Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during real-time flight.

To simplify these computations, the pressure–altitude relationship is approximated locally using linearization. This approach replaces the original nonlinear relationship with a straight-line approximation that is valid near a chosen reference pressure. The process begins by selecting an initial pressure value, such as ninety kilopascals, around which the approximation is constructed. The altitude corresponding to this reference pressure is first determined using the original pressure–altitude relationship and serves as the baseline for further estimation.

Next, the sensitivity of altitude to small pressure changes is evaluated at the reference pressure. This sensitivity describes how much the altitude changes in response to a slight change in pressure. For example, if the measured pressure drops slightly below the reference value, this small difference is scaled to estimate the resulting change in altitude.

The linear approximation combines these quantities using the standard tangent-line formula shown below.

This approximation enables the drone to efficiently estimate small altitude variations without requiring complex calculations. The method remains accurate as long as pressure changes remain close to the reference value, but it becomes less reliable as the pressure deviates farther from it. For this reason, linearization is well-suited for monitoring minor altitude changes during steady flight and must be updated when larger variations happen.