Sparse multidimensional exponential analysis with an application to radar imaging

We present a d-dimensional exponential analysis algorithm that offers a range of advantages compared to other methods. The technique does not suffer the curse of dimensionality and only needs O((d + 1)n) samples for the analysis of an n-sparse expression. It does not require a prior estimate of the sparsity n of the d-variate exponential sum. The method can work with sub-Nyquist sampled data and offers a validation step, which is very useful in low SNR conditions. A favourable computation cost results from the fact that d independent smaller systems are solved instead of one large system incorporating all measurements simultaneously. So the method also lends itself easily to a parallel execution. Our motivation to develop the technique comes from 2D and 3D radar imaging and is therefore illustrated on such examples

Regular sparse array direction of arrival estimation in one dimension

Traditionally regularly spaced antenna arrays follow the spatial Nyquist criterion to guarantee an unambiguous analysis. We present a novel technique that makes use of two sparse non-Nyquist regularly spaced antenna arrays, where one of the arrays is just a shifted version of the other. The method offers several advantages over the use of traditional dense Nyquist spaced arrays, while maintaining a comparable algorithmic complexity for the analysis. Among the advantages we mention: an improved resolution for the same number of receivers and reduced mutual coupling effects between the receivers, both due to the increased separation between the antennas. Because of a shared structured linear system of equations between the two arrays, as a consequence of the shift between the two, the analysis of both is automatically paired, thereby avoiding a computationally expensive matching step as is required in the use of so-called co-prime arrays. In addition, an easy validation step allows to automatically detect the precise number of incoming signals, which is usually considered a difficult issue. At the same time, the validation step improves the accuracy of the retrieved results and eliminates unreliable results in the case of noisy data. The performance of the proposed method is illustrated with respect to the influence of noise as well to the effect of mutual coupling

VEXPA: Validated EXPonential Analysis through regular sub-sampling

We present a procedure that adds a number of desirable features to standard exponential analysis algorithms , among which output reliability, a divide-and-conquer approach, the automatic detection of the exponential model order, robustness against some outliers, and the possibility to parallelize the analysis. The key enabler for these features is the introduction of uniform sub-Nyquist sampling through decima-tion of the dense signal data. We actually make use of possible aliasing effects to recondition the problem statement rather than that we avoid aliasing. In Section 2 the standard exponential analysis is described, including a sensitivity analysis. In Section 3 the ingredients for the new approach are collected, of which good use is made in Section 4 where we essentially bring everything together in what we call VEXPA. Some numerical examples of the new procedure illustrate in Section 5 that the additional features are indeed realized and that VEXPA is a valuable add-on to any stand-alone exponential analysis. While returning a lot of additional output, it maintains a favourable comparison to the CRLB of the underlying method, for which we here choose a matrix pencil method. Moreover, the output reliability of VEXPA is similar to that of atomic norm minimization, whereas its computational complexity is far less

Antenna Position Estimation Through Subsampled Exponential Analysis of Signals in the Near Field

In a previous article we explored the use of a subsampled exponential analysis algorithm to find the antenna-element positions in a large irregular planar array after the installation phase. The application requires an unmanned aerial vehicle to be flown over the antenna array while transmitting several odd harmonic signals. The received signal samples at a chosen reference antenna element are then compared to those at every other element in the array in order to find its position. Previously, the far-field approximation was used to calculate the time delay between received signals. In this article the method is reconsidered for the more realistic case of when the source is in the near field of the array. A number of problems that arise are addressed, and results from a controlled simulation are presented to illustrate that the computational method works

Antenna position estimation through sub-sampled exponential analysis of harmonically related input signals

Accurate placement of elements in large antenna arrays is a difficult and costly process. We explore the use of the validated exponential analysis (VEXPA) technique that was previously formulated to solve a direction-of-arrival (DOA) estimation problem, to find the antenna element positions in an array after the installation phase, so that cost-savings can be realised during placement of the antenna elements. Measurements are taken from harmonically related input signals transmitted from an Unmanned Aerial Vehicle (UAV) for which the position in the sky is known. It is shown how the UAV's zenith angle can be manipulated to generate parameters required for VEXPA's de-aliasing step. A simple simulation illustrates the functioning of the proposed method

Thinking like a fish: a key ingredient for development of effective fish passage facilities at river obstructions

Worldwide, obstructions on watercourses have interfered with migratory pathways of fish species, reducing life‐cycle success and often eliminating diadromous fish species altogether from river basins. Over the last century, efforts to mitigate these effects were initially directed at developing fishways for upstream, high‐value migrant adult salmon. In more recent years, efforts have turned to developing fishways for other species. Results of past research suggest that the development of effective fishways requires biological knowledge of fish behaviour when encountering variable flows, velocity and turbulence, combined with hydraulic and civil engineering knowledge and expertise to develop facilities that provide ppropriate hydraulic conditions that fish will exploit. Further, it often requires substantial financial resources for biological and hydraulic testing as well as engineering design, particularly where prior knowledge of the behaviour of target fish species does not exist. Where biological or engineering knowledge (or both) is absent, development of effective passage facilities must take on a trial and error approach that will almost certainly require years to attain success. Evaluations of existing adult and juvenile fish passage facilities, where they have been carried out, suggest that migrant fish reject areas with hydraulic conditions they determine unsuitable. Even well designed fish ladders or nature‐like bypass channels for upstream migrants, even those with good attraction flows, will fail if incorrectly sited. Although progress has been made, developing successful installations for downstream migrants remains much more difficult, probably because downstream fish move with the flow and have less time to assess cues at entrances to any bypasses that they encounter

The use of visual and automatized behavioral markers to assess methodologies: a study case on PIT-tagging in the Alpine newt

peer reviewedBiomarkers are now widely used as tools in various research fields to assess individual integrity. The recent advances in quantification methods of behavioral patterns, such as computerized video-tracking procedures, make them valuable biomarkers. However, the corollary of these novelties is that they remain relatively unknown and unused. In this study, we show that such tools can assess the validity of research methods, such as individual recognition. To demonstrate this we employed as a model a marking method (Passive Integrate Transponders: PIT-tagging) widely used in amphibians. Both detailed visual observations and video-tracking methods were complementary in highlighting components at different behavioral scales: locomotion, feeding, and breeding. We illustrate the scientific and ethical adequacy of the targeted marking method but also suggest that more studies should integrate behavioral analyses. Such biomarkers are a powerful tool to assess conservation concerns when other techniques cannot detect detrimental effects