Fredrik Gustafsson

Particle filters for positioning, navigation, and tracking

A framework for positioning, navigation, and tracking problems using particle filters (sequential Monte Carlo methods) is developed. It consists of a class of motion models and a general nonlinear measurement equation in position. A general algorithm is presented, which is parsimonious with the particle dimension. It is based on marginalization, enabling a Kalman filter to estimate all position derivatives, and the particle filter becomes low dimensional. This is of utmost importance for high-performance real-time applications. Automotive and airborne applications illustrate numerically the advantage over classical Kalman filter-based algorithms. Here, the use of nonlinear models and non-Gaussian noise is the main explanation for the improvement in accuracy. More specifically, we describe how the technique of map matching is used to match an aircrafts elevation profile to a digital elevation map and a cars horizontal driven path to a street map. In both cases, real-time implementations are available, and tests have shown that the accuracy in both cases is comparable with satellite navigation (as GPS) but with higher integrity. Based on simulations, we also argue how the particle filter can be used for positioning based on cellular phone measurements, for integrated navigation in aircraft, and for target tracking in aircraft and cars. Finally, the particle filter enables a promising solution to the combined task of navigation and tracking, with possible application to airborne hunting and collision avoidance systems in cars.

Mobile positioning using wireless networks: possibilities and fundamental limitations based on available wireless network measurements

Positioning in wireless networks is mainly used for safety, gaming, and commercial services. It is expected to increase in popularity when emergency call services become mandatory as well as with the advent of more advanced location-based services and mobile gaming. In this article, we discuss and illustrate the possibilities and fundamental limitations associated with mobile positioning based on available wireless network measurements. The possibilities include a sensor fusion approach and model-based filtering, while the fundamental limitations provide hard bounds on the accuracy of position estimates, given the information in the measurements in the most favorable situation. The focus of this article is to illustrate the relation between performance requirements, such as those stated by the Federal Communications Commission (FCC), and the available measurements. Specific issues on accuracy limitation in each measurement, such as synchronization and multipath problems, are briefly commented upon. A geometrical example, as well as a realistic example adopted from a cell planning tool, are used for illustration.

Slip-based tire-road friction estimation

An approach to estimate the tire-road friction during normal drive using only the wheel slip, that is, the relative difference in wheel velocities, is presented. The driver can be informed about the maximum friction force and be alarmed for sudden changes. Friction-related parameters are estimated using only signals from standard sensors in a modern car. An adaptive estimator is presented for a model linear in parameters, which is designed to work for periods of poor excitation, errors in variables, simultaneous slow and fast parameter drifts and abrupt changes. The physical relation between these parameters and the maximal friction force is determined from extensive field trials using a Volvo 850 GLT as a test car.

Marginalized particle filters for mixed linear/nonlinear state-space models

The particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and non-Gaussian filtering problems. While the particle filter is fairly easy to implement and tune, its main drawback is that it is quite computer intensive, with the computational complexity increasing quickly with the state dimension. One remedy to this problem is to marginalize out the states appearing linearly in the dynamics. The result is that one Kalman filter is associated with each particle. The main contribution in this paper is the derivation of the details for the marginalized particle filter for a general nonlinear state-space model. Several important special cases occurring in typical signal processing applications will also be discussed. The marginalized particle filter is applied to an integrated navigation system for aircraft. It is demonstrated that the complete high-dimensional system can be based on a particle filter using marginalization for all but three states. Excellent performance on real flight data is reported.

A unifying construction of orthonormal bases for system identification

This paper develops a general and very simple construction for complete orthonormal bases for system identification. This construction provides a unifying formulation of many previously studied orthonormal bases since the common FIR and recently popular Laguerre and two-parameter Kautz model structures are restrictive special cases of the construction presented here. However, in contrast to these special cases, the basis vectors in the unifying construction of this paper can have arbitrary placement of pole position according to the prior information the user wishes to inject. Results characterizing the completeness of the bases and the accuracy properties of models estimated using the bases are provided.

PaperSlip-based tire-road friction estimation☆

An approach to estimate the tire-road friction during normal drive using only the wheel slip, that is, the relative difference in wheel velocities, is presented. The driver can be informed about the maximum friction force and be alarmed for sudden changes. Friction-related parameters are estimated using only signals from standard sensors in a modern car. An adaptive estimator is presented for a model linear in parameters, which is designed to work for periods of poor excitation, errors in variables, simultaneous slow and fast parameter drifts and abrupt changes. The physical relation between these parameters and the maximal friction force is determined from extensive field trials using a Volvo 850 GLT as a test car.

Particle filter theory and practice with positioning applications

The particle filter (PF) was introduced in 1993 as a numerical approximation to the nonlinear Bayesian filtering problem, and there is today a rather mature theory as well as a number of successful applications described in literature. This tutorial serves two purposes: to survey the part of the theory that is most important for applications and to survey a number of illustrative positioning applications from which conclusions relevant for the theory can be drawn. The theory part first surveys the nonlinear filtering problem and then describes the general PF algorithm in relation to classical solutions based on the extended Kalman filter (EKF) and the point mass filter (PMF). Tuning options, design alternatives, and user guidelines are described, and potential computational bottlenecks are identified and remedies suggested. Finally, the marginalized (or Rao-Blackwellized) PF is overviewed as a general framework for applying the PF to complex systems. The application part is more or less a stand-alone tutorial without equations that does not require any background knowledge in statistics or nonlinear filtering. It describes a number of related positioning applications where geographical information systems provide a nonlinear measurement and where it should be obvious that classical approaches based on Kalman filters (KFs) would have poor performance. All applications are based on real data and several of them come from real-time implementations. This part also provides complete code examples.

On Resampling Algorithms for Particle Filters

In this paper a comparison is made between four frequently encountered resampling algorithms for particle filters. A theoretical framework is introduced to be able to understand and explain the differences between the resampling algorithms. This facilitates a comparison of the algorithms with respect to their resampling quality and computational complexity. Using extensive Monte Carlo simulations the theoretical results are verified. It is found that systematic resampling is favourable, both in terms of resampling quality and computational complexity.

Determining the initial states in forward-backward filtering

Forward-backward filtering is a common tool in off-line filtering for implementing noncausal filters. Filtering first forward and then backward or the other way around does not generally give the same result. Here, we propose a method to choose the initial state to obtain uniqueness and to remove transients at both ends.

Positioning using time-difference of arrival measurements

The problem of position estimation from time difference of arrival (TDOA) measurements occurs in a range of applications from wireless communication networks to electronic warfare positioning. Correlation analysis of the transmitted signal to two receivers gives rise to one hyperbolic function. With more than two receivers, we can compute more hyperbolic functions, which ideally intersect in one unique point. With TDOA measurement uncertainty, we face a non-linear estimation problem. We suggest and compare a Monte Carlo based method for positioning and a gradient search algorithm using a nonlinear least squares framework. The former has the feature of being easily extended to a dynamic framework where a motion model of the transmitter is included. A small simulation study is presented.