Relying on the reception and analysis of signals already present in the environment, has various applications across different domains, from acoustics to electromagnetics. However, the growing signal ...bandwidth poses tremendous challenges in data transmission, highlighting the advantages of the compressive sensing (CS) technique. In this study, we investigate the direct position determination (DPD) using sub-Nyquist sampling signals directly without reconstruction the full signal first. Leveraging the Hadamard matrix as the CS measurement matrix, the cost function for emitter source determination is first established with the sub-Nyquist sampled signals. Hence, the full signal recovery error and cumbersome computation are avoided compared with existing passive localization methods with CS signals. In addition, the Carmér-Rao Lower bound (CRLB) is theoretically derived and points out the trade-off between localization accuracy and sparse signal sampling rate. The effectiveness of the proposed method is demonstrated through Monte Carlo simulations and comparisons.
Transmitter localization is used extensively in civilian and military applications. In this paper, we focus on the Direct Position Determination (DPD) approach, based on Time of Arrival (TOA) ...measurements, in which the transmitter location is obtained directly, in one step, from the signals intercepted by all sensors. The DPD objective function is often non-convex and therefore finding the maximum usually require s exhaustive search, since gradient based methods usually converge to local maxima. In this paper we present an efficient technique for finding the extremum of the objective function that corresponds to the transmitter location. The proposed method is based on the Expectation-Maximization (EM) algorithm. The EM algorithm is designed to find the Maximum Likelihood (ML) estimate when the available data can be viewed as “incomplete data”, while the “complete data” is hidden in the model. By choosing the appropriate “incomplete data” we replace the high dimensional search, associated with the ML algorithm, with several sub-problems that require only one dimensional search. We demonstrate that although the EM algorithm does not guarantee a convergence to the global maximum, it does so with high probability and therefore it outperforms the common gradient-based methods.
•A framework to solve TOA/TDOA based localization in the presence of nuisance parameters, using the EM algorithm.•Application of the framework to the DPD method which is usually solved using variants of exhaustive search, due to the non-convex structure of the objective function.•Demonstration by simulations that the proposed EM approach achieves the global maximum at various scenarios, and SNR levels with high probability.•Application of the EM algorithm to the traditional two step method with a closed from solution at each iteration without using derivatives (or Jacobians).•Demonstration that the algorithm is more stable than the well-known Gauss-Newton algorithm, and generally converges quickly.
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In this study, an off-grid sparse Bayesian inference (OGSBI) based direct position determination (DPD) algorithm is investigated. Existing SBI-based DPD algorithms are confronted with the challenge ...of excessive computational loads and lack of consideration for non-circular (NC) signals. To address these limitations, we present an enhanced OGSBI-based DPD algorithm for multiple non-circular sources. By utilizing the conjugate information of the NC signals, we expand the dimensionality of the data matrix to achieve a significant improvement in the localization performance. Additionally, a grid refinement strategy is developed to alleviate the computational loads, which involves an initial search to determine the approximate source locations, followed by fine localization using a denser grid. Moreover, the computational complexity and Cramér-Rao lower bound are derived to provide a comprehensive analysis of the proposed algorithm. Numerical simulations demonstrate the superiority of the proposed algorithm in terms of both localization accuracy and computational efficiency.
•Enhance the localization accuracy by exploiting the property of non-circular signals.•A grid refinement strategy for direct position determination is introduced to reduce the complexity.•Off grid sparse Bayesian inference based model is applied for direct localization to address the grid mismatch problem.•Improve computational efficiency and noise resistance via SVD technique.•The Cramér-Rao lower bound of non-circular signals for direct position determination is derived.
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The global positioning system (GPS), which provides ubiquitous location-awareness with a constellation of satellites, has become an instrumental function of multiple mass-market applications. ...Satellite signals, however, may not be capable of penetrating obstacles in harsh environments (e.g., urban canyons, tree canopies, and flyovers). Hence, GPS may not provide adequate localization accuracy for applications like autonomous vehicles. Resorting to data fusion of heterogeneous signals emanating from multiple anchors, we advocate a self-localization method that provides accurate estimates of the vehicle position. To be more specific, several heterogenous emitters whose positions are known are used as anchors to determine the vehicle's position based on the weighted direct position determination (DPD) method that eliminates nonhomogeneity among different emitters. However, the weighted DPD method requires an exhaustive search of the parameter search space and is thus time-consuming. To reduce the computational burden, we propose a weighted cascade compensation estimator (WCCE) that is tailored for real-time tracking and self-localization. The proposed WCCE outperforms traditional DPD methods in terms of computational complexity while achieving nearly comparable localization accuracy. The effectiveness of the proposed method is corroborated by extensive simulated examples.
The direct position determination (DPD) approach is a single-step method, which uses the maximum likelihood estimator to localize sources emitting electromagnetic energy using combined data from all ...available sensors. The DPD is known to outperform the traditional two-step methods under low signal-to-noise ratio conditions. We propose an improvement to the DPD approach, using the well-known minimum-variance-distortionless-response (MVDR) approach. Unlike maximum likelihood, the number of sources needs not be known before applying the method. The combination of both the direct approach and MVDR yields unprecedented localization accuracy and resolution for weak sources. We demonstrate this approach on the problem of multistatic radar, but the method can easily be extended to general localization problems.
The most common methods for localization of radio frequency transmitters are based on two processing steps. In the first step, parameters such as angle of arrival or time of arrival are estimated at ...each base station independently. In the second step, the estimated parameters are used to determine the location of the transmitters. The direct position determination approach advocates using the observations from all the base stations together in order to estimate the locations in a single step. This single-step method is known to outperform two-step methods when the signal-to-noise ratio is low. In this paper, we propose a direct-position-determination-based method for localization of multiple emitters that transmit unknown signals. The method does not require knowledge of the number of emitters. It is based on minimum-variance-distortionless-response considerations to achieve a high resolution estimator that requires only a two-dimensional search for planar geometry, and a three-dimensional search for the general case.
Displacement experiments have demonstrated that experienced migratory birds translocated thousands of kilometers away from their migratory corridor can orient toward and ultimately reach their ...intended destinations.1 This implies that they are capable of “true navigation,” commonly defined2–4 as the ability to return to a known destination after displacement to an unknown location without relying on familiar surroundings, cues that emanate from the destination, or information collected during the outward journey.5–13 In birds, true navigation appears to require previous migratory experience5–7,14,15 (but see Kishkinev et al.16 and Piersma et al.17). It is generally assumed that, to correct for displacements outside the familiar area, birds initially gather information within their year-round distribution range, learn predictable spatial gradients of environmental cues within it, and extrapolate from those to unfamiliar magnitudes—the gradient hypothesis.6,9,18–22 However, the nature of the cues and evidence for actual extrapolation remain elusive. Geomagnetic cues (inclination, declination, and total intensity) provide predictable spatial gradients across large parts of the globe and could serve for navigation. We tested the orientation of long-distance migrants, Eurasian reed warblers, exposing them to geomagnetic cues of unfamiliar magnitude encountered beyond their natural distribution range. The birds demonstrated re-orientation toward their migratory corridor as if they were translocated to the corresponding location but only when all naturally occurring magnetic cues were presented, not when declination was changed alone. This result represents direct evidence for migratory birds’ ability to navigate using geomagnetic cues extrapolated beyond their previous experience.
•Birds respond to novel magnetic fields as if displaced to the equivalent location•Changing one magnetic cue only (declination) does not result in re-orientation•The “virtual displacement” only works when all magnetic cues match a real place•This strongly suggests birds can extrapolate beyond previous knowledge to new places
It is still unclear how migratory birds navigate from outside their familiar range. By testing their orientation in a changed magnetic field at the capture site, Kishkinev et al. show that birds respond to these changes as if displaced to the simulated location, suggesting they can extrapolate beyond their previous experience of the magnetic field.
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•The direct localization algorithm combining with the iterative approach is proposed for coherent sources.•The connected domain separation method can efficiently isolate and extract the domains ...containing different sources.•The proposed algorithm outperforms the existing methods in accuracy and robustness for locating coherent sources.•Increasing antennas can obtain better localization performance from energy gain and spatial filtering effect.
The direct position determination (DPD) approach is known to outperform the two-step localization at low signal to noise ratio, however, and it encounters many difficulties when locating multiple coherent sources. In this paper, we combine the DPD with the iterative adaptive approach (IAA) to address the localization problem of coherent sources without knowing the transmitted signals. The frequency-domain coherent signal model is established to obtain snapshot samples for jointly processing signals received by all distributed arrays. To avoid the covariance matrix becoming rank-deficient, we propose to use the IAA to compute it and the intercepted signals, instead of the traditional methods directly based on the snapshots. Once estimating the intercepted signals, the closed-form spatial power function is derived to determine the positions of multiple coherent sources. Additionally, the method based on connected domain separation is also proposed to extract the position of each source from the spatial power map. Numerical experiments show that the proposed algorithm is superior to the existing DPD algorithms in accuracy and robustness for coherent sources, and can obtain the same great performance with the existing ones for noncoherent sources.
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The global satellite navigation system is a common tool for self-positioning, but its performance may become weak or interrupted due to obstacles in harsh environments. The application of sensor ...arrays provides a more flexible and independent of satellites self-positioning scheme. We propose a direct self-position determination method based on the sensor array, which exploits multiple non-circular (NC) emitters with known locations and combines reduced dimension and weighted propagator method. Specifically, the proposed algorithm achieves direct self-position determination by means of the received NC signals. The sensor array aperture is extended by utilizing the elliptic covariance matrix of non-circular signals, and a reduced dimension approach is applied to eliminate the non-circular phase search dimension and thus reduce the complexity. Due to the different signal attenuation from emitters, a weight based on estimated signal-to-noise ratio (SNR) is deployed to further improve the performance of the algorithm. In addition, the Cramér-Rao Bound (CRB) of the self-positioning problem is derived. Numerical simulations also verify that the proposed method gains higher accuracy and lower complexity compared with the conventional methods.
•Closed-form FIMs for 3D DPD: We consider a 3D DPD system where ULAs with different array orientations are used to localize the emitter. We derive the closed-form FIM for the single emitter scenario. ...Also, in the context of large-scale antenna arrays, a closed-form FIM is derived for the multi-emitter scenario.•SDR Solutions of Optimal Array Orientations: Exploiting the property that the FIM is an affine function in rank-one bilinear variables, the SDR is applied, and the bilinear variables are replaced with matrices while the rank constrain is relaxed. By rewriting the formulated problem into the hypograph form, the optimization problem can be recast as an SDP, which is convex and can be solved using interior-point methods in polynomial time.•Simulations: Performance evaluations are conducted to verify the performance improvement brought by the proposed array orientation configuration strategy. The simulation results demonstrate that a simple change in array orientation can significantly improve the localization performance.
This paper presents an optimization strategy for array orientations in a three-dimensional (3D) direct position determination (DPD) system. Specifically, we consider a scenario in which uniform linear arrays (ULAs) are used to locate emitters, and we seek to optimize the array orientations in terms of localization accuracy. The E-optimality criterion, which minimizes the spectral norm of the Cramér-Rao lower bound (CRLB), is exploited to formulate this problem. As the objective function is non-convex with bilinear structures, we leverage semi-definite relaxation (SDR) to transform it into a convex semi-definite programming (SDP) problem by substituting the bilinear terms with a matrix variable. In addition, we tackle the array orientation configuration problem in the context of multi-emitter scenarios and develop an SDR solution for large-scale antenna array systems. Simulation results validate that the ULAs with array orientations designed by the proposed SDR-based method have near-optimal localization performance.
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