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Self-positioning of submerged Autonomous Underwater Vehicles (AUVs) is a challenging task due to nonavailability of GPS signals. One of the most recent solutions for this is the use of surface vehicles (sensors) for cooperative localization of the underwater vehicles (targets) by measuring their relative positions. However, correct placement of the surface sensors is very critical as their geometric configuration affects their observability and hence availability of their relative positions information to the targets. In this paper, a comparative survey of sensors’ optimal formation techniques for cooperative localization of AUVs has been presented. Introduction to the basic cooperative localization techniques and background theory of optimal sensor placements have been provided. This paper can also serve as a fundamental reading material for students and researchers pursuing research on optimal sensor placement for cooperative localization.

Since their introduction in 70s [

To overcome the limitations of traditional localization methods, a new technique, called cooperative localization, is being studied recently [

Cooperative localization of underwater vehicles is much complex and challenging task compared to that of aerial or ground autonomous vehicles. This is because of the fact that, for above water, range can be easily measured using RF or Laser signals. It is also easy to relate RSS of RF or laser to range of the target for above water measurements. It has been shown by [

Extensive research has been carried out in the field of cooperative localization and different estimation algorithms and techniques have been proposed. However, optimal formation of the sensors for cooperative navigation is relative new field and only few research papers are available. The lack of a review paper in this field is also one of the bottlenecks of wider acceptance of the idea. In this paper, we will briefly provide a comparative survey of sensors’ optimal formation techniques for cooperative localization of AUVs. First we have given a brief overview of the techniques and methods used for cooperative localization of AUVs in Section

To better understand the problem of optimal formation, this section provides a brief overview of various techniques used for cooperative localization of AUVs that is at the core of the paper at hand. As already mentioned in previous section, in cooperative localization, target AUVs are localized by taking reference from the sensor AUVs whose accurate positions are known. A general form of cooperative localization of AUVs is graphically shown in Figure

Analysis and comparison of cooperative localization techniques.

Localization techniques | Advantages | Disadvantages | Applicable conditions | In literature of optimal sensor placements |
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Time of Arrival | High accuracy which is not much affected by range; significant literature available | Time synchronization between sensors and targets required | Suitable for long rage, NLOS operations | [ |

Angle of Arrival | Clock synchronization not required between targets and sensors; Smaller number of sensors required | Accuracy decreases with range; High accuracy directional antennas are to be installed, additionally | Suitable for short ranges when there is limitation on number of sensors | [ |

Time Difference of Arrival | High accuracy even at long ranges; No time synchronization between sensors and target required | Larger number of sensors required as compared to other methods | Best option for long ranges operations when larger number of sensors are available | [ |

Received Signal strength | Does not need to install extra hardware in both, targets and sensors | Severely affected by multipath, NLOS and other underwater environmental conditions | Suitable for short ranges and LOS communication only | None |

By measuring the angle of the received signal at target from a reference sensor, we can draw a straight line in that direction. Using multiple reference sensors, we can get multiple straight lines crossing each other at a common intersection point which is the estimated position of the target. AOA based localization problem is explained in Figure

2D view of Angle of Arrival (AoA) based cooperative localization.

Let

The time of arrival (TOA) method relies on the propagation time of a signal from the sensors to the target. In this method, one-way or two-way propagation time is determined and the range of sensors from target is estimated. Multilateration principle is used to estimate the target position as shown in Figure

2D view of Time of Arrival (ToA) based cooperative localization.

In Figure

If we draw arcs of radii

If path loss propagation model is known, range of the transmitter can be estimated by measuring the strength of the received signal. After measuring the range of a target from different sensors, its position is estimated utilizing multilateration technique as shown in Figure

Received Signal Strength (RSS) based cooperative localization.

Estimating the target range based on RSS measurement is complicated for underwater environment. However, various underwater transmission loss models have been proposed in the past which may be utilized for this purpose [

In noise-free environment, the received power,

RSS based localization method offers some advantages; i.e., no extra hardware is required to be installed in sensors or in target except power detector. Moreover, time synchronization between the target and the sensors is also not required. However this method is difficult to implement for underwater localization especially for longer ranges due to sound wave propagation properties. Consequently, RSS based cooperative localization of AUVs has not been much explored by the researchers yet.

TDOA method depends on the time difference of two signals that are generated from two sensors when arriving to the target. Each TDOA measurement determines that the target should lie on a hyperbolic curve with constant range difference between the two transmitting reference sensors as shown in Figure

Time Difference of Arrival (TDOA) based cooperative localization.

A typical scenario of cooperative localization.

As TDOA method depends upon sensor pairs, it is important how the sensor pairs are made for these measurements. Two types of sensor pair strategies have been presented in the past literature, i.e., Centralized Sensor Pairing (CSP) and Decentralized Sensor Pairing (DSP). In CSP, one of the sensors is declared as reference sensor and all other sensors make pair with common reference for TDOA measurement. Hence, for CSP, maximum possible sensor pairs are

Consider that

In order to estimate the position of a target AUV, its relative position with respect to the sensor AUVs is measured using acoustic waves with the help of techniques mentioned in Section

For any cooperative localization problem, the optimal sensor configuration depends strongly on the constraints imposed by the problem itself, i.e., the maximum number of available sensors and limitation of the area where sensors can be placed. For example, for cooperative localization of AUVs, the sensors are mostly placed on water surface to enable them to achieve GPS feed. In fact, a poor sensor configuration may incorporate large positioning errors irrelevant of the positioning technique used. The optimal sensor configuration for any cooperative localization system can be computed by analyzing the corresponding Cramér–Rao lower bound (CRLB) or Fisher information matrix (FIM). FIM and CRLB can be defined in terms of position coordinates of the sensors and the optimal sensor configuration is estimated by maximizing FIM or minimizing CRLB.

CRLB or, alternatively, FIM has been utilized in most of the previous literature for estimation of optimal sensor positions for cooperative localization. For any particular experiment, the observations recorded at different time are different in a certain way. The variance of the estimator is obtained by the weighted summation of the variances at different times. It can be found that, regardless of the weight distribution, the variance of any unbiased estimator can only approach a lower limit infinitely, and not below that limit. This lower limit of achievable variance is called CRLB.

The cooperative localization process is actually a state prediction process. The positioning error covariance is the quantity used for evaluation of its performance. CRLB gives estimation of minimal achievable variance for unbiased estimator, i.e., maximum achievable positioning accuracy in this case. Therefore, CRLB can be used to analyse the influence of sensor formation on positioning accuracy. Consider that unbiased estimation of the target’s position

The idea of finding the optimal geometric configuration for surface-deployed sensors for localization of a submerged target was initially presented in 1990 by Zhang [

In most of the past literature of sensor placement for cooperative localization of AUVs, CRLB or FIM has been used as an indicator of accuracy of the estimated positions. The history of usage of CRLB/FIM as accuracy indicator for sensor placement goes back to [

Now we will discuss all the significant research papers available in research literature relevant to sensor placement for cooperative localization of AUVs. In [

Geometric representation of FIM was defined based on maximum likelihood function. Determinant of the FIM was calculated and was solved for its maximum value to estimate the optimal positions of the sensors.

Initially, the case of 3 sensors and zero mean Gaussian measurement noise with fixed variance was studied. Moreover, there was no constraints on placement of the sensors; i.e., sensors could be placed anywhere in 3D coordinates. It was analytically concluded that if the target was positioned at the origin of inertial coordinates and sensor 1 was placed on x-axis (y1=z1=0), then optimal formation of sensor 2 and sensor 3 would be in YZ plane(x2=x3=0) and there would be no restriction on x1, y2, y3, z2, and z3. Moreover, optimal FIM for 3 sensors' cooperative localization with fixed measurement variance was estimated as

The case of 3 sensors and 1 target was again studied keeping in view the distance dependent measurement noise, modeled as

Finally, the general case of n-sensors was discussed. In this case, the optimal formation was estimated as symmetrical distribution of all the sensors around the target at the same distance

In [

In [

A preliminary literature reviewer in the field of optimal sensors placement for underwater target positioning was presented in [

In [

An interesting case of underwater target localization with only single surface sensor using range measurements was studied in [

Another research similar to [

In [

In [

A very detailed research on 3D optimal sensor placement for cooperative localization of underwater targets using range measurements was presented in [

In [

Finally, in [

Table

Tabular comparison of literature review.

S No. | Reference No. | Cooperative Localization technique used | Sensor-target configuration | Optimality criteria for sensor placement | Research challenges considered | Solution type | Remarks | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Experimental verification | Targets type | Target’s position uncertainty considered? | Underwater Sound Speed | Underwater sound propagation | Measurement noise | Numerical | Analytical | |||||||

stationary | Moving | |||||||||||||

1. | [ | ToA | Multi-sensors | Determinant of FIM | | | CS | ST | CS | | | |||

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2. | [ | TDOA | Multi-sensors | Evaluation function based on FIM | | | VR | CR | DD | | ||||

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3. | [ | AoA | Multi-sensors | Trace of CRB matrix | | | CS | ST | DD | | | |||

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4. | [ | ToA | Multi-sensors | Determinant of FIM | | CS | ST | DD | | | ||||

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5. | [ | ToA | Multi-sensors | Determinant of FIM | | | CS | ST | DD | | ||||

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6. | [ | AoA | Multi-sensors | Trace of CRB matrix | | CS | ST | DD | | | ||||

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7. | [ | ToA | Multi-sensors | Determinant of FIM | | CS | ST | CS | | | ||||

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8. | [ | ToA | Single-target Single-sensor | Determinant of FIM | | CS | ST | CS | | | ||||

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9. | [ | ToA | Single-target | Determinant of FIM | | | CS | ST | CS | | | |||

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10. | [ | ToA | Single-target | Empirical Gramians | | | CS | ST | CS | | ||||

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11. | [ | ToA | Single-target | Empirical Gramians | | | NA | CS | ST | CS | | Target position was assumed to be unknown and was estimated using range measurements in each step. | ||

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12. | [ | ToA | Single-target Single-sensor | Determinant of FIM | | | CS | ST | CS | | | |||

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13. | [ | ToA | Multi-targets two-sensors | Determinant of FIM | | | CS | ST | CS | | |

In this section, various research challenges associated with the field of optimal formation estimation for cooperative localization of AUVs are discussed and future work is suggested.

For localization of sensor nodes in wireless sensor networks (WSN), the sensors can be placed anywhere around the node in 3D. However, for cooperative localization of AUVs, the sensor AUVs have to operate on water surface in order to receive the GPS signals. On the other hand, target AUVs operate underwater at various depths. Therefore, targets are operating underwater and are to be localized in 3D while sensors can only be placed on water surface in 2D as shown in Figure

Sensor placement options. (a) Distributed Sensor Networks. (b) Cooperative localization of AUVs.

Acoustic waves are used for measuring the relative position of targets with respect to the sensors. These measurements are plagued with noise that depends on multiple factors relating to propagation properties of acoustic waves in water, for example,

It is an established fact that speed of sound in water varies with the depth mainly depending upon temperature, pressure, and salinity. Moreover, in water, acoustic waves follow a curved propagation path instead of straight one. These characteristics of sound propagation make it very difficult and challenging for the sensors to estimate accurate relative position of the targets, no matter which of the techniques of cooperative localization is being used. However, in research literature of cooperative localization and sensor placement, sound speed was mostly taken as constant and sound wave was considered to be travelling in a straight line. One of the exceptions is in [

There are many underwater sound propagation models available in research literature [

With the advancement in technology, AUVs are now being utilized for more complex and sophisticated operations. In most of the modern-day applications of AUV, multiple AUVs are being operated together. As the number of target AUVs increases, the corresponding sensors AUVs are to be increased accordingly. In such situation, all sensors are to be placed in a formation that is optimal for the entire target AUVs. Therefore, the optimal position of all the sensors is to be computed simultaneously for all the targets. When the number of targets/sensors increases, the corresponding computation complexity and time increase drastically. Few researchers have proposed some optimization algorithms to ensure fast and achievable calculations [

Although adequate research has been carried out in the last decade in the field of sensors placement for cooperative localization of AUVs, main focus of the research remained theoretical recommendations and simulation analysis. There has not been any experimental verification of any of the proposed methods, yet. The theoretical results supported by mathematical verifications have their importance, but experimental verification will not only enhance researchers’ confidence on the proposed theories but also allow improving the proposed methods by addressing the shortcomings highlighted by the experiments. Therefore, experimental verification is also a potential future research area in this field.

Optimal sensor placement is challenging research task in the field of cooperative localization of AUVs. Adequate research has been carried out in the area in past decade, but there remain many challenges associated with it which require further and detailed investigation. In this paper, a comprehensive review of the past research has been presented. The future research challenges associated with the field have been highlighted and discussed in detail. The basic theories, methods, and techniques associated with cooperative localization and optimal sensor configuration have also been presented. Although it has been almost a decade since the initiation of research in the field of sensor placement for cooperative localization of AUVs, the lack of a review paper is one of the bottlenecks of wider acceptance of the idea. The paper is expected not only to seek researchers’ attention towards this promising future research area but also to provide the basic reading material for the students.

The authors declare no conflict of interest.