INTRODUCTION

The Global Positioning System, or GPS, is a satellite-based navigation system that is made up of at least 24 satellites at a time. GPS receivers work in any weather condition, any location in the world 24 hours a day (GARMIN, 2020). The United States Department of Defense originally put the satellites into the earth’s orbit for military use, but this feature became available for civilian use in the 1980s. GPS satellites circle the Earth twice a day in a precise orbit. Each satellite transmits a unique signal and orbital parameter that allows GPS devices to decode and compute the precise location of the satellite. GPS receiver devices use this information and trilateration, or true range multilateration, which is defined as the process of determining absolute or relative locations of points by measurement of distances, to calculate a user’s exact location (Britannica, 2017). Essentially, GPS receivers measure the distance to each satellite by the amount of time it takes to receive a transmitted signal. With distance measurements from a few satellites, a GPS receiver can determine a user’s position and display it electronically. To calculate a user's two-dimensional position, which accounts for longitude and latitude, a GPS receiver must be locked onto the signal of at least three satellites. If four or more satellites are in view, the receiver can determine a user’s three-dimension position, latitude, longitude, and altitude (NOAA, 2020). Generally, a GPS receiver will track eight or more satellites, but it depends on the time of day and location on Earth. GPS satellites transmit at least two low-power radio signals. These signals travel by line of sight, meaning they will pass through clouds, glass and plastic, but will not be able to go through most solid objects, such as buildings and mountains. This being said a GPS signal contains three different types of information: pseudorandom code, ephemeris data, and almanac data. Pseudorandom case is an I.D. code that identifies which satellite is transmitting information (PennState, 2017). This allows GPS based companies to see which satellites they are getting signals from. Ephemeris data is needed to determine a satellite’s position and it gives important information about the health of a satellite, as well as the current date and time. Lastly, almanac data tells the GPS receiver where each GPS satellite should be at any time throughout the day and shows the orbital information for the satellite and every other satellite in the system (GARMIN, 2018).
Today's GPS receivers are extremely accurate because of their parallel multi-channel design, meaning that there are 12 parallel channel receivers that are quick to lock onto satellites where they are first turned on and they maintain strong locks, even in dense foliage or urban settings with tall buildings (Civil Engineering Dictionary, 2014). This being said, there are certain atmospheric factors and other sources of error that can affect the accuracy of GPS receivers. These include: signal multipath, receiver clock errors, orbital errors, number of satellites visible, satellite geometry, and selective availability. Signal multipath is the error that occurs when GPS signals reflect off of objects such as tall buildings or large rock surfaces before they reach the receiver, which increases the travel time of the signal. The longer that it takes for GPS signals to be obtained, the more error they will contain (PennState, 2017). Receiver clock errors occur when a receiver’s built-in clock may have slight timing errors because it is less accurate than the atomic clocks on GPS satellites. This time difference can account for a reasonable amount of error. Orbital errors occur when a satellite’s reported position is not accurately recorded because of inaccuracies in orbital rotation that are also not properly studied or observed. In regard to the number of satellites visible, as mentioned previously, the more satellites a GPS receiver can get information from, the more accurate the results are. When a signal is blocked, users may get position errors or possibly no position reading at all. Satellite geometry errors or shading occurs when satellites are in a line or tight grouping, because satellite signals are more effective when satellites are located at wide angles relative to each other. Selective Availability is an error that the The United States Department of Defense once applied to satellites, making signals less accurate in order to keep enemy countries from using highly accurate GPS signals (GARMIN, 2020). Although the government turned off the Selective Availability setting in May of 2000, civilian GPS receivers may be susceptible to this error. All of the aforementioned errors that can occur contribute to inaccurate longitude, latitude, and altitude values. However, one of the leading causes of errors for GPS signals occurs as a result of ionosphere and troposphere delays because of geomagnetic storms (Jamal, 2017).
A geomagnetic storm is a major disturbance of Earth's magnetosphere that occurs when there is an efficient energy exchange from the solar wind into the space environment surrounding Earth. These storms occur because of variations in solar wind that produce major changes in the currents, plasmas, and fields in Earth’s magnetosphere (Space Weather Prediction Center, 2019). The solar wind conditions that are effective for creating geomagnetic storms are sustained for several hour periods of high-speed solar wind, and most importantly, a southward directed solar wind magnetic field, opposite the direction of Earth’s field, at the dayside of the magnetosphere. This condition is effective for transferring energy from the solar wind into Earth’s magnetosphere. During geomagnetic storms, the currents in the ionosphere, as well as the energetic particles that precipitate into the ionosphere add energy in the form of heat that can increase the density and distribution of density in the upper atmosphere, which causes extra drag on satellites in low-earth orbit. The local heating also creates strong horizontal variations in the ionospheric density that can modify the path of radio signals and, as mentioned previously, can disrupt navigation systems such as the Global Positioning System (GPS) and create harmful geomagnetic induced currents (GICs) in the power grid and pipelines. The K-Index, and by extension the Planetary K-index, Kp, is used to characterize the magnitude of geomagnetic storms. Kp is an excellent indicator of disturbances in the Earth’s magnetic field and is used to decide whether geomagnetic alerts and warnings need to be issued for users who are affected by these disturbances (SWPC Boulder, 2015). The K-index quantifies whether or not a disturbance is occurring, as well as quantifying storms in the horizontal component of earth’s magnetic field with an integer in the range of 0-5 with 1 being calm and 5 or more indicating a geomagnetic storm that are actively occurring. This is derived from the maximum fluctuations of horizontal components observed on a magnetometer during a three-hour interval. The planetary 3-hour-range index Kp is the mean standardized K-index from 13 geomagnetic observatories between 44 degrees and 60 degrees northern or southern geomagnetic latitude. 
Geomagnetic storm activity, along with the rest of the aforementioned error possibilities, can severely affect GPS signals, but some of this error can be lessened using the Wide Area Augmentation System (WAAS). The Federal Aviation Administration (FAA) and the Department of Transportation (DOT) originally developed the WAAS program for use in precision flight approaches because GPS alone did not meet the FAA’s navigation requirements for accuracy, integrity and availability, but it has since been adapted to fix civilian GPS errors (Federal Aviation Administration, 2020). WAAS is useful because it corrects for GPS signal errors caused by ionospheric disturbances, timing and satellite orbit errors, and it provides vital integrity information regarding the health of each GPS satellite. WAAS consists of multiple ground reference stations positioned across the United States that monitor GPS satellite data (Martin, 2018). Two master stations, located on the east and west coast, collect data from the reference stations and create a GPS correction message. This accounts for GPS satellite orbit and clock drift, along with signal delays caused by the atmosphere and ionosphere. The corrected differential message is then broadcasted through one of the two geostationary satellites, which are satellites with a fixed position over the equator (Yeazel, 2010). This information is compatible with the basic GPS signal structure, which means that any WAAS-enabled GPS receiver can read the signal. Currently, WAAS Satellite coverage is only available in North America because there are no ground reference stations in other parts of the world. All of this being said, WAAS capabilities provide a measurement that is up to five times more accurate than regular GPS measurements.
Geomagnetic storms are often associated with magnetism and ejections from the sun. More specifically, geomagnetic storms are often associated with solar coronal mass ejections (CMEs). CMEs are large explosions of plasma and magnetic fields from the Sun’s corona. They can eject billions of tons of coronal material and can carry an embedded magnetic field that is stronger than the background solar wind magnetic field strength (SWPC, 2019).These ejections expand in size as they propagate away from the sun, and they can reach a size comprising nearly a quarter of the space between Earth and the Sun. The more explosive CMEs generally begin when highly twisted magnetic field structures contained in the Sun’s lower corona become too stressed and realign into a less tense configuration – a process called magnetic reconnection (Garner, 2020). This can result in the sudden release of electromagnetic energy in the form of a solar flare; which typically accompanies the explosive acceleration of plasma away from the Sun – the CME. CME are reported utilizing GOES X-Ray Flux measurements. These measurements incorporate solar flares, x-ray flares, and CMEs into one measurement that can be directly related to geomagnetic storms. Although CMEs are important to understanding geomagnetic storms, they also affect solar proton events (Tranquille, 2014). Solar Proton Events (SPEs) become serious threats to the cosmonautical activities of human beings, the prediction of the flux of solar protons within a certain period has important guiding significance for the projection of the anti-radiation solidification of space vehicles. Throughout geomagnetic storm events, proton fluxes are greatly affected. More specifically, the temporal and spatial characteristics of the solar proton flux are correlated with details of geomagnetic storms (Cong et al., 2017). Further, a sharp decrease in the flux in the main phase is followed by a slower exponential decay. This decay begins after the peak of the main phase and extends through the recovery period of the storm, during which the geomagnetic cutoff gradually returns to its prestorm value. The current proton values are recorded on a daily basis at five minute intervals utilizing the GOES proton flux system. These events are measured using the GOES-16 satellite system, and differ based on threshold. . The ≥10 MeV products match the NOAA Solar Radiation Storm (S-scale) thresholds (10, 100, 1000, 10000, 100000 pfu), based upon values observed or expected on the primary GOES satellite. The ≥100 MeV products are based on a single flux threshold of 1 proton flux unit (pfu).
Another noteworthy condition that causes fluctuation in geomagnetic storm activity is the earth's current position in the solar cycle (Silbergleit, 2008). The sun is a huge ball of electrically-charged hot gas that generates a powerful magnetic field. The Sun’s magnetic field goes through a cycle, which is called the solar cycle. About every 11 years or so, the Sun’s magnetic field completely flips. This means that the Sun’s north and south poles switch places. Then, it takes another 11 years for the north and south poles to resume their previous position. The solar cycle affects activity on the surface of the Sun, such as sunspots which are caused by the Sun’s magnetic fields. As the magnetic fields change, so does the amount of activity on the Sun’s surface. One way to track the solar cycle is by counting the number of sunspots (NASA, 2019). The beginning of a solar cycle is a solar minimum, which is when the Sun has the least amount of sunspots in the cycle. Over time, solar activity, and the number of sunspots, increases. The middle of the solar cycle is the solar maximum, or when the Sun has the most sunspots. As the cycle ends, it fades back to the solar minimum and then a new cycle begins. Scientists charged with predicting the Sun’s activity for the next 11-year solar cycle say that it’s likely to be weak, much like the current one. The current solar cycle, Cycle 24, is at its approximate solar minimum, the period when the Sun is least active (Farmer’s Almanac, 2020). Solar Cycle 25 Prediction Panel experts said Solar Cycle 25 may have a slow start, but is anticipated to peak with solar maximum occurring between 2023 and 2026, and a sunspot range of 95 to 130. This is well below the average number of sunspots, which typically ranges from 140 to 220 sunspots per solar cycle. The panel has high confidence that the coming cycle should break the trend of weakening solar activity seen over the past four cycles (National Weather Service, 2019). This research will consider the current position in the solar cycle in relation to the strength and frequency of geomagnetic storms. 
Ultimately, geomagnetic storms can have adverse effects on multiple aspects of human life. Utilizing Global Positioning Systems with a Wide Area Augmentation System, absolute error will be compared to Goes Proton Flux Index and Planetary K-Index values to track geomagnetic storms occurring in the ionosphere. A prediction model for future geomagnetic storms will be created to insure preparedness for these occasions. This is crucial because of the possibly detrimental effects geomagnetic storms can cause. Lastly, this research will consider the current position in the solar cycle in relation to the strength and frequency of geomagnetic storms and make predictions about geomagnetic storms during different points in the solar cycle.