9Inertial Navigation and Kalman Filtering

9.1 Basic Principle of Inertial Navigation

Inertial navigation is unique among navigation systems in that it requires no external references and can be carried out entirely by the measurement of acceleration within the vehicle. The initial position and state of motion of the vehicle has to be known but then all subsequent tracks and locations can be determined. The principle is illustrated in Figure 9.1 for a vehicle starting at rest and then moving on a flat surface for 600 s with two accelerometers fitted orthogonal to each other aligned along x and y directions. As shown in Figure 9.1a, an initial acceleration is applied in the x‐direction that builds quickly to 1 m s−2 and then slowly decreases as the wind resistance builds up reducing after about three minutes to zero. Integrating the acceleration with respect to time yields the velocity as a function of time illustrated in Figure 9.1b and during the acceleration phase the calculation shows that vehicle’s x‐velocity increases to vx = 52.6 m s−1. Integrating the velocity with respect to time gives the distance traveled and Figure 9.1c shows how the distance increases in the x‐direction with time.

Image described by caption and surrounding text.

Figure 9.1 (a) Accelerations applied to a vehicle starting at rest at (0, 0). (b) x and y velocities of the vehicle. (c) x and y positions of the vehicle. (d) Track of the vehicle.

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