and sensors attached to the object, the proposed approach directly uses the amplitude values measured at the sensors for estimation purposes without an intermediate TOF estimation step. This is achieved by modeling the wave propagation by a nonlinear dynamic system comprising a system and a measurement equation. The nonlinear system equation includes a model of the time-variant structure of the object rotation based on rotation vectors. As a result, the measured amplitude values at the sensors can be processed instantaneously in a recursive fashion. Uncertainties in the measurement process are systematically considered by employing a stochastic filter for estimating the pose, i.e., the state of the nonlinear dynamic system.

Probabilistic instantaneous model-based signal processing applied to localization and tracking

In this paper, a probabilistic approach for estimating time and space-variant parameters of a system, based on sequentially received discrete-time signal values, is presented. The system description is the solution of a linear partial differential equation (PDE). The PDE describes for example the wave propagation of an acoustic wave in a localization system. The solution of the PDE is given by a time-variant and space-variant impulse response. This impulse response is characterized by the time and space-variant parameters in order to track an object, which emits for example an acoustic signal. For estimating the position of the object in an instantaneous way a Bayesian approach has to be used, which considers the dynamic behavior of the parameters in a system model and uncertainties in a stochastic manner by means of probability density functions. Hence, the new approach provides a probabilistic instantaneous model-based signal processing, where the sequentially measured signal values are processed directly and known reference signal sequences are interpreted as part of a time-variant nonlinear measurement equation.

(Semi-)Analytic Gaussian Mixture Filter

Abstract 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.

Efficient multilateration tracking with concurrent offset estimation using stochastic filtering techniques

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, 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 approach, using raw receiving times. Thus, estimating the signals emission time is required, captured as a common offset within an augmented version of the system state. This way, the multilateration problem is reduced to intersecting cones. Estimation of the aircrafts position based on a nonlinear measurement model and an underlying linear system model is achieved using a linear regression Kalman filter [1, 2]. A decomposed computation of the filter step is introduced, allowing a more efficient calculation.