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In this study, we investigate online Bayesian estimation of the measurement noise density of a given state space model using particle filters and Dirichlet process mixtures. Dirichlet processes are widely used in statistics for nonparametric density estimation. In the proposed method, the unknown noise is modeled as a Gaussian mixture with unknown number of components. The joint estimation of the state and the noise density is done via particle filters. Furthermore, the number of components and the noise statistics are allowed to vary in time. An extension of the method for the estimation of time varying noise characteristics is also introduced.

With the electromagnetic theory as basis, we present a sensor model for three-axis magnetometers suitable for localization and tracking applications. The model depends on a physical magnetic dipole model of the target and its relative position to the sensor. Furthermore, the dependency between the magnetic dipole and the target orientation has been modeled enabling tracking of a maneuvering target. Due to multimodality, a bank of Extended Kalman Filters is proposed for tracking road vehicles. Results from field test data indicate excellent tracking of target position.

A new approach to track bicycles from imagery sensor data is proposed. It is based on detecting ellipsoids in the images, and treat these pair-wise using a dynamic bicycle model. One important application area is in automotive collision avoidance systems, where no dedicated systems for bicyclists yet exist and where very few theoretical studies have been published. Possible conflicts can be predicted from the position and velocity state in the model, but also from the steering wheel articulation and roll angle that indicate yaw changes before the velocity vector changes. An algorithm is proposed which consists of an ellipsoid detection and estimation algorithm and a particle filter. A simulation study of three critical single target scenarios is presented, and the algorithm is shown to produce excellent state estimates. An experiment using a stationary camera and the particle filter for state estimation is performed and has shown encouraging results.

When designing robust controllers, H-infinity synthesisis a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex,even when the order of the system is low. The approach used in this work is based on formulating the constraint on the maximum order of the controller as a polynomial (or rational) equation. By using the fact that the polynomial (or rational) is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex function is to be minimized over a convex set defined by linear matrix inequalities. The proposed method is evaluated together with a wellknown method from the literature. The results indicate that the proposed method performs slightly better.

When designing robust controllers, H-infinity synthesisis a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex,even when the order of the system is low. The approach used in this work is based on formulating the constraint on the maximum order of the controller as a polynomial (or rational) equation. By using the fact that the polynomial (or rational) is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex function is to be minimized over a convex set defined by linear matrix inequalities. The proposed method is evaluated together with a wellknown method from the literature. The results indicate that the proposed method performs slightly better.

It is getting more common that premium cars areequipped with a forward looking radar and a forward looking camera. The data is often used to estimate the road geometry, tracking leading vehicles, etc. However, there is valuable information present in the radar concerning stationary objects, that is typically not used. The present work shows how stationary objects, such as guard rails, can be modeled and tracked as extended objects using radar measurements. The problem is cast within a standard sensor fusion framework utilizing the Kalman filter. The approach has been evaluated on real datafrom highways and rural roads in Sweden., IVSS - SEFS, MOVIII

The Direct Weight Optimization (DWO) approach is a nonparametric estimation approach that has appeared in recent years within the field of nonlinear system identification. In previous work, all function classes for which DWO has been studied have included only continuous functions. However, in many applications it would be desirable also to be able to handle discontinuous functions. Inspired by the bilateral filter method from image processing, such an extension of the DWO framework is proposed for the smoothing problem. Examples show that the properties of the new approach regarding the handling of discontinuities are similar to the bilateral filter, while at the same time DWO offers a greater flexibility with respect to different function classes handled.

This work investigates feedforward control of elastic robot structures. A general serial link elastic robot model which can describe a modern industrial robot in a realistic way is presented. The feedforward control problem is discussed and a solution method for the inverse dynamics problem is proposed. This method involves solving a differential algebraic equation (DAE). A simulation example for an elastic two axis planar robot is also included and shows promising results.

This contribution presents a unified framework for localization and tracking in sensor networks based on fusing a variety of signal energy measurements as provided by for instance acoustic, seismic, magnetic, radio, microwave and infrared sensors. The received energy from such sensors generally decays exponentially, and a log range model is introduced for the sensor observations in logarithmic scale, which is linear in transmitted power and the path loss exponent. Field trial sensor data confirms the validity of the log range model. The novelty in this contribution ties in a systematic least squares approach to eliminate these nuisance parameters and also the sensor noise variances. Details on how to solve the resulting low-dimensional non-linear least squares criterion are given, and how to extend the algorithms to target tracking. Explicit formulas for the Cramer-Rao lower bound are given for both localization and tracking.

We discuss how to implement an efficient interior-point algorithm for semi-definite programs that result from integral quadratic constraints. The algorithm is a primal-dual potential reduction method, and the computational effort is dominated by a least-squares system that has to be solved in each iteration. The key to an efficient implementation is to utilize iterative methods and the specific structure of integral quadratic constraints. The algorithm has been implemented in Matlab. To give a rough idea of the efficiencies obtained, it is possible to solve problems resulting in a linear matrix inequality of dimension 130 × 130 with approximately 5000 variables in about 5 minutes on a lap-top. Problems with approximately 20000 variable and a linear matrix inequality of dimension 230 × 230 are solved in about 45 minutes. It is not assumed that the system matrix has no eigenvalues on the imaginary axis, nor is it assumed that it is Hurwitz.

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.

Parallel AD converter structures is one way to increase the sampling rate. Instead of increasing the sample rate in one AD converter, several AD converters with lower sampling rate can be used instead. A problem in these structures is that the time between samples is usually not equal because there are errors in the delays between the AD converters. We will here present a method to estimate the timing offset errors. The estimation algorithm works without any special calibration signal, instead the normal input signal is used. The only assumption that we need on the input signal is that most of the energy is concentrated to a low pass band, below about 1/3 of the Nyquist frequency. Simulations of the time interleaved AD converter show that the method estimates the errors with high accuracy.

The design of optimal controllers for systems subject to hard bounds on the control signal is considered. Optimality refers to the fact that we achieve the smallest possible worst case error (i.e. difference between reference signal and plant output) during runtime. The external reference signal is bounded in amplitude and rate, which encounters for many practical situations. Moreover, a conservative design is avoided by these assumptions. The resulting constrained and infinite dimensional optimisation problem is re-casted to an unconstrained and finite dimensional one by applying the notion of Pareto-optimal solutions and Ritz approximation. Moreover, the presented framework allows to assess feasibility of the constraint control problem, and to display the tradeoff between the two objectives. A simulation example illustrates the developed theory.

A general framework for the design of multivariable control systems subject to hard constraints on each control channel is developed. The design procedure is an extension of the well-known H∞ Loop Shaping Design Procedure and is based on the calculation of the maximum possible control amplitude for a certain class of reference signals. Special attention is given to the adaption of the design weights in order to meet the prescribed bounds on the control signal. A multivariable simulation example, the control of the vertical dynamics of an aircraft, illustrates the suggested procedure.

A black-box model of a system is one that does not use any particular prior knowledge of the character or physics of the relationships involved. It is therefore more a question of "curve- fitting" than "modeling". In this presentation several examples of such black-box model structures will be given. Both linear and non-linear structures are treated. Relationships between linear models, fuzzy models, neural networks and classical non-parametric models are discussed. Some reasons for the usefulness of these model types will also be given. Ways to fit black box structures to measured input-output data are described, as well as the more fundamental (statistical) properties of the resulting models.

Aspects on the behavior of a general second order iterative learning control (ILC) algorithm is presented from a frequency domain perspective. This includes stability as well as performance and robustness issues. The basis for the analysis is linear iterative systems and these are briefly described. A design algorithm for second order ILC schemes is proposed and analyzed both theoretically as well as in an experiment. In the experiment, done on a commercial industrial robot control system, the second order ILC design is compared with a first order ILC design. The result from both the analysis and the experiment is that the second order design is not better with respect to performance or robustness.

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 tracks, or particles. Each particle is assigned a probability weight determined by its likelihood. The maina dvantage 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. Moreover, incorporation of physical constraints with sustained optimal performance is straight forward, 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.

A robust controller is designed for a system consisting of two carts coupled by a spring. Special eff ort is investigated to the input saturations. This problem was posed within a benchmark collection and treated for example at the 1992 ACC. Analysis and simulation studies illustrate the suggested design.

We determine the maximum output amplitude of a system, when the input is bounded by certain constraints. In particular, amplitude and rate of change (i.e. the first derivative) have to be bounded. We show properties of the worst case input and present an algorithm that allows construction of this input and calculates the maximum amplitude of the output. The solution of this problem is a necessary and important step within a couple of recently developed controller-design procedures, dealing with plants with hard-bounded inputs. Nevertheless, it is interesting as a system theoretic task itself and therefore stated separately.

In future versions of Saab Gripen, the mechanical artifical horizon will be replaced by a computer calculated attitude and heading, independent of the inertial navigation system (INS). The system uses data from sensors already existing in the aircraft, which are easily available in a highly integrated, 4th generation combat aircraft such as the Gripen. The sensors used are a three-axis magnetic detector, true airspeed, angle of attack, barometric altitude, flight control rate gyros and load factor. The sensor data are fused together in an extended Kalman filter (EKF). Each sensor by itself is of relatively poor quality. For instance, the accuracy of the rate gyros is in the order of degrees per second, rather than degrees per hour as is the case in gyros dedicated for navigational use. However, when all data are combined, they provide an attitude and heading estimate with sufficient quality for its purpose; to cross-monitor the INS, and to serve as a backup in case of an INS or data bus failure. The system is called synthetic attitude and heading reference system (SAHRS), and is a Saab patent. A similar system is developed for and is operational in the Saab Viggen.

A Wiener model consists of a linear dynamic system followed by a static nonlinearity. The input and output are measured, but not the intermediate signal. We discuss the Maximum Likelihood estimate for Gaussian measurement and process noise, and the special cases when one of the noise sources is zero.

We present a method to increase the feasibility in model predictive control (MPC) algorithms that use ellipsoidal terminal state constraints and performance bounds from nominal controllers. The method is based on estimating a bound on the achievable performance with a saturated nominal controller and using this bound in the MPC algorithm. The resulting MPC controller can be implemented efficiently with second order cone programming

For small integrated CMOS digital chips that communicate via analog signals the size and the cost of the AD-converters is a problem. An integrated CMOS AD-converter that could be built into the chip would solve this problem. In a CMOS process, the manufacturers only guarantee a very low accuracy of the resistances. The components of the ADC are therefore very inaccurate. The purpose here is to present a method for identification of the errors in the ADC. The algorithm works while the ADC is used and it does not assume any knowledge of the input signal except that the distribution function is smooth. The estimated values can then be used in the chip to compensate for the errors in the ADC. The algorithm is evaluated on simulated data.

Some previously existing results on locally optimal backstepping controllers are extended to a larger class of nonlinear systems and another performance index. The result is a design procedure that gives a nonlinear controller with LQ performance in the origin and tries to recover the quadratic performance index also globally. As a part of the controller design, a novel approach for solving an inverse optimality problem is presented

Closed-loop power control is considered as an important component in the management of radio resources in cellular radio systems. The algorithms are typically based on feedback information, which for practical reasons is outdated. These time delays in the system, hamper the performance and might even result in unstable systems. Several power control strategies have been proposed in order to improve the capacity of cellular radio systems, but time delays are usually neglected. Here, time delay compensation is introduced as a means to improve the dynamical behavior of power controlled cellular systems, despite time delays. The improvements are validated both in theory with respect to global convergence and stability and in some illuminating simulations.

Transmission power control is essential in CDMA systems in order to reduce the near-far effect and to optimize the bandwidth utilization, which is critical when variable data rates are used. One remaining problem is oscillations in the output powers due to round-trip delays in the power control loops together with the power up-down command device. The oscillations are naturally quantified using discrete-time describing functions, which are introduced and applied. More importantly, Time Delay Compensation (TDC) is proposed to mitigate the oscillations. It is also formally proven that TDC result in a stable overall system, with power control errors that converges to a defined bounded region. These bounds are tighter, compared to when not employing TDC. Simulations illustrate the oscillations and the significant performance gains using TDC.

We examine some recent methods for System Identication, that also deliver non-parametric error bounds, suited for a robust controller design. In particular, we look at Stochastic Embed-ding, Set Membership Identication and Model Error Modelling. We briefly review the main ideas together with existing computational solutions and present a comparative example.

The concept of tree classifiers is combined with the popular neural net structure. Instead of having one large neural net to capture all the regions in the feature space, the authors suggest the compromise of using small single-output nets at each tree node. This hybrid classifier is referred to as a neural tree. The performance of this classifier is evaluated on real data from a problem in speech recognition. When verified on this particular problem, it turns out that the classifier concept drastically reduces the computational complexity compared with conventional multilevel neural nets. It is also noted that these data make it possible to grow trees online from a continuous data stream.