<p>Shooter localization systems are used to detect and locate the origin of gunfire. A wireless sensor network is one possible implementation of such a system. A wireless sensor network is sensitive to synchronization errors. Localization techniques that rely on the timing will give less accurate or even useless results if the synchronization errors are too large.</p><p>This thesis focuses on the influence of synchronization errors on the abilityto localize a shooter using a wireless sensor network. A localization algorithm</p><p>is developed and implemented and the effect of synchronization errors is studied. The localization algorithm is evaluated using numerical experiments, simulations, and data from real gunshots collected at field trials.</p><p>The results indicate that the developed localization algorithm is able to localizea shooter with quite good accuracy. However, the localization performance is to a high degree influenced by the geographical configuration of the network as well as the synchronization error.</p> / <p><p>Skottlokaliseringssystem används för att upptäcka och lokalisera ursprunget för avlossade skott. Ett trådlöst sensornätverk är ett sätt att utforma ett sådant system.Trådlösa sensornätverk är känsliga för synkroniseringsfel. Lokaliseringsmetoder som bygger på tidsobservationer kommer med för stora synkroniseringsfel ge dåliga eller helt felaktiga resultat.</p><p>Detta examensarbete fokuserar på vilken inverkan synkroniseringsfel har på möjligheterna att lokalisera en skytt i ett trådlöst sensornätverk. En lokaliseringsalgoritm utvecklas och förmågan att korrekt lokalisera en skytt vid olika synkroniseringsfel undersöks. Lokaliseringsalgoritmen prövas med numeriska experiment, simuleringar och även för data från riktiga skottljud, insamlade vid fältförsök.</p><p>Resultaten visar att lokaliseringsalgoritmen fungerar tillfredställande, men att lokaliseringsförmågan till stor del påverkas av synkroniseringsfel men även av sensornätverkets geografiska utseende.</p></p>

Designing estimators based on low rank signal models is a common practice in signal processing. Some of these estimators are designed to use a single low rank snapshot vector, while others employ multiple snapshots. This dissertation deals with both these cases in different contexts. Separable nonlinear least squares is a popular tool to extract parameter estimates from a single snapshot vector. Asymptotic statistical properties of the separable non-linear least squares estimates are explored in the first part of the thesis. The assumptions imposed on the noise process and the data model are general. Therefore, the results are useful in a wide range of applications. Sufficient conditions are established for consistency, asymptotic normality and statistical efficiency of the estimates. An expression for the asymptotic covariance matrix is derived and it is shown that the estimates are circular. The analysis is extended also to the constrained separable nonlinear least squares problems. Nonparametric estimation of the material functions from wave propagation experiments is the topic of the second part. This is a typical application where a single snapshot vector is employed. Numerical and statistical properties of the least squares algorithm are explored in this context. Boundary conditions in the experiments are used to achieve superior estimation performance. Subsequently, a subspace based estimation algorithm is proposed. The subspace algorithm is not only computationally efficient, but is also equivalent to the least squares method in accuracy. Estimation of the frequencies of multiple real valued sine waves is the topic in the third part, where multiple snapshots are employed. A new low rank signal model is introduced. Subsequently, an ESPRIT like method named R-Esprit and a weighted subspace fitting approach are developed based on the proposed model. When compared to ESPRIT, R-Esprit is not only computationally more economical but is also equivalent in performance. The weighted subspace fitting approach shows significant improvement in the resolution threshold. It is also robust to additive noise.

Shooter localization systems are used to detect and locate the origin of gunfire. A wireless sensor network is one possible implementation of such a system. A wireless sensor network is sensitive to synchronization errors. Localization techniques that rely on the timing will give less accurate or even useless results if the synchronization errors are too large. This thesis focuses on the influence of synchronization errors on the abilityto localize a shooter using a wireless sensor network. A localization algorithm is developed and implemented and the effect of synchronization errors is studied. The localization algorithm is evaluated using numerical experiments, simulations, and data from real gunshots collected at field trials. The results indicate that the developed localization algorithm is able to localizea shooter with quite good accuracy. However, the localization performance is to a high degree influenced by the geographical configuration of the network as well as the synchronization error. / Skottlokaliseringssystem används för att upptäcka och lokalisera ursprunget för avlossade skott. Ett trådlöst sensornätverk är ett sätt att utforma ett sådant system.Trådlösa sensornätverk är känsliga för synkroniseringsfel. Lokaliseringsmetoder som bygger på tidsobservationer kommer med för stora synkroniseringsfel ge dåliga eller helt felaktiga resultat. Detta examensarbete fokuserar på vilken inverkan synkroniseringsfel har på möjligheterna att lokalisera en skytt i ett trådlöst sensornätverk. En lokaliseringsalgoritm utvecklas och förmågan att korrekt lokalisera en skytt vid olika synkroniseringsfel undersöks. Lokaliseringsalgoritmen prövas med numeriska experiment, simuleringar och även för data från riktiga skottljud, insamlade vid fältförsök. Resultaten visar att lokaliseringsalgoritmen fungerar tillfredställande, men att lokaliseringsförmågan till stor del påverkas av synkroniseringsfel men även av sensornätverkets geografiska utseende.

<p>Designing estimators based on low rank signal models is a common practice in signal processing. Some of these estimators are designed to use a single low rank snapshot vector, while others employ multiple snapshots. This dissertation deals with both these cases in different contexts.</p><p>Separable nonlinear least squares is a popular tool to extract parameter estimates from a single snapshot vector. Asymptotic statistical properties of the separable non-linear least squares estimates are explored in the first part of the thesis. The assumptions imposed on the noise process and the data model are general. Therefore, the results are useful in a wide range of applications. Sufficient conditions are established for consistency, asymptotic normality and statistical efficiency of the estimates. An expression for the asymptotic covariance matrix is derived and it is shown that the estimates are circular. The analysis is extended also to the constrained separable nonlinear least squares problems.</p><p>Nonparametric estimation of the material functions from wave propagation experiments is the topic of the second part. This is a typical application where a single snapshot vector is employed. Numerical and statistical properties of the least squares algorithm are explored in this context. Boundary conditions in the experiments are used to achieve superior estimation performance. Subsequently, a subspace based estimation algorithm is proposed. The subspace algorithm is not only computationally efficient, but is also equivalent to the least squares method in accuracy.</p><p>Estimation of the frequencies of multiple real valued sine waves is the topic in the third part, where multiple snapshots are employed. A new low rank signal model is introduced. Subsequently, an ESPRIT like method named R-Esprit and a weighted subspace fitting approach are developed based on the proposed model. When compared to ESPRIT, R-Esprit is not only computationally more economical but is also equivalent in performance. The weighted subspace fitting approach shows significant improvement in the resolution threshold. It is also robust to additive noise.</p>