Department of Electrical Engineering (ISY)

A novel method for accurate speed estimation of a vehicle using a deep learning convolutional neural network (CNN), with accelerometer and gyroscope measurements as input, is presented. It does not suffer from the fundamental drift problem present in all dead reckoning methods, and yet yields about 2 m/s in accuracy. Efficient drift-free vehicle speed estimates are essential in many automotive applications, where internal wheel speed sensors or GPS are unavailable. Using extensive experimental data, the proposed CNN method is compared to an existing frequency analysis method. The proposed method is shown to perform significantly better, particularly during low speed and rapid speed changes where the frequency method struggles.

Most navigation systems today rely on global navigation satellite systems (gnss), including in cars. With support from odometry and inertial sensors, this is a sufficiently accurate and robust solution, but there are future demands. Autonomous cars require higher accuracy and integrity. Using the car as a sensor probe for road conditions in cloud-based services also sets other kind of requirements. The concept of the Internet of Things requires stand-alone solutions without access to vehicle data. Our vision is a future with both invehicle localization algorithms and after-market products, where the position is computed with high accuracy in gnss-denied environments. We present a localization approach based on a prior that vehicles spend the most time on the road, with the odometer as the primary input. When wheel speeds are not available, we present an approach solely based on inertial sensors, which also can be used as a speedometer. The map information is included in a Bayesian setting using the particle filter (PF) rather than standard map matching. In extensive experiments, the performance without gnss is shown to have basically the same quality as utilizing a gnss sensor. Several topics are treated: virtual measurements, dead reckoning, inertial sensor information, indoor positioning, off-road driving, and multilevel positioning.

The norm-optimal iterative learning control (ilc) algorithm for linear systems is extended to an estimation-based norm-optimal ilc  algorithm where the controlled variables are not directly available as measurements. A separation lemma is presented, stating that if a stationary Kalman filter is used for linear time-invariant systems then the ilc  design is independent of the dynamics in the Kalman filter. Furthermore, the objective function in the optimisation problem is modified to incorporate the full probability density function of the error. Utilising the Kullback–Leibler divergence leads to an automatic and intuitive way of tuning the ilc  algorithm. Finally, the concept is extended to non-linear state space models using linearisation techniques, where it is assumed that the full state vector is estimated and used in the ilc  algorithm. Stability and convergence properties for the proposed scheme are also derived.

A sensor fusion method for state estimation of a flexible industrial robot is developed. By measuring the acceleration at the end-effector, the accuracy of the arm angular position, as well as the estimated position of the end-effector are improved. The problem is formulated in a Bayesian estimation framework and two solutions are proposed; the extended Kalman filter and the particle filter. In a simulation study on a realistic flexible industrial robot, the angular position performance is shown to be close to the fundamental Cramér-Rao lower bound. The technique is also verified in experiments on an ABB robot, where the dynamic performance of the position for the end-effector is significantly improved.

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.

This work presents a particle filter (PF) 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 a UAV (helicopter) are presented. The algorithm fuses measurements from on-board inertial sensors (accelerometer and gyro), barometer, and vision in order to solve the SLAM problem.

For certain types of sensor-target configurations, a point target model or approach is not suitable and the physical extent of the target is accounted for during processing. An extended target track-before-detect (TBD) algorithm is presented and the performance is compared to an algorithm based on the point target assumption. Simulations illustrate the gain in performance obtained by using the extended target model where a particle filter is used for the TBD implementation.

Recursive Bayesian estimation methods are applied to several angle-only applications. Air-to-air passive ranging, in addition to an air-to-sea application with terrain induced constraints, is discussed. The incorporation of terrain information improves estimation performance. The bearings-only problem is also discussed using experimental data from a torpedo, i.e. sea-to-sea with a passive sonar sensor. The Bayesian estimation problem is solved using the particle filter and the marginalised particle filter. For comparison, a filter bank method using range parameterised extended Kalman filters is used.

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 non-linear 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 non-linear 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 aircraft's elevation profile to a digital elevation map, and a car's 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 to 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.

The Handbook of Intelligent Vehicles provides a complete coverage of the fundamentals, new technologies, and sub-areas essential to the development of intelligent vehicles; it also includes advances made to date, challenges, and future trends. Significant strides in the field have been made to date; however, so far there has been no single book or volume which captures these advances in a comprehensive format, addressing all essential components and subspecialties of intelligent vehicles, as this book does. Since the intended users are engineering practitioners, as well as researchers and graduate students, the book chapters do not only cover fundamentals, methods, and algorithms but also include how software/hardware are implemented, and demonstrate the advances along with their present challenges. Research at both component and systems levels are required to advance the functionality of intelligent vehicles. This volume covers both of these aspects in addition to the fundamentals listed above. 

In this paper, an indoor vehicle multi-level positioning algorithm is proposed that makes use of an indoor map, as well as dead-reckoning sensor information that is available in every car. A particle filter framework is used for online optimal Bayesian vehicle positioning with indoor-outdoor transitions. The method is validated experimentally in two indoor multi-level car parks. The achieved results indicate that accurate indoor positioning is possible already today without relying on expensive technology such as e.g. laser scanners or additional hardware.

The speed of a wheeled vehicle is usually estimatedusing wheel speed sensors (WSS) or GPS. If these signals are unavailable, other methods must be used. We propose a novelapproach exploiting the fact that vibrations from rotating axles,with fundamental frequency proportional to vehicle speed, aretransmitted via the vehicle chassis. Using an accelerometer, these vibrations can be tracked to estimate vehicle speed whileother sources of vibrations act as disturbances. A state-space model for the dynamics of the harmonics is presented andformulated such that there is a conditional linear-Gaussiansubstructure, enabling efficient Rao-Blackwellized methods. Avariant of the Rao-Blackwellized point-mass filter is derived, significantly reducing computational complexity, and reducingthe memory requirements from quadratic to linear in thenumber of grid points. It is applied to experimental data from the sensor cluster of a car and validated using therotational frequency from WSS data. The proposed methodshows improved performance and robustness in comparisonto a Rao-Blackwellized particle filter implementation and afrequency spectrum maximization method.

An estimation-based iterative learning control (ILC) algorithm is applied to a realistic industrial manipulator model. By measuring the acceleration of the end-effector, the arm angular position accuracy is improved when the measurements are fused with motor angle observations. The estimation problem is formulated in a Bayesian estimation framework where three solutions are proposed: one using the extended Kalman filter (EKF), one using the unscented  Kalman filter (UKF), and one using the particle filter (PF).  The estimates are used in an ILC method to improve the accuracy for following a given reference trajectory.  Since the ILC algorithm is repetitive no computational restrictions on the methods apply explicitly. In an extensive Monte Carlo simulation study it is shown that the PF method outperforms the other methods and that the ILC control law is substantially improved using the PF estimate.

A sensor fusion method for state estimation of a flexible industrial robot is presented. By measuring the acceleration at the end-effector, the accuracy of the arm angular position is improved significantly when these measurements are fused with motor angle observation. The problem is formulated in a Bayesian estimation framework and two solutions are proposed; one using the extended Kalman filter (EKF) and one using the particle filter (PF). The technique is verified on experiments on the ABB IRB4600 robot, where the accelerometer method is showing a significant better dynamic performance, even when model errors are present.

This contribution aims at unifying two recent trends in applied particle filtering (PF). The first trend is the major impact in simultaneous localization and mapping (SLAM) applications, utilizing the FastSLAM algorithm. Thesecond one is the implications of the marginalized particle filter (MPF) or the Rao-Blackwellized particle filter (RBPF) in positioning and tracking applications. Using the standard FastSLAM algorithm, only low-dimensional vehicle modelsare computationally feasible. In this work, an algorithm is introduced which merges FastSLAM and MPF, and the result is an algorithm for SLAM applications, where state vectors of higher dimensions can be used. Results using experimental data from a UAV (helicopter) are presented. The algorithmfuses measurements from on-board inertial sensors (accelerometer and gyro) and vision in order to solve the SLAM problem, i.e., enable navigation over a long period of time.

For performance gain and efficiency it is important to utilize model structure in particle filtering. Applying Bayes- rule, present linear Gaussian substructure can be efficiently handled by a bank of Kalman filters. This is the standard formulation of the Rao-Blackwellized particle filter (RBPF), by some authors denoted the marginalized particle filter (MPF), and usually presented in a way that makes it hard to implement in an object oriented fashion. This paper discusses how the solution can be rewritten in order to increase the understanding as well as simplify the implementation and reuse of standard filtering components, such as Kalman filter banks and particle filters. Calculations show that the new algorithm is equivalent to the classical formulation, and the new algorithm is exemplified in a target tracking simulation study.

In this paper, several recursive Bayesian filtering methods for target tracking are discussed. Performance for target tracking problems is usually measured using the second-order moment. For nonlinear or non-Gaussian applications, this measure is not always sufficient. The Kullback divergence is proposed as an alternative to mean square error analysis, and it is extensively used to compare estimated posterior distributions for various applications. The important issue of efficient software development, for nonlinear and non-Gaussian estimation, is also addressed. A new framework in C++ is detailed. Utilizing modern design techniques an object oriented filtering and simulation framework is provided to allow for easy and efficient comparisons of different estimators. The software environment is extensively used in several applications and examples.

The marginalized particle filter is a powerful combination of the particle filter and the Kalman filter, which can be used when the underlying model contains a linear substructure subject to Gaussian noise. This paper surveys state of the art for theory and practice.

Performance for many filtering problems is usually measured using the second order moment. For non-Gaussian application this measure is not always sufficient. In the paper the Kullback divergence is extensively used to compare distributions. Several estimation techniques are compared, and methods such as the particle filter are shown to give superior performance over some classical second-order estimators.

In the CDIO-project course in Automatic Control, an Autonomous Unmanned Aerial vehicle (UAV) is constructed, utilizing an existing radio controlled model aircraft. By adding an inertial sensor measuring acceleration and rotation, together with a Global Positioning System (GPS) sensor, the aim is to construct an accurate positioning system. This is used by an on board computer to calculate rudder control signals to a set of DC-servos in order to follow a predefined way-point trajectory. The project involves 17 students, which is roughly three times as big as previous projects, and it comprises both positioning, control, and hardware design. Since the project is still ongoing some preliminary results and conclusions are presented.

The marginalized particle filter is a powerful combination of the particle filter and the Kalman filter, which can be used when the underlying model contains a linear sub-structure, subject to Gaussian noise. This paper will illustrate several positioning and target tracking applications, solved using the marginalized particle filter. Furthermore, we analyze several properties of practical importance, such as its computational complexity and how to cope with quantization effects.

A map-aided navigation method for positioning at sea 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 radar and information from databases. For the described system, the fundamental navigation performance expressed as the Cramér-Rao lower bound (CRLB) is analyzed and an analytic solution as a function of the position is derived. As a solution to the recursive Bayesian navigation problem, the particle filter is proposed. In an extensive Monte Carlo simulation performance equals a GPS system.

A sensor fusion technique is presented and it is shown to achieve good estimates of the position for a 3 degrees-of-freedom industrial robot model. By using an accelerometer the estimate of the tool position accuracy can be improved. The computation of the position is formulated as a Bayesian estimation problem and two solutions are proposed. One using the extended Kalman filter and one using the particle filter. Since the aim is to use the positions estimates to improve trajectory tracking with an iterative learning control method, no computational constraints arise. In an extensive simulation study the performance is compared to the Cramér-Rao lower bound. A significant improvement in position accuracy is achieved using the sensor fusion technique.

In this paper the computational complexity of the marginalized particle lter is analyzed. We introduce an equivalent flop measure to capture floating-point operations as well as other features, which cannot be measured using flops, such as the complexity in generating random numbers and performing the resampling. From the analysis we conclude how to partition the estimation problem in an optimal way for some common target tracking models. Some guidelines on how to increase performance based on the analysis is also given. In an extensive Monte Carlo simulation we study different computational aspects and compare with theoretical results.

A modern industrial robot control system is often based only upon measurements from the motors of the manipulator. Hence to follow a trajectory with the tool an accurate description of the system must be used. In the paper a sensor fusion technique is presented to achieve good estimates of the position of the robot using a simple model. By using information from an accelerometer the effect of unmodelled dynamics can be measured. Hence, the estimate of the tool position can be improved to enhance the positioning. We formulate the computation of the position as a Bayesian estimation problem and propose two solutions. First using the extended Kalman filter EKF as a fast but linearized estimator. Second the particle filter which can solve the Bayesian estimation problem without linearizations or any Gaussian noise assumptions. Since the aim is to use the estimates to improve position accuracy using an iterative learning control method, no computational constraints arises. The methods are applied to experimental data from an ABBIRB1400 commercial industrial robot. We also discuss some preliminary results from using a detailed simulation model.

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 Cramér-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 Cramér-Rao lower bound can be interpreted and used in 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.

A framework for positioning, navigation and tracking problems using particle filters (recursive Monte Carlo methods) is developed. Automotive and airborne applications, approached in this framework, have proven a numerical advantage over classical Kalman filter based algorithms. Here the use of non-linear measurement models and non-Gaussian measurement noise is the main explanation for the improvement in accuracy, and models for relevant sensors are surveyed.

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).

We consider the recursive state estimation of a highly maneuverable target. 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 maneuvering target tracking problem. These Monte Carlo filters perform optimal inference by simulating a large number of independent 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 comparisons with current state-of-the-art tracking algorithms we show that our approach yields performance improvements at a moderately increased computational cost. Moreover, incorporation of physical constraints with sustained optimal performance is straightforward, which is virtually impossible to incorporate for linear Gaussian filters. With the particle filtering approach we advocate these constraints are easily introduced and improve the results substantially.

A Bayesian approach to positioning and tracking applications naturally leads to a recursive estimation formulation. The recently invented particle filter provides a numerical solution to the non-tractable recursive Bayesian estimation problem. As an alternative, traditional methods such as the extended Kalman filter. which is based on a linearized model and an assumption on Gaussian noise, yield approximate solutions.

In many practical applications, signal quantization and algorithmic complexity are fundamental issues. For measurement quantization, estimation performance is analyzed in detail. The algorithmic complexity is addressed for the marginalized particle filter, where the Kalman filter solves a linear subsystem subject to Gaussian noise efficiently.

The particle filter is adopted to several positioning and tracking applications and compared to traditional approaches. Particularly, the use of external database information to enhance estimation performance is discussed. In parallel, fundamental limits are derived analytically or numerically using the Cramér-Rao lower bound, and the result from estimation studies is compared to the corresponding lower bound. A framework for map-aided positioning at sea is developed, featuring an underwater positioning system using depth information and readings from a sonar sensor and a novel surface navigation system using radar measurements and sea chart information. Bayesian estimation techniques are also used to improve position accuracy for an industrial robot. The bearings-only tracking problem is addressed using Bayesian techniques and map information is used to improve the estimation performance. For multiple-target tracking problems data association is an important issue. A method to incorporate classical association methods when the estimation is based on the particle filter is presented. A real-time implementation of the particle filter as well as hypothesis testing is introduced for a collision avoidance application.

The iterative learning control (ILC) method improvesperformance of systems that repeat the same task several times. In this paper the standard norm-optimal ILC control law for linear systems is extended to an estimation-based ILC algorithm where the controlled variables are not directly available as measurements. The proposed ILC algorithm is proven to be stable and gives monotonic convergence of the error. The estimation-based part of the algorithm uses Bayesian estimation techniques such as the Kalman filter. The objective function in the optimisation problem is modified to incorporate not only the mean value of the estimated variable, but also information about the uncertainty of the estimate. It is further shown that for linear time-invariant systems the ILC design is independent of the estimation method. Finally, the concept is extended to non-linear state space models using linearisation techniques, where it is assumed that the full state vector is estimated and used in the ILC algorithm. It is also discussed how the Kullback-Leibler divergence can be used if linearisation cannot be performed. Finally, the proposed solution for non-linear systems is applied and verified in a simulation study with a simplified model of an industrial manipulator system.

A sensor fusion method for state estimation of a flexible industrial robot is presented. By measuring the acceleration at the end-effector, the accuracy of the arm angular position is improved significantly when these measurements are fused with motor angle observation. The problem is formulated in a Bayesian estimation framework and two solutions are proposed; one using the extended Kalman filter (EKF) and one using the particle filter (PF). The technique is verified on experiments on the ABB IRB4600 robot, where the accelerometer method is showing a significant better dynamic performance, even when model errors are present.

This contribution aims at unifying two recent trends in applied particle filtering (PF). The first trend is the major impact in simultaneous localization and mapping (SLAM) applications, utilizing the FastSLAM algorithm. Thesecond one is the implications of the marginalized particle filter (MPF) or the Rao-Blackwellized particle filter (RBPF) in positioning and tracking applications. Using the standard FastSLAM algorithm, only low-dimensional vehicle modelsare computationally feasible. In this work, an algorithm is introduced which merges FastSLAM and MPF, and the result is an algorithm for SLAM applications, where state vectors of higher dimensions can be used. Results using experimental data from a UAV (helicopter) are presented. The algorithmfuses measurements from on-board inertial sensors (accelerometer and gyro) and vision in order to solve the SLAM problem, i.e., enable navigation over a long period of time.

For performance gain and efficiency it is important to utilize model structure in particle filtering. Applying Bayes- rule, present linear Gaussian substructure can be efficiently handled by a bank of Kalman filters. This is the standard formulation of the Rao-Blackwellized particle filter (RBPF), by some authors denoted the marginalized particle filter (MPF), and usually presented in a way that makes it hard to implement in an object oriented fashion. This paper discusses how the solution can be rewritten in order to increase the understanding as well as simplify the implementation and reuse of standard filtering components, such as Kalman filter banks and particle filters. Calculations show that the new algorithm is equivalent to the classical formulation, and the new algorithm is exemplified in a target tracking simulation study.

The basic nonlinear ltering problem for dynamical systems is considered. Approximating the optimal lter estimate by particle lter methods has become perhaps the most common and useful method in recent years. Many variants of particle lters have been suggested, and there is an extensive lit- erature on the theoretical aspects of the quality of the approximation. Still,a clear cut result that the approximate solution, for unbounded functions, converges to the true optimal estimate as the number of particles tends to innity seems to be lacking. It is the purpose of this contribution to give such a basic convergence result.

In the CDIO-project course in Automatic Control, an Autonomous Unmanned Aerial vehicle (UAV) is constructed, utilizing an existing radio controlled model aircraft. By adding an inertial sensor measuring acceleration and rotation, together with a Global Positioning System (GPS) sensor, the aim is to construct an accurate positioning system. This is used by an on board computer to calculate rudder control signals to a set of DC-servos in order to follow a predefined way-point trajectory. The project involves 17 students, which is roughly three times as big as previous projects, and it comprises both positioning, control, and hardware design. Since the project is still ongoing some preliminary results and conclusions are presented.

Modern graphics cards for computers, and especially their graphics processing units (GPUs), are designed for fast rendering of graphics. In order 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 GPU implementation of state-of-the-art recursive Bayesian estimation using particle filters (PF). 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 one achieved with a traditional CPU implementation. The resulting GPU filter is faster with the same accuracy as the CPU filter for many particles, and it shows how the particle filter can be parallelized.

The implication of quantized sensor information on estimation and filtering problems is studied. The close relation between sampling and quantization theory was earlier reported by Widrow, Kollar and Liu (1996). They proved that perfect reconstruction of the probability density function (pdf) is possible if the characteristic function of the sensor noise pdf is band-limited. These relations are here extended by providing a class of band-limited pdfs, and it is shown that adding such dithering noise is similar to anti-alias filtering in sampling theory. This is followed up by the implications for Maximum Likelihood and Bayesian estimation. The Cramer-Rao lower bound (CRLB) is derivedfor estimation and filtering on quantized data. A particle filter (PF) algorithm that approximates the optimal nonlinear filter is provided, and numerical experiments show that the PF attains the CRLB, while second-order optimal Kalman filter approaches can perform quite bad.

A map-aided navigation method for positioning at sea 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 radar and information from databases. For the described system, the fundamental navigation performance expressed as the Cramér-Rao lower bound (CRLB) is analyzed and an analytic solution as a function of the position is derived. As a solution to the recursive Bayesian navigation problem, the particle filter is proposed. In an extensive Monte Carlo simulation performance equals a GPS system.

In this paper the computational complexity of the marginalized particle lter is analyzed. We introduce an equivalent flop measure to capture floating-point operations as well as other features, which cannot be measured using flops, such as the complexity in generating random numbers and performing the resampling. From the analysis we conclude how to partition the estimation problem in an optimal way for some common target tracking models. Some guidelines on how to increase performance based on the analysis is also given. In an extensive Monte Carlo simulation we study different computational aspects and compare with theoretical results.

For certain types of sensor-target configurations, a point target model or approach is not suitable and the physical extent of the target is accounted for during processing. An extended target track-before-detect (TBD) algorithm is presented and the performance is compared to an algorithm based on the point target assumption. Simulations illustrate the gain in performance obtained by using the extended target model where a particle filter is used for the TBD implementation.

In this paper the computational complexity of the marginalized particle lter is analyzed. We introduce an equivalent flop measure to capture floating-point operations as well as other features, which cannot be measured using flops, such as the complexity in generating random numbers and performing the resampling. From the analysis we conclude how to partition the estimation problem in an optimal way for some common target tracking models. Some guidelines on how to increase performance based on the analysis is also given. In an extensive Monte Carlo simulation we study different computational aspects and compare with theoretical results.

A modern industrial robot control system is often based only upon measurements from the motors of the manipulator. Hence to follow a trajectory with the tool an accurate description of the system must be used. In the paper a sensor fusion technique is presented to achieve good estimates of the position of the robot using a simple model. By using information from an accelerometer the effect of unmodelled dynamics can be measured. Hence, the estimate of the tool position can be improved to enhance the positioning. We formulate the computation of the position as a Bayesian estimation problem and propose two solutions. First using the extended Kalman filter EKF as a fast but linearized estimator. Second the particle filter which can solve the Bayesian estimation problem without linearizations or any Gaussian noise assumptions. Since the aim is to use the estimates to improve position accuracy using an iterative learning control method, no computational constraints arises. The methods are applied to experimental data from an ABBIRB1400 commercial industrial robot. We also discuss some preliminary results from using a detailed simulation model.

In an earlier contribution we proposed a particle filter for under water (UW) navigation, and applied it to an experimental underwater mental trajectory. Here we focus 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 simiulations on the map demonstrate a performance comparable to the CRLB.