Rickard Karlsson

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.

Complexity analysis of the marginalized particle filter

In this paper, the computational complexity of the marginalized particle filter is analyzed and a general method to perform this analysis is given. The key is the introduction of the equivalent flop measure. In an extensive Monte Carlo simulation, different computational aspects are studied and compared with the derived theoretical results.

Particle filtering: the need for speed

The particle filter(PF) has during the last decade been proposed for a wide range of localization and tracking applications. There is a general need in such embedded system to have a platform for efficient and scalable implementation of the PF. One such platform is the graphics processing unit (GPU), originally aimed to be used for fast rendering of graphics. To achieve this, GPUs are equipped with a parallel architecture which can be exploited for general-purpose computing on GPU (GPGPU) as a complement to the central processing unit (CPU). In this paper, GPGPU techniques are used to make a parallel recursive Bayesian estimation implementation using particle filters. The modifications made to obtain a parallel particle filter, especially for the resampling step, are discussed and the performance of the resulting GPU implementation is compared to the one achieved with a traditional CPU implementation. The comparison is made using a minimal sensor network with bearings-only sensors. The resulting GPU filter, which is the first complete GPU implementation of a PF published to this date, is faster than the CPU filter when many particles are used, maintaining the same accuracy. The parallelization utilizes ideas that can be applicable for other applications.

Particle filtering and Cramer-Rao lower bound for underwater navigation

We have studied a sea navigation method relying on a digital underwater terrain map and sonar measurements. The method is applicable for both ships and underwater vessels. We have used experimental data to build an underwater map and to investigate the estimation performance. Since the problem is non-linear, due to the measurement relation, we apply a sequential Monte Carlo method, or particle filter, for the state estimation. The fundamental limitations in navigation uncertainty can be described in terms of the Cramer-Rao lower bound, which is interpreted in terms of the inertial navigation system (INS) error, the sensor accuracy and the terrain map excitation. Hence, the Cramer-Rao lower bound can be interpreted and used in the design for INS systems, sensor performance or, if these are given, how much terrain or depth excitation that is needed for use in positioning and navigation.

Particle filter for underwater terrain navigation

In an earlier contribution a particle filter for underwater (UW) navigation is proposed, and applied to an experimental trajectory. This paper focuses on performance improvements and analysis. First, the Cramer Rao lower bound (CRLB) along the experimental trajectory is computed, which is only slightly lower than the particle filter estimate after initial transients. Simple rule of thumbs for how performance depends on the map and sensor quality are derived. Second, a more realistic five state model is proposed, and Rao-Blackwellization is applied to decrease computational complexity. Monte-Carlo simulations on the map demonstrate a performance comparable to the CRLB.

Auxiliary particle filters for tracking a maneuvering target

We consider the recursive state estimation of a highly maneuverable target. We apply optimal recursive Bayesian filters directly to the nonlinear target model. We present novel sequential simulation based algorithms developed explicitly for the maneuvering target tracking problem. These Monte Carlo filters perform optimal inference by simulating a large number of tracks, or particles. Each particle is assigned a probability weight determined by its likelihood. The main advantage of our approach is that linearizations and Gaussian assumptions need not be considered. Instead, a nonlinear model is directly used during the prediction and likelihood update. Detailed nonlinear dynamics models and non-Gaussian sensors can therefore be utilized in an optimal manner resulting in high performance gains. In a simulation comparison with current state-of-the-art tracking algorithms we show that our approach yields performance improvements.

Statistical results for system identification based on quantized observations

System identification based on quantized observations requires either approximations of the quantization noise, leading to suboptimal algorithms, or dedicated algorithms tailored to the quantization noise properties. This contribution studies fundamental issues in estimation that relate directly to the core methods in system identification. As a first contribution, results from statistical quantization theory are surveyed and applied to both moment calculations (mean, variance etc) and the likelihood function of the measured signal. In particular, the role of adding dithering noise at the sensor is studied. The overall message is that tailored dithering noise can considerably simplify the derivation of optimal estimators. The price for this is a decreased signal to noise ratio, and a second contribution is a detailed study of these effects in terms of the Cramer–Rao lower bound. The common additive uniform noise approximation of quantization is discussed, compared, and interpreted in light of the suggested approaches.

Range estimation using angle-only target tracking with particle filters

We consider the recursive state estimation of a maneuverable aircraft using an airborne passive IR-sensor. The main issue addressed in the paper is the range- and velocity estimation using angle-only measurements. In contrast to standard target tracking literature we do not rely on linearized motion models and measurement relations, or on any Gaussian assumptions. Instead, we apply optimal recursive Bayesian filters directly to the nonlinear target model. We present novel sequential simulation based algorithms developed explicitly for the angle-only target tracking problem. These Monte Carlo filters approximate optimal inference by simulating a large number of tracks, or particles. In a simulation study our particle filter approach is compared to a range parameterized extended Kalman filter (RPEKF). Tracking is performed in both Cartesian and modified spherical coordinates (MSC).

Bayesian Surface and Underwater Navigation

A common framework for maritime surface and underwater (UW) map-aided navigation is proposed as a supplement to satellite navigation based on the global positioning system (GPS). The proposed Bayesian navigation method is based on information from a distance measuring equipment (DME) which is compared with the information obtained from various databases. As a solution to the recursive Bayesian navigation problem, the particle filter is proposed. For the described system, the fundamental navigation performance expressed as the Crameacuter-Rao lower bound (CRLB) is analyzed and an analytic solution as a function of the position is derived. Two detailed examples of different navigation applications are discussed: surface navigation using a radar sensor and a digital sea chart and UW navigation using a sonar sensor and a depth database. In extensive Monte Carlo simulations, the performance is shown to be close to the CRLB. The estimation performance for the surface navigation application is in comparison with usual GPS performance. Experimental data are also successfully applied to the UW application

Particle Filter SLAM with High Dimensional Vehicle Model

This work presents a particle filter method closely related to Fastslam for solving the simultaneous localization and mapping (slam) problem. Using the standard Fastslam algorithm, only low-dimensional vehicle models can be handled due to computational constraints. In this work, an extra factorization of the problem is introduced that makes high-dimensional vehicle models computationally feasible. Results using experimental data from an unmanned aerial vehicle (helicopter) are presented. The proposed algorithm fuses measurements from on-board inertial sensors (accelerometer and gyro), barometer, and vision in order to solve the slam problem.