Direct position detection and localization of emitters using distributed sensors
In this thesis we addressed the problem of passively gathering information about an emitter of electronic signals using distributed sensors. First we proposed an asymptotically optimal technique for detection of the presence or absence of such signals in the data collected at the distributed sensors. This is a centralized detector unlike the commonly used decentralized decision fusion techniques. The derived detector is the generalized likelihood ratio test (GLRT) detector. We also derived simpler detectors from the GLRT by making various assumptions. Receiver operating characteristics (ROC) curves for currently used detectors are computed and compared to the ROC curves for the GLRT detector. After the presence of such signals is detected, the next step is to estimate the location of the emitter. For this we proposed the maximum likelihood estimator (MLE). The conventional approach for localization using multiple sensors is to first estimate the time difference of arrivals (TDOAs) of the signals, independently between pairs of sensors and then to find the location of the emitter using the intersection point of the hyperbolas defined by these TDOAs. This is referred to as the conventional TDOA technique and it has been shown in the literature that this two-step approach is suboptimal in comparison to what is called the direct position determination (DPD) approach. In the DPD approach, the intermediate step of estimating the TDOAs is bypassed and the location is estimated directly from the observations. In this paper we take the DPD approach instead of the conventional two-step approach. The DPD type localizers that have been proposed in the literature are based on certain assumptions on the transmitted signal such as narrowband or wideband, lowpass or bandpass etc. We make no such assumptions on the signal and this paper covers a wide variety of transmitted signals. In passive localization, it is common to not know the transmission time of the signal and more often the signal waveform itself is unknown. So, we have analyzed these two commonly occurring cases of (i) signal waveform unknown and (ii) signal waveform known with unknown transmission time. The localizers proposed in literature assumed discrete time but they have not addressed the quantization like effect on the location estimate due to sampling of the received signals. To avoid this quantization like effect, we have used a continuous time model. We have also derived the Fisher Information Matrix (FIM) which gives a deeper insight into the relations between various parameters in the model and their identifiability. We showed that the proposed MLE outperforms the conventional two-step localizers and also attains the Cramer Rao Lower Bound (CRLB) for high signal-to-noise ratios (SNR). Though the performance of the MLE attains the CRLB, there is still scope for improvement. This improvement comes from the geometry of the sensors. We showed that for a given SNR, the CRLB depends on the sensor geometry. Thus, the sensor geometry can be optimized in order to further reduce the CRLB and also the variance of the MLE. We have defined this problem of optimizing the sensor geometry and derived the optimal sensor configurations for a few specific scenarios. The optimization of the sensor geometry for a general scenario is quite elusive and still open for research. In addition to efficient signal processing as in the MLE and optimizing the sensor geometries, the localization performance can further be enhanced by using information about the terrain. This is commonly referred to as the knowledge aided design (KAD). KAD is particularly useful for localization in urban environments where the distances are small and the knowledge of the terrain is very well known. We investigated the aspect of amplitude modulation induced by various objects in the terrain and the usefulness of this modulation for localization. In particular, we have shown that when an obstacle blocks the signal to one of the sensors, then there is increase in the over all information of the location of the emitter. All the concepts mentioned above are for improving the localization performance and do require altering/increasing the existing physical resources. For example the MLE requires high bandwidth links between all the sensors and the fusion center in order to transmit all the data collected at each sensor for simultaneous processing at the fusion center. This is in contrast to the conventional TDOA which only requires low bandwidth links to the fusion center because, here only the TDOA instead of the complete observation, is transmitted to the fusion center. So finally we propose an improvement to the conventional TDOA approach which requires very little additional physical resources but significantly increases the localization performance particularly for SNRs at the break down range. The only additional piece of information that needs to be transmitted to the fusion center along with the TDOA is the curvature of the likelihood function. In the conventional TDOA approach the first step is to estimate the TDOAs and the second step, called the position fixing, is to estimate the emitter location as the intersection of the hyperboloids defined by these TDOAs. For the TDOA estimation the commonly used estimator is the time-delay that maximizes the cross-correlation function. This is the MLE of the TDOA (note that this is not the MLE of the emitter location which we have derived) and the cross-correlation function is the maximum likelihood function. Now, since the asymptotic variance of an MLE is equal to the negative of the expected value of the curvature of the likelihood function, we proposed a weighted least squares type position fixing technique where the weights can be computed from the curvature of the likelihood function. Hence, we have addressed the problem of passively gathering information about an emitter of electronic signals using distributed sensors and investigated various aspects that can increase this information. ^
Engineering, Electronics and Electrical
"Direct position detection and localization of emitters using distributed sensors"
Dissertations and Master's Theses (Campus Access).