In geospatial search and data analysis, precision is critical. Geospatial projections play an essential role in translating the three-dimensional world onto two-dimensional maps useful for spatial visualization while enabling accurate spatial analysis. This is particularly crucial for applications in military operations, space exploration, and specialized geospatial processing, where even minor location inaccuracies can lead to detrimental operational errors. This post will discuss how Lucenia’s advanced geospatial indexing implementation ensures precise and cost-effective spatial searches for critical geo applications.

What are Geospatial Projections?

Geospatial projections are mathematical methods used to represent the curved surface of the Earth on a flat map. These projections are necessary because the Earth is a three-dimensional oblate spheroid, and translating its surface to a two-dimensional plane involves distortions. Different types of projections are used depending on the purpose of the map, each with its own advantages and limitations. For example, the Mercator projection is commonly used for navigation because it preserves angles and shapes of small objects. This projection is also found in almost every classroom in the United States. However it radically distorts the size of objects as they near the poles. The figure below, known as Tissot’s Indicatrix, illustrates this distortion (source: Esri).

Importance of Spatial Accuracy in Military and Space Exploration

For the military, precision in spatial data can mean the difference between mission success and failure. Accurate geospatial data ensures that targeting systems, navigation, and reconnaissance are reliable. Military operations rely on precise coordinates to direct artillery, deploy troops, and navigate vehicles. Any spatial inaccuracies can lead to missed targets, lost troops, or collisions, potentially resulting in significant operational failures and casualties.

In space exploration, precise mapping and data analysis are vital for landing site selection, rover navigation, and resource allocation on other planetary bodies. For instance, when planning a mission to Mars, scientists and engineers need highly accurate maps to select safe landing sites, avoiding areas with large rocks or steep slopes that could damage the lander. Once on the surface, rovers need precise coordinates to navigate and perform scientific experiments. Even small errors in spatial data can result in a rover getting stuck, missing important scientific targets, or losing communication with Earth.

The EPSG Database

The EPSG (European Petroleum Survey Group) database is an extensive collection of coordinate reference systems (CRS) and geodetic parameters. It serves as a standard reference for defining how geographic data is mapped onto the Earth’s surface. The EPSG database includes thousands of coordinate systems, each with its own parameters and use cases, ensuring that geospatial data is consistent, accurate, and interoperable across different systems and applications.

By leveraging the EPSG database, organizations can select the most appropriate CRS for their specific needs. For example, a global positioning system (GPS) typically uses a geographic coordinate system like WGS84, while local surveys might use a projected coordinate system like UTM (Universal Transverse Mercator). The EPSG database provides the necessary parameters to transform data between these systems accurately.

Dynamic Coordinate Reference Systems: Addressing Tectonic Motion

Tectonic motion constantly alters the Earth’s surface, leading to spatial inaccuracies over time. The Earth’s crust is divided into 7 major and many minor  tectonic plates that are steadily and slowly moving in perpetuity. Over years, these movements can accumulate, causing significant changes in the positions of geographic features. Traditional static coordinate reference systems cannot account for these changes, resulting in continually increasing spatial inaccuracies as time passes.

Dynamic coordinate reference systems (CRS) address these inaccuracies by accounting for the shifting positions of tectonic plates. These systems include a temporal component, allowing for the continuous updating of coordinates as tectonic motion occurs. For example, the ITRF (International Terrestrial Reference Frame) is a dynamic CRS that provides a set of coordinates which change over time to reflect the movements of tectonic plates. By using dynamic CRS, geospatial data remains the most accurate over time, ensuring that spatial analyses and operations remain precise.

Challenges: Real-World Examples of Spatial Inaccuracies

Spatial inaccuracies can arise from improper support for mathematical planet models. For instance, the failure to account for the Earth’s oblate spheroid shape (flattened at the poles) can lead to significant errors in distance measurements and area calculations. In military applications, this can affect targeting accuracy. Similarly, in space exploration, inaccurate planetary models can result in errors in rover navigation and landing site selection.

A notable example of spatial inaccuracies due to tectonic motion is the 2011 Tōhoku earthquake in Japan. The earthquake caused significant shifts in the Earth’s crust, moving parts of Japan by several meters. Any geospatial data that did not account for these changes would have been rendered inaccurate, affecting everything from navigation systems to disaster response efforts.

Mathematical Planet Models

Accurate representation of planetary bodies is challenging. A flat Cartesian coordinate system (x, y) fails to capture the true curvature of a planet, resulting in land masses appearing larger than they actually are when projected on a 2D map. This example is wonderfully discussed in Geospatial World’s 2023 post and illustrated in the image below:

Oblate spheroid models, on the other hand, offer a more accurate representation by considering the major and minor axes, eccentricity, and flattening factors. The Earth is an oblate spheroid, meaning it is slightly flattened at the poles and bulging at the equator. This shape results from the Earth’s rotation, which causes the equatorial diameter to be slightly larger than the polar diameter. Similar to a basketball squashed at the poles, this results in the equatorial diameter being larger than the polar diameter. To represent this shape accurately, geospatial models use parameters such as the semi-major axis (the equatorial radius), the semi-minor axis (the polar radius), eccentricity, and flattening.

Comparing Earth and Mars

The Earth and Mars, while both oblate spheroids, exhibit distinct differences in their shapes due to their unique geophysical characteristics. Mars, though also influenced by rotational flattening, has a more pronounced equatorial bulge and is often described as having an “egg-shaped” form. This distinction arises from Mars’ different rotational dynamics and internal structure. These differences highlight the need for precise mathematical models to ensure spatial accuracy in geospatial analyses. Accurate geospatial projections must account for these unique planetary geometries to ensure precise location and measurements. Using a generic spherical model is insufficient, leading to significant spatial errors. These errors adversely affect applications such as landing site selection, rover navigation, and surface exploration on different planetary bodies, as well as military targeting and geographic information systems (GIS) applications here on Earth.

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Exaggerated comparisons of the shape of (a) Earth and (b) Mars (source: ResearchGate)

Lucenia’s Geospatial Indexing

To address the challenges of geospatial projection support, we have developed a robust indexing implementation with two primary components:

1. Reprojection Ingest Processor: This processor reprojects decimal degree coordinates from one projection to another, ensuring that data is accurately transformed and indexed. This process involves converting coordinates from the source CRS to the target CRS using the parameters defined in the EPSG database. By performing this transformation during the data ingestion phase, we ensure that all data is stored in a consistent projection, simplifying subsequent spatial analyses and searches.

2. Native PlanetModel Indexing: This approach supports centimeter accuracy in the index, allowing for highly precise spatial searches. By storing and indexing data using native planet models that account for the oblate spheroid shape of planetary bodies, we can achieve unprecedented levels of spatial accuracy. This is particularly important for applications requiring precise location data, such as military targeting and space exploration.

Performance and Accuracy Tradeoffs

Indexing and searching in native projection space involves complex mathematical calculations to ensure centimeter accuracy. These calculations are computationally expensive, creating a tradeoff between performance and accuracy. To balance this, we perform initial skip index pruning in reduced resolution space, deferring the more expensive calculations to the final search filtering phase. This approach optimizes both performance and accuracy, ensuring efficient and precise spatial searches.

During the initial search phase, we use a lower resolution index to quickly narrow down the search space. This skip index pruning significantly reduces the number of candidate locations that need to be evaluated in detail. Once the initial pruning is complete, we perform the more computationally intensive calculations on the remaining candidates to ensure centimeter-level accuracy. This two-phase approach balances the need for speed and precision, making our system both efficient and accurate.

Lucenia’s Search Advantages

Our search system offers several advantages over others:

• Centimeter Accuracy: Essential for military targeting, specialized GIS applications, and space exploration. By supporting native planet models and dynamic CRS, we ensure that our spatial searches are accurate down to the centimeter level, providing unparalleled precision.
• Cost Efficiency: We achieve this precision at nearly half the cost of our competitors, providing a cost-effective solution without compromising on quality. Our efficient indexing and search algorithms allow us to deliver high accuracy without the high costs typically associated with such precision.
• Dynamic CRS Support: By integrating dynamic coordinate reference systems, we ensure long-term spatial accuracy, accommodating tectonic shifts and other geological changes. This makes our system particularly suited for applications where long-term accuracy is crucial, such as monitoring tectonic activity or planning long-duration space missions.

Conclusion

Lucenia’s advanced geospatial projection support enhances spatial accuracy for critical applications in GIS, military, and space exploration use cases. By leveraging the EPSG database, supporting dynamic CRS, and implementing precise mathematical models, we deliver superior spatial search capabilities. Our innovative indexing implementation balances performance and accuracy, providing a competitive edge in delivering precise, cost-effective geospatial solutions.

Our commitment to precision and efficiency ensures that our clients can rely on our system for their most demanding geospatial needs, whether they are planning a military operation, navigating a rover on Mars, or conducting advanced GIS analyses. With our advanced geospatial projection support, we are setting new standards for accuracy and performance in the field of spatial data management.

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