Raman spectroscopy in conjunction with a Coded Aperture Snapshot Spectral Imaging (CASSI) system allows for detection of small amounts of explosives from stand-off distances. The obtained Compressed Sensing (CS) measurements from CASSI consists of mixed spatial and spectral information, from which a HyperSpectral Image (HSI) can be reconstructed. The HSI contains Raman spectra for all spatial locations in the scene, revealing the existence of substances. In this paper we present the possibility of utilizing a learned prior in the form of a conditional generative model for HSI reconstruction using CS. A Generative Adversarial Network (GAN) is trained using simulated samples of HSI, and conditioning on their respective CASSI measurements to refine the prior. Two different types of simulated HSI were investigated, where spatial overlap of substances was either allowed or disallowed. The results show that the developed method produces precise reconstructions of HSI from their CASSI measurements in a matter of seconds.

Neural Networks (NNS) can solve very hard classification and estimation tasks but are less well suited to solve complex sensor fusion challenges, such as end-to-end control of autonomous vehicles. Nevertheless, NN can still be a powerful tool for particular sub-problems in sensor fusion. This would require a reliable and quantifiable measure of the stochastic uncertainty in the predictions that can be compared to classical sensor measurements. However, current NN'S output some figure of merit, that is only a relative model fit and not a stochastic uncertainty. We propose to embed the NN'S in a proper stochastic system identification framework. In the training phase, the stochastic uncertainty of the parameters in the (last layers of the) NN is quantified. We show that this can be done recursively with very few extra computations. In the classification phase, Monte-Carlo (MC) samples are used to generate a set of classifier outputs. From this set, a distribution of the classifier output is obtained, which represents a proper description of the stochastic uncertainty of the predictions. We also show how to use the calculated uncertainty for outlier detection by including an artificial outlier class. In this way, the NN fits a sensor fusion framework much better. We evaluate the approach on images of handwritten digits. The proposed method is shown to be on par with MC dropout, while having lower computational complexity, and the outlier detection almost completely eliminates false classifications.

Despite the great success of neural networks (NN) in many application areas, it is still not obvious how to integrate an NN in a sensor fusion framework. The reason is that the computation of the for fusion required variance of NN is still a rather immature area. Here, we apply a methodology from system identification where uncertainty of the parameters in the NN are first estimated in the training phase, and then this uncertainty is propagated to the output in the prediction phase. This local approach is based on linearization, and it implicitly assumes a good signal-to-noise ratio and persistency of excitation. We illustrate the proposed method on a fundamental problem in advanced driver assistance systems (ADAS), namely to estimate the tire-road friction. This is a single input single output static nonlinear relation that is simple enough to provide insight and it enables comparisons with other parametric approaches. We compare both to existing methods for how to assess uncertainty in NN and standard methods for this problem, and evaluate on real data. The goal is not to improve on simpler methods for this particular application, but rather to validate that our method is on par with simpler model structures, where output variance is immediately provided.

Inom forskning och utveckling har det har alltid varit centralt att skapa modeller av verkligheten. Dessa modeller har bland annat använts till att förutspå framtida händelser eller för att styra ett system till att bete sig som man önskar. Modellerna kan beskriva allt från hur friktionen hos ett bildäck påverkas av hur mycket hjulen glider till hur ett virus kan sprida sig i ett samhälle. I takt med att mer och mer data blir tillgänglig ökar potentialen för datadrivna black-box modeller. Dessa modeller är universella approximationer vilka ska kunna representera vilken godtycklig funktion som helst. Användningen av dessa modeller har haft stor framgång inom många områden men för att verkligen kunna etablera sig inom säkerhetskritiska områden såsom självkörande farkoster behövs en förståelse för osäkerhet i prediktionen från modellen.

Neuronnät är ett exempel på en sådan black-box modell. I denna avhandling kommer olika sätt att tillförskaffa sig kunskap om osäkerhet i prediktionen av neuronnät undersökas. En metod som bygger på linjärisering av modellen för att tillförskaffa sig osäkerhet i prediktionen av neuronnätet kommer att presenteras. Denna metod är välbeprövad inom systemidentifiering och sensorfusion under antagandet att modellen är identifierbar. För modeller såsom neuronnät, vilka inte är identifierbara behövs det att det tas hänsyn till tvetydigheterna i modellen.

En annan utmaning med datadrivna black-box modeller, är att veta om den valda modellmängden är tillräckligt generell för att kunna modellera det sanna systemet. En lösning på detta problem är att använda modeller som har mer flexibilitet än vad som behövs, det vill säga en överparameteriserad modell.  Men hur påverkas osäkerheten i prediktionen av detta? Detta är något som undersöks i denna avhandling, vilken visar att osäkerheten i den överparameteriserad modellen kommer att vara begränsad underifrån av modellen med minst flexibilitet som ändå är tillräckligt generell för att modellera det sanna systemet. Som avslutning kommer dessa resultat att demonstreras i både en simuleringsstudie och en experimentstudie inspirerad av självkörande farkoster. Fokuset i simuleringsstudien är hur osäkerheten hos modellen är i områden med och utan tillgång till träningsdata medan experimentstudien fokuserar på jämförelsen mellan osäkerheten i olika typer av modeller.Resultaten från dessa studier visar att metoden som bygger på linjärisering ger liknande resultat för skattningen av osäkerheten i prediktionen av neuronnät, jämfört med existerande metoder.

The prediction uncertainty of a neural network is considered from a classical system identification point of view. To know this uncertainty is extremely important when using a network in decision and feedback applications. The asymptotic covariance of the internal parameters in the network due to noise in the observed dependent variables (output) and model class mismatch, i.e., the true system cannot be exactly described by the model class, is first surveyed. This is then applied to the prediction step of the network to get a closed form expression for the asymptotic, in training data information, prediction variance. Another interpretation of this expression is as the non-asymptotic Cramér-Rao Lower Bound. To approximate this expression, only the gradients and residuals, already computed in the gradient descent algorithms commonly used to train neural networks, are needed. Using a toy example, it is illustrated how the uncertainty in the output of a neural network can be estimated.

In urban environments, cellular network-based positioning of user equipment (UE) is a challenging task, especially in frequently occurring non-line-of-sight (NLOS) conditions. This paper investigates the use of two machine learning methods – neural networks and random forests – to estimate the position of UE in NLOS using best received reference signal beam power measurements. We evaluated the suggested positioning methods using data collected from a fifth-generation cellular network (5G) testbed provided by Ericsson. A statistical test to detect NLOS conditions with a probability of detection that is close to 90% is suggested. We show that knowledge of the antenna are crucial for accurate position estimation. In addition, our results show that even with a limited set of training data and one 5G transmission point, it is possible to position UE within 10 meters with 80% accuracy.