Department of Electrical Engineering

Target tracking is a mature topic with over half a century of mainly military and aviation research. The field has lately expanded into a range of civilian applications due to the development of cheap sensors and improved computational power. With the rise of new applications, new challenges emerge, and with better hardware there is an opportunity to employ more elaborated algorithms.

There are five main contributions to the field of target tracking in this thesis. Contributions I-IV concern the development of non-conventional models for target tracking and the resulting estimation methods. Contribution V concerns a reformulation for improved performance. To show the functionality and applicability of the contributions, all proposed methods are applied to and verified on experimental data related to tracking of animals or other objects in nature.

In Contribution I, sparse Gaussian processes are proposed to model behaviours of targets that are caused by influences from the environment, such as wind or obstacles. The influences are learned online as a part of the state estimation using an extended Kalman filter. The method is also adapted to handle time-varying influences and to identify dynamic systems. It is shown to improve accuracy over the nearly constant velocity and acceleration models in simulation. The method is also evaluated in a sea ice tracking application using data from a radar on Svalbard.

In Contribution II, a state-space model is derived that incorporates observations with uncertain timestamps. An example of such observations could be traces left by a target. Estimation accuracy is shown to be better than the alternative of disregarding the observation. The position of an orienteering sprinter is improved using the control points as additional observations.

In Contribution III, targets that are confined to a certain space, such as animals in captivity, are modelled to avoid collision with the boundaries by turning. The proposed model forces the predictions to remain inside the confined space compared to conventional models that may suffer from infeasible predictions. In particular the model improves robustness against occlusions. The model is successfully used to track dolphins in a dolphinarium as they swim in a basin with occluded sections.

In Contribution IV, an extension to the jump Markov model is proposed that incorporates observations of the mode that are state-independent. Normally, the mode is estimated by comparing actual and predicted observations of the state. However, sensor signals may provide additional information directly dependent on the mode. Such information from a video recorded by biologists is used to estimate take-off times and directions of birds captured in circular cages. The method is shown to compare well with a more time-consuming manual method.

In Contribution V, a reformulation of the labelled multi-Bernoulli filter is used to exploit a structure of the algorithm to attain a more efficient implementation.Modern target tracking algorithms are often very demanding, so sound approximations and clever implementations are needed to obtain reasonable computational performance. The filter is integrated in a full framework for tracking sea ice, from pre-processing to presentation of results.

Using images to reconstruct the world in three dimensions is a classical computer vision task. Some examples of applications where this is useful are autonomous mapping and navigation, urban planning, and special effects in movies. One common approach to 3D reconstruction is ”structure from motion” where a scene is imaged multiple times from different positions, e.g. by moving the camera. However, in a twist of irony, many structure from motion methods work best when the camera is stationary while the image is captured. This is because the motion of the camera can cause distortions in the image that lead to worse image measurements, and thus a worse reconstruction. One such distortion common to all cameras is motion blur, while another is connected to the use of an electronic rolling shutter. Instead of capturing all pixels of the image at once, a camera with a rolling shutter captures the image row by row. If the camera is moving while the image is captured the rolling shutter causes non-rigid distortions in the image that, unless handled, can severely impact the reconstruction quality.

This thesis studies methods to robustly perform 3D reconstruction in the case of a moving camera. To do so, the proposed methods make use of an inertial measurement unit (IMU). The IMU measures the angular velocities and linear accelerations of the camera, and these can be used to estimate the trajectory of the camera over time. Knowledge of the camera motion can then be used to correct for the distortions caused by the rolling shutter. Another benefit of an IMU is that it can provide measurements also in situations when a camera can not, e.g. because of excessive motion blur, or absence of scene structure.

To use a camera together with an IMU, the camera-IMU system must be jointly calibrated. The relationship between their respective coordinate frames need to be established, and their timings need to be synchronized. This thesis shows how to automatically perform this calibration and synchronization, without requiring e.g. calibration objects or special motion patterns.

In standard structure from motion, the camera trajectory is modeled as discrete poses, with one pose per image. Switching instead to a formulation with a continuous-time camera trajectory provides a natural way to handle rolling shutter distortions, and also to incorporate inertial measurements. To model the continuous-time trajectory, many authors have used splines. The ability for a spline-based trajectory to model the real motion depends on the density of its spline knots. Choosing a too smooth spline results in approximation errors. This thesis proposes a method to estimate the spline approximation error, and use it to better balance camera and IMU measurements, when used in a sensor fusion framework. Also proposed is a way to automatically decide how dense the spline needs to be to achieve a good reconstruction.

Another approach to reconstruct a 3D scene is to use a camera that directly measures depth. Some depth cameras, like the well-known Microsoft Kinect, are susceptible to the same rolling shutter effects as normal cameras. This thesis quantifies the effect of the rolling shutter distortion on 3D reconstruction, depending on the amount of motion. It is also shown that a better 3D model is obtained if the depth images are corrected using inertial measurements.

The past decades have seen a rapid growth of mobile data traffic,both in terms of connected devices and data rate. To satisfy the evergrowing data traffic demand in wireless communication systems, thecurrent cellular systems have to be redesigned to increase both spectralefficiency and energy efficiency. Massive MIMO(Multiple-Input-Multiple-Output) is one solution that satisfy bothrequirements. In massive MIMO systems, hundreds of antennas areemployed at the base station to provide service to many users at thesame time and frequency. This enables the system to serve the userswith uniformly good quality of service simultaneously, with low-costhardware and without using extra bandwidth and energy. To achievethis, proper resource allocation is needed. Among the availableresources, transmit power beamforming are the most important degrees offreedom to control the spectral efficiency and energy efficiency. Dueto the use of excessive number of antennas and low-end hardware at thebase station, new aspects of power allocation and beamforming compared to currentsystems arises.

In the first part of the thesis, new uplink power allocation schemes that based on long term channel statistics isproposed. Since quality of the channel estimates is crucial in massive MIMO, in addition to data power allocation, joint power allocationthat includes the pilot power as additional variable should be considered. Therefore a new framework for power allocation thatmatches practical systems is developed, as the methods developed in the literature cannot be applied directly to massive MIMO systems. Simulation results confirm the advantages brought by the the proposed new framework.

In the second part, we introduces a new approach to solve the joint precoding and power allocation for different objective in downlink scenarios by a combination of random matrix theory and optimization theory. The new approach results in a simplified problem that, though non-convex, obeys a simple separable structure. Simulation results showed that the proposed scheme provides large gains over heuristic solutions when the number of users in the cell is large, which is suitable for applying in massive MIMO systems.

In the third part we investigate the effects of using low-end amplifiers at the basestations. The non-linear behavior of power consumption in these amplifiers changes the power consumption model at the basestation, thereby changes the power allocation and beamforming design. Different scenarios are investigated and resultsshow that a certain number of antennas can be turned off in some scenarios.

In the last part we consider the use of non-orthogonal-multiple-access (NOMA) inside massive MIMO systems in practical scenarios where channel state information (CSI) is acquired through pilot signaling. Achievable rate analysis is carried out for different pilot signaling schemes including both uplink and downlink pilots. Numerical results show that when downlink CSI is available at the users, our proposed NOMA scheme outperforms orthogonal schemes. However with more groups of users present in the cell, it is preferable to use multi-user beamforming in stead of NOMA.

Massive MIMO (multiple-input–multiple-output) is a multi-antenna technology for cellular wireless communication, where the base station uses a large number of individually controllable antennas to multiplex users spatially.  This technology can provide a high spectral efficiency.  One of its main challenges is the immense hardware complexity and cost of all the radio chains in the base station.  To make massive MIMO commercially viable, inexpensive, low-complexity hardware with low linearity has to be used, which inherently leads to more signal distortion.  This thesis investigates how the degenerated linearity of some of the main components—power amplifiers, analog-to-digital converters (ADCs) and low-noise amplifiers—affects the performance of the system, with respect to data rate, power consumption and out-of-band radiation. The main results are: Spatial processing can reduce PAR (peak-to-average ratio) of the transmit signals in the downlink to as low as 0B; this, however, does not necessarily reduce power consumption.  In environments with isotropic fading, one-bit ADCs lead to a reduction in effective signal-to-interference-and-noise ratio (SINR) of 4dB in the uplink and four-bit ADCs give a performance close to that of an unquantized system.  An analytical expression for the radiation pattern of the distortion from nonlinear power amplifiers is derived.  It shows how the distortion is beamformed to some extent, that its gain never is greater than that of the desired signal, and that the gain of the distortion is reduced with a higher number of served users and a higher number of channel taps.  Nonlinear low-noise amplifiers give rise to distortion that partly combines coherently and limits the possible SINR.  It is concluded that spatial processing with a large number of antennas reduces the impact of hardware distortion in most cases.  As long as proper attention is paid to the few sources of coherent distortion, the hardware complexity can be reduced in massive MIMO base stations to overcome the hardware challenge and make massive MIMO commercial reality.

Flight control design for modern fighter aircraft is a challenging task. Aircraft are dynamical systems, which naturally contain a variety of constraints and nonlinearities such as, e.g., maximum permissible load factor, angle of attack and control surface deflections. Taking these limitations into account in the design of control systems is becoming increasingly important as the performance and complexity of the aircraft is constantly increasing.

The aeronautical industry has traditionally applied feedforward, anti-windup or similar techniques and different ad hoc engineering solutions to handle constraints on the aircraft. However these approaches often rely on engineering experience and insight rather than a theoretical foundation, and can often require a tremendous amount of time to tune.

In this thesis we investigate model predictive control as an alternative design tool to handle the constraints that arises in the flight control design.

We derive a simple reference tracking MPC algorithm for linear systems that build on the dual mode formulation with guaranteed stability and low complexity suitable for implementation in real time safety critical systems.

To reduce the computational burden of nonlinear model predictive control we propose a method to handle the nonlinear constraints, using a set of dynamically generated local inner polytopic approximations. The main benefit of the proposed method is that while computationally cheap it still can guarantee recursive feasibility and convergence.

An alternative to deriving MPC algorithms with guaranteed stability properties is to analyze the closed loop stability, post design. Here we focus on deriving a tool based on Mixed Integer Linear Programming for analysis of the closed loop stability and robust stability of linear systems controlled with MPC controllers.

To test the performance of model predictive control for a real world example we design and implement a standard MPC controller in the development simulator for the JAS 39 Gripen aircraft at Saab Aeronautics. This part of the thesis focuses on practical and tuning aspects of designing MPC controllers for fighter aircraft. Finally we have compared the MPC design with an alternative approach to maneuver limiting using a command governor.