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Water monitoring is important in domains including documenting climate change, weather prediction and fishing. This paper presents a simple and energy efficient localization strategy for near surface buoy based sensors. Sensors can be dropped randomly in the ocean and thus self-calibrate in terms of geographic location such that geo-tagged observations of water quality can be made without the need for costly and energy consuming GPS-hardware. The strategy is based on nodes with an accurate clock and light sensors that can regularly sample the level of light intensity. The measurements are fitted into a celestial model of the earth motion around the sun. By identifying the trajectory of the sun across the skies one can accurately determine sunrise and sunset times, and thus extract the longitude and latitude of the sensor. Unlike previous localization techniques for underwater sensors, the current approach does not rely on stationary or mobile reference points.

Most of the Earth’s surface is covered in water which affects us in numerous ways. We depend on the oceans as a vital source for food. Moreover, the conditions in the oceans greatly affect the weather on land. Increasingly, we have become aware that our actions also affect the world’s oceans and there is currently much focus on climate change. For instance, variations in ocean salinity are important as it is a vital indicator of water cycle and used for climate forecasting [

There is a vast body of research on underwater sensors and sensor networks. Issues addressed include energy consumption [

This paper is organized as follows. In Section 2 the proposed localization system is described, outlining hardware requirements and software algorithms. Next, Section 3 shows the simulation results and how they validate the model. Following, Section 4 contains the results of the system working with real sunlight data. In Section 5 the advantages and disadvantages are discussed. Last, Section 6 summarizes the conclusions obtained.

The Sunlight Intensity based Global Positioning System (SGPS) is able to localize outdoor objects by its earth coordinates (longitude and latitude) using only light intensity information.

The system described takes into account stationary objects. This means that the object has to be in the same position during the whole day (or at least during the daylight time). Due to the accuracy of the system and due to the fact that the sunlight intensity can be considered constant in small areas, small movements are possible. In this case the term

The method proposed herein is based on electronic devices with a built-in clock which maintains a relatively accurate account of time and date. Digital clocks are built into most electronic hardware and can run for many years on one single battery with limited drift. It is therefore assumed that at any time the object can enquire the current time

Next, the strategy requires that the device has some form of light sensor that is capable of measuring the lighting condition _{x,y}

The system proposed in this paper is designed to be as simple as possible. Therefore, apart from the light sensor, a microprocessor is required in order to analyze the data given by the sensor. This element consumes most of the energy in the system.

A feasible option for implementing the proposed system is to use

The SGPS operation is summarized in the flowchart presented in

This paper presents a new algorithm to localize outdoor objects using only sunlight intensity data for a given location. With this information, it is possible to obtain the sunrise and sunset times for that location. Only with these two values, the celestial model determines the coordinates (both longitude and latitude). Thus, the coordinates can be expressed as a function of the sunrise and sunset times as shown in

There is an accurate, well-known algorithm based on Julian Day which allows to find out the sunrise and sunset times for a specific place by only knowing the coordinates of that place and also the date [

Then, the method described herein can be reduced to the problem of identifying the sunset and sunrise times for a given day. Given an accurate measurement of the sunrise time _{sunrise}_{sunset}_{midday}

The UTC representation of time assumes that sunrise occurs before sunset. If the sunset occurs before the sunrise within the 24 h UTC time window then it means that it is a fractional day, since the sunrise happens the day before (in UTC format) that sunset. This has to be taken into account when applying this equation, since if the equation is applied directly with a sunset time earlier than the sunrise time, the noon time will not be correct (in fact, the result would be the

As stated in Section 2.1 the times have to be expressed in UTC and in decimal format (from 0 to 24). For the next formulas all the times will be expressed in this format and the angles in radians. The angular sunset can be computed as follows:

Finally, the coordinates can be obtained. For the longitude

The system is designed to work autonomously, being able to localize itself within the first 24 h of being switched on. This implies that the system can determine its coordinates without any previous information besides the time.

Given a sufficient supply of electric power, for instance if the object has a steady power supply, the initialization can be simply performed using brute force by continuously sampling the lighting condition. If the light sensor is sampled at

The accuracy of the measurements will therefore be in the range of:

It will take maximum 24 h to identify the location and the effort involved is defined by

Several theoretical enhancements are possible. Sunrises can be predicted if early measurements are taken. This is because the light intensity increases gradually over some time interval before one passes the threshold. If a light intensity measurement is taken that is above the night baseline value but yet below the threshold then this is a sign that a sunrise is approaching soon and the sample rate can be dynamically increased. This is illustrated by

However, it may be more difficult to get a pre-warning of a sunset in this way as this will suddenly drop below the threshold value. One way to overcome this is to observe additional features. If the light sensor is capable of capturing color spectrum information then additional information can be exploited to better predict sunrises and sunsets. For instance, the CCD sensors in digital cameras are capable of detecting color as well as intensity. This is because sunsets and sunrises often are characterized by large changes in hue which affect entire scenes. Such changes in hue occur prior to sunsets and thus a detection in hue change can be used to predict an upcoming sunset. This is illustrated in

The steady line shows the overall image intensity and the other line illustrates overall image hue. Clearly, the hue is changing dramatically just before the sunrise and sunset. In fact, these can be seen as the two peaks in the hue plot. However, the exploitation of such features is a topic of future research.

In order to be able to evaluate the system independently of the problem of finding the sunrise and sunset time accurately, the algorithm proposed in Section 2.2 is tested with a theoretical celestial model. Thanks to this model, the sunrise and sunset times can be used as inputs to the system with a low error. Stationary objects are assumed since the objective of this section is to validate the celestial model and extract some conclusions prior to applying it to a real measurements.

The theoretical celestial model used in the simulations is based on [

Note that our system operates according to civil time (without taking into account the established time zones) while the NOAA calculations are based on solar times. The following equation can be used to convert between the two time-formats:

The NOAA sunrise and sunset time predictions have been verified to be accurate within a minute for locations between

The simulation involves finding the sunrise and sunset times, in UTC, using the NOAA approach for 2011. For each value the algorithm described in Section 2.2 is applied.

One conclusion drawn from the simulation results is that the system works according to theory. The fact that the computational complexity is not critical allows to modify the algorithm, creating complex error compensation algorithms and even to use numerical solving in order to improve the accuracy.

Section 2.2 mentioned that fractional days require special treatment for the algorithm to work. We define as fractional days those days where the sunset occurs before the sunset within the 24 h UTC time window.

For example, imagine that there is a day in which the sunrise occurs at 22 h and the sunset occurs at 4 h into the following day. Then, applying the algorithm midday is reported to occur at 13 h. This make no sense as midday occur at night. To avoid complex modifications of the algorithm the following strategy is employed: Midday of a fractional day within 24 h window is equal to the midday time calculated by the standard _{midday}

Applying this strategy to the previous example, in which the standard _{midday}

This strategy allows the coordinates having the sunset of one day and the sunrise of the next day to be found on hardware platforms where the UTC days are treated independently. A small error is introduced, since the times of two different days are used. This error is practically insignificant since the difference of a sunrise (or sunset) times of two consecutive days is only a few minutes and by itself lower than the error of the light sensors used to detect sunrise or sunset times.

In order to evaluate the feasibility, reliability and accuracy of the proposed system tests have been carried out. These tests comprised measuring the light intensity throughout the entire day and later analyzing the data, obtaining the sunrise and sunset times and then applying the algorithm explained in Section 2.2.

The sunlight measures were obtained from the NOAA Public FTP server [

Only the downwelling global solar radiation was used in the experiment, since it is the most representative of light intensity combining both direct and diffuse radiation. Furthermore, radiation is the one which the most low cost sensors measure. The downwelling global solar radiation is expressed in ^{2} where theoretically the minimum value is 0. However, the sensors employed by NOAA are thermopile-based, and it is not unusual for these solar instruments to register small negative signals at night. This offset is attributed to the thermopile cooling to space.

The problem of accurately identifying the sunrise and sunset times is difficult using only light intensity data. Comparing the measured data with the times given by the NOAA celestial model, it can be assumed that when the data is close to 0 ^{2} a transition occurs, that is, a transition from day to night, or vice versa. Using such a threshold to identify the sunrise and sunset times is a very simple solution, and its accuracy depends on the atmospheric conditions for that day since a cloudy day the light intensity value will be lower at the same hour than for a sunny day. However, due to the measurement system offset, setting a threshold of 0 gives accurate sunrise and sunset measurements. Of course, this threshold depends on the hardware employed and should be calibrated.

However, due to signal noise, using a simple zero crossing condition is not enough, as it may result in many transitions per day. For days with more than two transitions, the mean time of the two transitions closest to those of neighbouring days are used (see

The strategy for handling fractional days relies on information about the previous day. When this information is not available the sunrise time for the current day is used instead.

The main steps of the approach can be summarised as follows:

The celestial model used is described in Section 2.2.

The downwelling global solar radiation measurements available at the NOAA FTP server are used.

Each day is treated independently of each other.

A time window based algorithm is employed to discover the sunrise and sunset transitions.

The equinoxes have not been taken into account when running the program (days 81, 82, 265 and 266 for each year).

The interpretation of these histograms is that most days only have a small error. For instance, more than 10.000 days (almost 35% of the total number of tested days) had less than 1% error in longitude. The red line shows the accumulated percentage. The errors for longitude is less than those for latitude.

Next,

Finally,

Most global localization methods are based on GPS [

On the other hand, the SGPS is a stand-alone system that is not dependent on any technical infrastructure. It requires a modest hardware and simple software. SGPS is a low cost system with a prototype cost of less than 40 dollars (30 euros).

SGPS system is energy efficient. The energy consumption depends mainly on the number of measures taken. The system only need to take measurements during sunrises and sunsets, and the system can remain asleep the rest of the time.

On the down side, the accuracy of the SGPS accuracy is low compared with other systems. Moreover, the position refresh rate is lower than for other systems. For instance, GPS or GSM can refresh the position every few seconds.

Another drawback is that the object must be stationary and the system does not work properly during the equinoxes, which means that there are several days in which the results are not reliable at all. However, this problem can be solved by interpolation as it is well known when equinoxes occur.

The system will not work beyond the Northern or Southern polar circles during the summer or winter seasons since there are no sunrises or sunsets. More specifically, the limitation implies that the system can be used only when there is a sunrise or sunset in those latitudes which satisfy the following conditions:

This paper presents a novel global localization system, based on measuring the cyclic variations in light intensity resulting from the movement of the celestial bodies. In this case, the rotation of the earth and the resulting sunrises and sunsets are taken into account.

Thus, an algorithm is proposed to find the geographic coordinates for an outdoor object which measures the light intensity throughout a day and is able to identify accurately the sunrise and sunset times.

The conclusion obtained from the results are that the accuracy of the system is relatively high taking into account the devices which are required to build the system. Also, it is denoted that the total accuracy mainly depends on the precision when identifying sunrises and sunsets, and not on the celestial model employed.

Compared to current global localization methods, SGPS can not be applied to tasks requiring a high accuracy, such as search and rescue, navigation,

Future research includes improving the accuracy using other magnitudes such light spectrum and improving robustness towards impurities in the water. Moreover, artificial intelligence techniques may be employed to better identify the sunrise and sunset times. Another improvement is to study ways of counteracting the systematic error in longitude due to the usage of the Spencer EqT and latitude due to the equinoxes.

SGPS flowchart showing what steps are done by hardware and what by software.

Hardware implementation based on Arduino Mega: power source, SD storage, clock and light dependent resistor (LDR) sensor. The simplest SGPS implementation costs less than US $40 in components.

Daylight parameters influenced by latitude and longitude.

(

Comparison between the Meeus and Spencer Equations of Time.

Simulation results of the SGPS using Oslo coordinates. (

Correcting the midday error by the initial midday equation.

Sunrise and sunset times identification (threshold = 0). (

Histograms showing the absolute percentage error. (

Histograms showing the absolute error in kilometers. (

Dispersion plots of the results. (

Dispersion plots of the results for days with noisy measurements.

Error percentage against elevation of the stations.

Error of the algorithm for all days of 2010. (