**1. Introduction**

Navigation refers to the method of determining aspects such as position, speed, and direction during travel. In the pre-modern era, direction and position were determined using an altazimuth, a compass, and a map; these are now considered primitive forms of navigation. As a result of modern developments in science and technology, exact positions and speeds are determined using equipment such as artificial satellites, global navigation satellite system (GNSS), inertial navigation systems (INS), etc. In the modern sense, navigation is mechanical devices equipped in ground vehicles, ships, and aircraft to determine their positions.

Navigation is classified into two categories in this study: physical model-based methods (PMMs) and external data-based methods (EDMs). Examples of PMMs are inertial navigation systems (INS) and dead-reckoning navigation. They determine the existing position of an object by measuring various changes in its state, such as velocity and acceleration. The global

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navigation satellite system (GNSS) is an excellent representative of EDMs. Methods to determine longitude and latitude using polar stars or the sun considered as EDMs, which is utilized in the spacecraft nowadays. PMM and EDM have duality. The accuracy of PMMs is exponentially proportional to the cost, and the error increases over time. However, information can be obtained for three axes (X, Y, and Z); this is a stable configuration as no communication problems are incurred. EDMs are relatively cheap and the accuracy is pre-defined according to sensor. However, there may be some restrictions on communication. The navigation equipment in ground vehicles and the orbit propagator in spacecraft are designed to complement each other, considering the properties of tools such as the INS/GNSS.

*2.1.2. Inertial navigation system (INS)*

vector components.

**Figure 1.** Principle of strapdown inertial navigation systems [5].

**2.2. EDMs**

The Inertial Navigation System is a stand-alone navigation system that continuously calculates the position, direction, and velocity of the main body through its own accelerometer, rotation sensor, and arithmetic unit, without receiving any external information [4]. Although GPS offers a precise navigation system, it has limitations in space, deep seas, tunnels, and similar places because the GPS operates only when it can receive signals from the satellite. Furthermore, INS can avoid GPS jamming issues. Because an INS is a PMM, the error increases with time. Moreover, the price increases exponentially as the precision is enhanced. One critical factor in an INS is the accurate entry of the initial position and velocity. After that, the data measured by the accelerometer and rotation sensor are integrated consecutively. The accelerometer provides position data whereas the rotation sensor (gyroscope) provides attitude data. **Figure 1** shows an example of a strapdown inertial navigation system. Velocity and position data can be obtained by integrating the acceleration twice. It is strapped with an accelerometer that considers the acceleration of the tangent and

Introduction to Navigation Systems http://dx.doi.org/10.5772/intechopen.71047 5

EDMs include GNSS, which is represented by GPS. The application scope is very broad, and includes ground vehicles, ships, and airplanes. In this chapter, the use of GNSS for satellites and deep space probes is explained. Defining the current position and velocity of a satellite is called "orbit determination." The orbit determination problem can be largely divided into a system model part, a measurement model part, and an estimation technique part. Each can be explained as follows. First, the system model is a mathematical model that represents the orbital motion and various specific variables. It has to be approximated to some degree because many assumptions are included in the process of deriving the equation of motion. Second, for the measurement model, the GPS navigation solution or the tracking data (line of sight, elevation angle, azimuth angle, etc.) of the ground station is used. Here, the measurement values cannot be the true values due to sensor errors and other reasons, and always include some errors. Third, the estimation technique part estimates the optimum prediction values, that is, the position and velocity of the satellite using the approximated system model

In the case of spacecraft, auxiliary navigation systems using data compression were proposed due to the unpredictable space environment and limited communication. The orbital equation used in spacecraft is represented by a nonlinear differential equation containing multiple perturbation terms, which makes the determination of orbit numerically complex. Generally, a precise determination of orbit is made on the ground, and the information is then transmitted to the spacecraft periodically. However, Deep space communication is restrictive and expensive. Therefore, the cost of communication can be reduced by compressing orbital data. For Low Earth Orbit satellites, the deviations between nominal and real orbit are compressed in the form of Fourier coefficients by using the periodic characteristics of the trajectory [1, 2]. Deep space explorer orbit compression and transmission were proposed using B-spline [3].
