Institutionen för systemteknik (ISY)

Downsizing and turbocharging of engines provide a way to meet increasing demands for efficiency and performance in the automotive industry. An engine design is a result of compromises, e.g. the selection of charging system, and the trend is to reduce these compromises by increasing system complexity. Models have come to play a central role to handle this rise in complexity, and are used for simulation, system optimization and control synthesis. The models should describe the entire operating range, be capable of extrapolation, be easily parameterizable, and wide cover a range of applications.

A novel compressor model is developed which, in addition to the nominal operation, also covers surge, choke and operation at pressure ratios less than one. The model is based on data from more than 300 compressor maps, measurements from engine test stands, and a surge test stand. The general knowledge gained from the in-depth analysis is condensed in the model equations. The model can be automatically parametrized using a compressor map, is based on static functions for low computational cost, and is shown to extrapolate low speed compressor operation well. Furthermore, it is shown to be applicable to compressors of different size, ranging from small car applications to large heavy duty vehicles. Compressor restriction operation is modeled down to a standstill compressor, and shown to agree well with gas stand measurements. Further, the analysis contributes with new knowledge and models for choking pressure ratio and flow.

A method to automatically determine a turbo map, when the turbo is installed on an engine in an engine test stand is developed. The method can be used to validate manufacturer maps or expand the region covered in a map. An analysis of the limits that an engine installation imposes on the reachable points in the compressor map is performed. The addition of a throttle before the compressor is suggested to increase the reachable map region, and an engine and test cell control structure that can be used to automate the measurements is proposed. Two methods that compensate for the deviation between measured and desired speeds, are proposed and investigated. A gas stand map is compared to the map generated in the engine test stand, and a generally good agreement results.

An experimental analysis of the applicability of the commonly used correction factors, used for estimating compressor performance when the inlet conditions deviate from nominal, is performed. Correction factors are vital, to e.g. estimate turbocharger performance for driving at high altitude or to characterize second stage compressor performance, where the variations in inlet conditions are large. Measurements from an engine test stand and a gas stand show a small but clearly measurable trend, with decreasing compressor pressure ratio for decreasing compressor inlet pressure, for points with equal corrected shaft speed and corrected mass flow. A method that enables measurements to be analyzed with modified corrections is developed. As a result, an adjusted shaft speed correction quantity is proposed, incorporating also the inlet pressure in the shaft speed correction.

In system identification, the choice of model structure is important and it is sometimes desirable to use a flexible model structure that is able to approximate a wide range of systems. One such model structure is the Wiener class of systems, that is, systems where the input enters a linear time-invariant subsystem followed by a time-invariant nonlinearity. Given a sequence of input and output pairs, the system identification problem is often formulated as the minimization of the mean-square prediction error. Here, the prediction error has a nonlinear dependence on the parameters of the linear subsystem and the nonlinearity. Unfortunately, this formulation of the estimation problem is often nonconvex, with several local minima, and it is therefore difficult to guarantee that a local search algorithm will be able to find the global optimum.

In the first part of this thesis, we consider the application of dimension reduction methods to the problem of estimating the impulse response of the linear part of a system in the Wiener class. For example, by applying the inverse regression approach to dimension reduction, the impulse response estimation problem can be cast as a principal components problem, where the reformulation is based on simple nonparametric estimates of certain conditional moments. The inverse regression approach can be shown to be consistent under restrictions on the distribution of the input signal provided that the true linear subsystem has a finite impulse response. Furthermore, a forward approach to dimension reduction is also considered, where the time-invariant nonlinearity is approximated by a local linear model. In this setting, the impulse response estimation problem can be posed as a rank-reduced linear least-squares problem and a convex relaxation can be derived.

Thereafter, we consider the extension of the subspace identification approach to include linear time-invariant rational models. It turns out that only minor structural modifications are needed and already available implementations can be used. Furthermore, other a priori information regarding the structure of the system can incorporated, including a certain class of linear gray-box structures. The proposed extension is not restricted to the discrete-time case and can be used to estimate continuous-time models.

The final topic in this thesis is the estimation of discrete-time models containing polynomial nonlinearities. In the continuous-time case, a constructive algorithm based on differential algebra has previously been used to prove that such model structures are globally identifiable if and only if they can be written as a linear regression model. Thus, if we are able to transform the nonlinear model structure into a linear regression model, the parameter estimation problem can be solved with standard methods. Motivated by the above and the fact that most system identification problems involve sampled data, a discrete-time version of the algorithm is developed. This algorithm is closely related to the continuous-time version and enables the handling of noise signals without differentiations.

Cognitive radio is a new concept of reusing spectrum in an opportunistic manner. Cognitive radio is motivated by recent measurements of spectrum utilization, showing unused resources in frequency, time and space. Introducing cognitive radios in a primary network inevitably creates increased interference to the primary users. Secondary users must sense the spectrum and detect primary users' signals at very low SNR, to avoid causing too much interference.This dissertation studies this detection problem, known as spectrum sensing.

The fundamental problem of spectrum sensing is to discriminate an observation that contains only noise from an observation that contains a very weak signal embedded in noise. In this work, detectors are derived that exploit known properties of the second-order moments of the signal. In particular, known structures of the signal covariance are exploited to circumvent the problem of unknown parameters, such as noise and signal powers or channel coefficients.

The dissertation is comprised of six papers, all in different ways related to spectrum sensing based on second-order statistics. In the first paper, we considerspectrum sensing of orthogonal frequency-division multiplexed (OFDM) signals in an additive white Gaussian noise channel. For the case of completely known noise and signal powers, we set up a vector-matrix model for an OFDM signal with a cyclic prefix and derive the optimal Neyman-Pearson detector from first principles. For the case of completely unknown noise and signal powers, we derive a generalized likelihood ratio test (GLRT) based on empirical second-order statistics of the received data. The proposed GLRT detector exploits the non-stationary correlation structure of the OFDM signal and does not require any knowledge of the noise or signal powers.

In the second paper, we create a unified framework for spectrum sensing of signals which have covariance matrices with known eigenvalue multiplicities. We derive the GLRT for this problem, with arbitrary eigenvalue multiplicities under both hypotheses. We also show a number of applications to spectrum sensing for cognitive radio.

The general result of the second paper is used as a building block, in the third and fourth papers, for spectrum sensing of second-order cyclostationary signals received at multiple antennas and orthogonal space-time block coded (OSTBC) signals respectively. The proposed detector of the third paper exploits both the spatial and the temporal correlation of the received signal, from knowledge of the fundamental period of the cyclostationary signal and the eigenvalue multiplicities of the temporal covariance matrix.

In the fourth paper, we consider spectrum sensing of signals encoded with an OSTBC. We show how knowledge of the eigenvalue multiplicities of the covariance matrix are inherent owing to the OSTBC, and propose an algorithm that exploits that knowledge for detection. We also derive theoretical bounds on the performance of the proposed detector. In addition, we show that the proposed detector is robust to a carrier frequency offset, and propose another detector that deals with timing synchronization using the detector for the synchronized case as a building block.

A slightly different approach to covariance matrix estmation is taken in the fifth paper. We consider spectrum sensing of Gaussian signals with structured covariance matrices, and propose to estimate the unknown parameters of the covariance matrices using covariance matching estimation techniques (COMET). We also derive the optimal detector based on a Gaussian approximation of the sample covariance matrix, and show that this is closely connected to COMET.

The last paper deals with the problem of discriminating samples that containonly noise from samples that contain a signal embedded in noise, when the variance of the noise is unknown. We derive the optimal soft decision detector using a Bayesian approach. The complexity of this optimal detector grows exponentially with the number of observations and as a remedy, we propose a number of approximations to it. The problem under study is a fundamental one andit has applications in signal denoising, anomaly detection, and spectrum sensing for cognitive radio.

Vision and infrared sensors are very common in surveillance and security applications, and there are numerous examples where a critical infrastructure, e.g. a harbor, an airport, or a military camp, is monitored by video surveillance systems. There is a need for automatic processing of sensor data and intelligent control of the sensor in order to obtain efficient and high performance solutions that can support a human operator. This thesis considers two subparts of the complex sensor fusion system; namely target tracking and sensor control.The multiple target tracking problem using particle filtering is studied. In particular, applications where road constrained targets are tracked with an airborne video or infrared camera are considered. By utilizing the information about the road network map it is possible to enhance the target tracking and prediction performance. A dynamic model suitable for on-road target tracking with a camera is proposed and the computational load of the particle filter is treated by a Rao-Blackwellized particle filter. Moreover, a pedestrian tracking framework is developed and evaluated in a real world experiment. The exploitation of contextual information, such as road network information, is highly desirable not only to enhance the tracking performance, but also for track analysis, anomaly detection and efficient sensor management. Planning for surveillance and reconnaissance is a broad field with numerous problem definitions and applications. Two types of surveillance and reconnaissance problems are considered in this thesis. The first problem is a multi-target search and tracking problem. Here, the task is to control the trajectory of an aerial sensor platform and the pointing direction of its camera to be able to keep track of discovered targets and at the same time search for new ones. The key to successful planning is a measure that makes it possible to compare different tracking and searching tasks in a unified framework and this thesis suggests one such measure. An algorithm based on this measure is developed and simulation results of a multi-target search and tracking scenario in an urban area are given. The second problem is aerial information exploration for single target estimation and area surveillance. In the single target case the problem is to control the trajectory of a sensor platform with a vision or infrared camera such that the estimation performance of the target is maximized. The problem is treated both from an information filtering and from a particle filtering point of view. In area exploration the task is to gather useful image data of the area of interest by controlling the trajectory of the sensor platform and the pointing direction of the camera. Good exploration of a point of interest is characterized by several images from different viewpoints. A method based on multiple information filters is developed and simulation results from area and road exploration scenarios are presented.

Complexity reduction is one of the major issues in today’s digital system designfor many obvious reasons, e.g., reduction in area, reduced power consumption,and high throughput. Similarly, dynamically adaptable digital systems requireflexibility considerations in the design which imply reconfigurable systems, wherethe system is designed in such a way that it needs no hardware modificationsfor changing various system parameters. The thesis focuses on these aspects ofdesign and can be divided into four parts.

The first part deals with complexity reduction for non-frequency selectivesystems, like differentiators and integrators. As the design of digital processingsystems have their own challenges when various systems are translated from theanalog to the digital domain. One such problem is that of high computationalcomplexity when the digital systems are intended to be designed for nearly fullcoverage of the Nyquist band, and thus having one or several narrow don’t-carebands. Such systems can be divided in three categories namely left-band systems,right-band systems and mid-band systems. In this thesis, both single-rate andmulti-rate approaches together with frequency-response masking techniques areused to handle the problem of complexity reduction in non-frequency selectivefilters. Existing frequency response masking techniques are limited in a sensethat they target only frequency selective filters, and therefore are not applicabledirectly for non-frequency selective filters. However, the proposed approachesmake the use of frequency response masking technique feasible for the non-frequency filters as well.

The second part of the thesis addresses another issue of digital system designfrom the reconfigurability perspective, where provision of flexibility in the designof digital systems at the algorithmic level is more beneficial than at any otherlevel of abstraction. A linear programming (minimax) based technique forthe coefficient decimation FIR (finite-length impulse response) filter design isproposed in this part of thesis. The coefficient decimation design method findsuse in communication system designs in the context of dynamic spectrum accessand in channel adaptation for software defined radio, where requirements can bemore appropriately fulfilled by a reconfigurable channelizer filter. The proposedtechnique provides more design margin compared to the existing method whichcan in turn can be traded off for complexity reduction, optimal use of guardbands, more attenuation, etc.

The third part of thesis is related to complexity reduction in frequencyselective filters. In context of frequency selective filters, conventional narrow-band and wide-band frequency response masking filters are focused, where variousoptimization based techniques are proposed for designs having a small number ofnon-zero filter coefficients. The use of mixed integer linear programming (MILP)shows interesting results for low-complexity solutions in terms of sparse andnon-periodic subfilters.

Finally, the fourth part of the thesis deals with order estimation of digitaldifferentiators. Integral degree and fractional degree digital differentiators areused in this thesis work as representative systems for the non-frequency selectivefilters. The thesis contains a minimax criteria based curve-fitting approach fororder estimation of linear-phase FIR digital differentiators of integral degree upto four.