Sonar Sequences Research Articles

Some Constructions and Mathematical Properties of Zero-Correlation-Zone Sonar Sequences.

In this paper, we propose the zero-correlation-zone (ZCZ) of radius r on two-dimensional m×n sonar sequences and define the (m,n,r) ZCZ sonar sequences. We also define some new optimality of an (m,n,r) ZCZ sonar sequence which has the largest r for given m and n. Because of the ZCZ for perfect autocorrelation, we are able to relax the distinct difference property of the conventional sonar sequences, and hence, the autocorrelation of ZCZ sonar sequences outside ZCZ may not be upper bounded by 1. We may sometimes require such an ideal autocorrelation outside ZCZ, and we define ZCZ-DD sonar sequences, indicating that it has an additional distinct difference (DD) property. We first derive an upper bound on the ZCZ radius r in terms of m and n≥m. We next propose some constructions for (m,n,r) ZCZ sonar sequences, which leads to some very good constructive lower bound on r. Furthermore, this construction suggests that for m and r, the parameter n can be as large as possible indefinitely. We present some exhaustive search results on the existence of (m,n,r) ZCZ sonar sequences for some small values of r. For ZCZ-DD sonar sequences, we prove that some variations of Costas arrays construct some ZCZ-DD sonar sequences with ZCZ radius r=2. We also provide some exhaustive search results on the existence of (m,n,r) ZCZ-DD sonar sequences. Lots of open problems are listed at the end.

New Constructions of Extended Sonar Sequences From Sidon Sets

A <inline-formula> <tex-math notation="LaTeX">$(m,n)$ </tex-math></inline-formula> sonar sequence is an <inline-formula> <tex-math notation="LaTeX">$m\times n$ </tex-math></inline-formula> array with exactly one dot in each column and where all lines connecting two dots in the array are distinct as vectors. These arrays are known to have many applications such as sonar and radar detection and these are studied as a particular case of Golomb rectangles or two-dimensional Sidon sets. The main open problem for sonar sequences is: for fixed <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula>, find the largest <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> for which there is an <inline-formula> <tex-math notation="LaTeX">$(m,n)$ </tex-math></inline-formula> sonar sequence, these sequences are called the best sonar sequences. The extended sonar sequences are generalizations of sonar sequences where each column has at most one dot, the motivation to study these arrays are the best results obtained when applied to radar and sonar detection. In this paper, we give the best sonar sequences with <inline-formula> <tex-math notation="LaTeX">$m\leq 100$ </tex-math></inline-formula> obtained from an exhaustive computational search based on the Caicedo, Ruiz and Trujillo constructions and we present new constructions of extended sonar sequences that use Sidon sets.

A submarine pipeline segmentation method for noisy forward-looking sonar images using global information and coarse segmentation

The submarine pipeline is an important way to transport marine resources such as oil and gas. For maintaining submarine pipelines, autonomous underwater vehicles (AUVs) equipped with sonars are leveraged. Whether the complete submarine pipelines can be segmented from the complex and noisy background is the key to path planning and navigation, which determines the efficiency of AUVs. Existing methods for segmenting sonar images such as Markov random field (MRF) are insufficient to achieve this goal. Inspired by the similarities between submarine pipelines in sonar images and salient objects in natural images, we propose a novel method to extract pipelines which can be summarized as three steps. First, an effective denoising method via curvelet thresholding is proposed to suppress speckle noise. Second, we attempt to compute the probability whether a pixel belongs to submarine pipelines by global information containing four similarities. Two of them are shape similarity and angle similarity, which are proposed according to the characteristics of pipelines in sonar images. Third, we propose a coarse segmentation method based on bootstrapped support vector machines (SVMs) and a fusion strategy to generate binary segmentation results precisely and completely. We captured 15 sonar sequences via the AUV equipped with a forward-looking sonar at Qingdao National Deep-Sea Base and selected 262 sonar images from the sequences for evaluating the segmentation performance. The proposed method is compared with other advanced methods. The experimental results show that our method achieves a better performance than other methods, and demonstrate the feasibility of segmenting submarine pipelines inspired by saliency segmentation.

A novel high precision mosaic method for sonar video sequence

The mosaic of sonar images is more difficult than the mosaic of traditional optical images due to their poor quality and the difficulty in extracting feature points. The existing mosaic methods of sonar images have a series of problems, such as low correct matching rate, large cumulative errors and high requirements for the quality of collected sonar images. In this paper, we proposed a high precision method to implement the mosaic of the underwater sonar video image sequence. Firstly, Accelerated Unsharp Masking (AUSM) algorithm is proposed to preprocess the original image. Then we extract KAZE feature points from preprocessed sonar images. A matching method combining multiple matching strategies with Progressive Sample Consensus (PROSAC) algorithm is followed to complete the image registration. Weighted fusion method and a region of interest (ROI) acquisition method based on the slope of right border is used to optimize the mosaicked image. Finally, we can obtain a high-quality panoramic image of underwater sonar video by a global mosaic strategy. Mosaic experiments on the sonar video image sequence collected by multi-beam sonar demonstrate that the proposed method in this paper can increase the number of feature points by about 70% and make the correct matching rate higher than 70%. The proposed method also has good robustness and the cumulative error during multi-image mosaic is less.

Secuencia Sonar Bose y algunas propiedades

Se presenta la secuencia sonar Bose y se muestra que satisfacen algunas de las características de las secuencias sonar conocidas, las cuales se relacionan mediante algunas propiedades geométricas y algebraicas de los conjuntos de Sidon. Se especifica una metodología para la obtención de la secuencia Bose utilizando el software Matlab, éstas secuencias pueden ser aplicadas a diversos campos de la ingeniería que involucren técnicas Radar y/o Sonar.

Natural echolocation sequences evoke echo-delay selectivity in the auditory midbrain of the FM bat, Eptesicus fuscus.

Echolocating bats must process temporal streams of sonar sounds to represent objects along the range axis. Neuronal echo-delay tuning, the putative mechanism of sonar ranging, has been characterized in the inferior colliculus (IC) of the mustached bat, an insectivorous species that produces echolocation calls consisting of constant frequency and frequency modulated (FM) components, but not in species that use FM signals alone. This raises questions about the mechanisms that give rise to echo-delay tuning in insectivorous bats that use different signal designs. To investigate whether stimulus context may account for species differences in echo-delay selectivity, we characterized single-unit responses in the IC of awake passively listening FM bats, Eptesicus fuscus, to broadcasts of natural sonar call-echo sequences, which contained dynamic changes in signal duration, interval, spectrotemporal structure, and echo-delay. In E. fuscus, neural selectivity to call-echo delay emerges in a population of IC neurons when stimulated with call-echo pairs presented at intervals mimicking those in a natural sonar sequence. To determine whether echo-delay selectivity also depends on the spectrotemporal features of individual sounds within natural sonar sequences, we studied responses to computer-generated echolocation signals that controlled for call interval, duration, bandwidth, sweep rate, and echo-delay. A subpopulation of IC neurons responded selectively to the combination of the spectrotemporal structure of natural call-echo pairs and their temporal patterning within a dynamic sonar sequence. These new findings suggest that the FM bat's fine control over biosonar signal parameters may modulate IC neuronal selectivity to the dimension of echo-delay. NEW & NOTEWORTHY Echolocating bats perform precise auditory temporal computations to estimate their distance to objects. Here, we report that response selectivity of neurons in the inferior colliculus of a frequency modulated bat to call-echo delay, or target range tuning, depends on the temporal patterning and spectrotemporal features of sound elements in a natural echolocation sequence. We suggest that echo responses to objects at different distances are gated by the bat's active control over the spectrotemporal patterning of its sonar emissions.

Selectivity of bat midbrain neurons to stimulus elements embedded in natural echolocation sequences

We investigated response selectivity of single neurons in the inferior colliculus (IC) of the big brown bat, Eptesicus fuscus, to acoustic elements embedded in the natural temporal patterning of dynamic frequency modulated (FM) echolocation sequences. Acoustic stimuli consisted of species-specific sonar sequences, with natural dynamic spectro-temporal features, containing both bat-emitted FM pulses and echoes from a moving target. Roughly 50% of sampled IC neurons showed responses to a restricted subset of stimulus elements in the natural sonar sequence and selectivity to the time delay between pulses and echoes, the bat’s cue for target distance. Importantly, response selectivity emerged only when stimulus elements were embedded in natural sequences and was absent when the same neurons were stimulated with isolated pulse-echo pairs presented randomly at 300 ms stimulus intervals. These data provide compelling evidence that natural and dynamic sound sequences are necessary to evoke selectivity to pulse-echo delay in midbrain neurons of an FM bat. Our findings suggest that the FM bat’s fine temporal control of pulse interval during insect pursuit contributes to neuronal selectivity that can serve to sharpen acoustic imaging by sonar.

Distinct Difference Configurations: Multihop Paths and Key Predistribution in Sensor Networks

A distinct difference configuration is a set of points in <emphasis emphasistype="italic" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"><tex Notation="TeX">$\BBZ ^{2}$</tex></formula></emphasis> with the property that the vectors ( <emphasis emphasistype="boldital" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">difference vectors</emphasis> ) connecting any two of the points are all distinct. Many specific examples of these configurations have been previously studied: the class of distinct difference configurations includes both Costas arrays and sonar sequences, for example. Motivated by an application of these structures in key predistribution for wireless sensor networks, we define the <emphasis emphasistype="italic" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"> <tex Notation="TeX">$k$</tex></formula></emphasis> -hop coverage of a distinct difference configuration to be the number of distinct vectors that can be expressed as the sum of <emphasis emphasistype="italic" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"> <tex Notation="TeX">$k$</tex></formula></emphasis> or fewer difference vectors. This is an important parameter when distinct difference configurations are used in the wireless sensor application, as this parameter describes the density of nodes that can be reached by a short secure path in the network. We provide upper and lower bounds for the <emphasis emphasistype="italic" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"> <tex Notation="TeX">$k$</tex></formula></emphasis> -hop coverage of a distinct difference configuration with <emphasis emphasistype="italic" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"> <tex Notation="TeX">$m$</tex></formula></emphasis> points, and exploit a connection with <emphasis emphasistype="italic" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"><tex Notation="TeX">$B_{h}$</tex> </formula></emphasis> sequences to construct configurations with maximal <emphasis emphasistype="italic" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"><tex Notation="TeX">$k$</tex> </formula></emphasis> -hop coverage. We also construct distinct difference configurations that enable all small vectors to be expressed as the sum of two of the difference vectors of the configuration, an important task for local secure connectivity in the application.

Feature Tracking in Video and Sonar Subsea Sequences with Applications

This paper deals with automatic target tracking in video and sonar subsea sequences, an essential capability for automating tasks currently performed by remotely operated vehicles under pilot control. We describe two trackers, one for video sequences, the other for sector scan sonar sequences. No assumptions are made about the images, scene, or motion observed. To illustrate applications, we report results of our systems for 3-D structure reconstruction and panoramic mosaic building from video sequences and describe in some detail our path planning and obstacle avoidance system using sonar sequences.

Extended sonar sequences

Sonar sequences were introduced by Golomb and Taylor in 1982. We introduce the concept of extended sonar sequences, which is similar to that of sonar sequences except that blank columns are permitted. Several constructions for extended sonar sequences are offered here. Some of these are close to constructions for ordinary sonar sequences, but they provide improvements to the list of best sonar sequences with up to 100 symbols.

On generalization of sonar sequences and intermodulation-free frequencies assignment sequences

On generalization of sonar sequences and intermodulation-free frequencies assignment sequences

Sonar sequences from Costas arrays and the best known sonar sequences with up to 100 symbols

The authors construct new and improved sonar sequences by applying rotation, multiplication, and shearing transformations to Costas sequence constructions. A catalog of the best known sonar sequences with up to 100 symbols is given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Bounds for arrays of dots with distinct slopes or lengths

Ann×m sonar sequence is a subset of then×m grid with exactly one point in each column, such that the\(\mathop 2\limits^m \) vectors determined by them are all distinct. We show that for fixedn the maximalm for which a sonar sequence exists satisfiesn−Cn11/20 n+c logn log logn for infinitely manyn.

Node-graceful graphs

A disconnected forest F = ( V, E) with | V | = p and | E | = q cannot be graceful as there is no possible numbering of V with distinct integers from the set {0,…, q. However, the augmented set {0,…, p − 1} has just enough numbers for V and suggests the concept of a node-graceful graph. On the other hand, some problems arising from radar and sonar sequences of distinct frequencies in consecutive time slots can be regarded as the two-dimensional analog of the one-dimensional “ruler problems”. These two-dimensional synchronization patterns are formulated in terms of node-graceful graphs. It is shown that the matching graph nK 2 is node-graceful if and only if there exists an ( s, n)-Skolem sequence with s = 2. Other results are obtained and the current state of knowledge is summarized.

An Algebraic Construction of Sonar Sequences Using M-Sequences

An algebraic construction of sonar sequences that is based on the properties of q-ary M -sequences for q a prime power is presented. Sonar sequences give two-dimensional synchronization patterns that have two-dimensional spatial aperiodic autocorrelation functions with minimum out-of-phase values. The best sonar sequences with length $q^m \leqq 128$ that are obtained from the construction are tabulated. Based on a comparison with the limited number of known optimal values, the construction performs quite well, producing optimal sonar sequences in the majority of applicable cases.

Crosscorrelation of M-sequences and GMW-sequences with the same primitive polynomial

The periodic crosscorrelation function of an M-sequence and a GMW-sequence that have been constructed from the same primitive polynomial is calculated in terms of the perodic crosscorrelation function of two smaller M-sequences. Along the way, a rather nice property satisfied by a collection of differences arising from the trace function Tr m n : GF(2 n )→GF(2 m ) is described and a connection to sonar sequences is made.

Sonar sequences and Sidon sets

Sonar sequences and Sidon sets