Name: estimating altitude changes with linearization
Uploaded: 2026-01-12T12:24:59.000Z
Duration: 1 min 29 s
Channel: JoVE

Un dron que sobrevuela terrenos complejos utiliza la presión atmosférica como método complementario para estimar pequeños cambios de altitud.En términos de altitud, la presión suele modelarse como decaimiento exponencial, y su inverso da la altitud en función de la presión.Esta fórmula suele ser demasiado compleja para cálculos repetidos, por lo que se aproxima localmente como una función lineal mediante linealización.Esto implica tres pasos, comenzando con un punto de presión inicial, P i , como 90 kilopascales, donde la aproximación está centrada. Primero, la altitud en Pi se calcula usando la ecuación original, etiquetada como h(Pi).Segundo, la pendiente se determina evaluando la derivada de la función altitud en Pi. Esta pendiente muestra cómo varía la altitud con pequeños cambios de presión.Por ejemplo, si la presión cae de 90 a 89,2 kilopascales, la caída se multiplica por la pendiente en la presión inicial para estimar el cambio de altitud.Finalmente, estos valores se combinan en la ecuación de aproximación lineal para obtener la nueva altitud aproximada.Este método es preciso para pequeños cambios de presión, pero se vuelve menos fiable a medida que la presión se aleja de la presión inicial.

aplicación de la linealización y la aproximación

Application of Linearization and Approximation

Un dron que vuela sobre terrenos complejos suele apoyarse en m&#xE1;s de un m&#xE9;todo de detecci&#xF3;n para estimar peque&#xF1;os cambios de altitud. Adem&#xE1;s de las mediciones directas, la presi&#xF3;n atmosf&#xE9;rica proporciona un indicador indirecto fiable del movimiento vertical. La presi&#xF3;n atmosf&#xE9;rica disminuye a medida que aumenta la altitud, y esta relaci&#xF3;n se describe com&#xFA;nmente mediante un modelo exponencial. Aunque es preciso, convertir las mediciones de presi&#xF3;n en valores de altitud requiere c&#xE1;lculos demasiado complejos para ser realizados repetidamente durante el vuelo en tiempo real.Para simplificar estos c&#xE1;lculos, la relaci&#xF3;n presi&#xF3;n&#x2013;altitud se aproxima localmente mediante linealizaci&#xF3;n. Este enfoque reemplaza la relaci&#xF3;n no lineal original con una aproximaci&#xF3;n lineal v&#xE1;lida cerca de la presi&#xF3;n de referencia seleccionada. El proceso comienza seleccionando un valor de presi&#xF3;n inicial, como 90 kPa, alrededor del cual se construye la aproximaci&#xF3;n. La altitud correspondiente a esta presi&#xF3;n de referencia se determina primero utilizando la relaci&#xF3;n presi&#xF3;n&#x2013;altitud original y sirve de referencia para estimaciones posteriores.A continuaci&#xF3;n, se eval&#xFA;a la sensibilidad de la altitud a peque&#xF1;os cambios de presi&#xF3;n en la presi&#xF3;n de referencia. Esta sensibilidad describe cu&#xE1;nto cambia la altitud en respuesta a un ligero cambio de presi&#xF3;n. Por ejemplo, si la presi&#xF3;n medida cae ligeramente por debajo del valor de referencia, esta peque&#xF1;a diferencia se escala para estimar el cambio de altitud resultante.La aproximaci&#xF3;n lineal combina estas cantidades mediante la f&#xF3;rmula est&#xE1;ndar de la tangente que se muestra a continuaci&#xF3;n.\begin{equation*} L(P) = h(P_i) + h&#x27;(P_i)\,(P - P_i) \end{equation*}Esta aproximaci&#xF3;n permite al dron estimar eficientemente peque&#xF1;as variaciones de altitud sin necesidad de c&#xE1;lculos complejos. El m&#xE9;todo mantiene su precisi&#xF3;n mientras los cambios de presi&#xF3;n se mantengan cerca del valor de referencia, pero se vuelve menos preciso a medida que la presi&#xF3;n se aleja de &#xE9;l. Por esta raz&#xF3;n, la linealizaci&#xF3;n es id&#xF3;nea para supervisar peque&#xF1;os cambios de altitud durante un vuelo estable y debe actualizarse cuando se produzcan variaciones mayores.

Aplicación de la linealización y la aproximación

Un dron que vuela sobre terrenos complejos suele apoyarse en m&#xE1;s de un m&#xE9;todo de detecci&#xF3;n para estimar peque&#xF1;os cambios de altitud. ...

application-of-linearization-and-approximation

Education

JoVE Core

Calculus

Unit

Differentiation Rules

KEY TERMS AND CONCEPTS

estimating altitude changes with linearization

Linearization can help a drone estimate small altitude changes from air pressure readings. Atmospheric pressure drops as altitude rises, and this relationship is often modeled with an exponential function. The model is accurate, but the math needed to convert pressure into altitude can be too complex for repeated calculations during flight.

To make the calculation easier, the pressure-altitude relationship is approximated locally with a straight line. This line is built near a chosen reference pressure, such as 90 kilopascals. First, the altitude at that reference pressure is found from the original relationship. That value becomes the starting point for the estimate.

Next, the sensitivity of altitude to pressure is measured at the reference pressure. Sensitivity means how much the altitude changes when pressure changes a little. If the measured pressure is slightly lower than the reference value, that small difference is scaled to estimate the change in altitude.

The straight-line estimate uses the standard tangent-line formula. It lets the drone quickly track small altitude changes without doing the full nonlinear calculation each time. The approximation works best when pressure stays close to the reference pressure. It becomes less reliable as the pressure moves farther away, so it must be updated when larger changes occur.

Estimating Altitude Changes with Linearization

estimating-altitude-changes-with-linearization

derivatives of simple functions

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application of linearization and approximation

Linearization can help a drone estimate small altitude changes from air pressure readings. Atmospheric pressure drops as altitude rises, and this relationship is often modeled with an exponential function. The model is accurate, but the math needed to convert pressure into altitude can be too complex for repeated calculations during flight. To make the calculation easier, the pressure-altitude relationship is approximated locally with a straight line. This line is built near a chosen reference...

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key terms and concepts

Learn how linearization turns a pressure-altitude exponential model into a quick straight-line estimate for small drone altitude changes near a reference pressure.

Estimating Altitude Changes with Linearization | JoVE K12

The JoVE Core Calculus collection provides a comprehensive visual guide to the entire calculus sequence, seamlessly connecting mathematical theory to real-world applications in physics and economics. Through dynamic animated lessons, the course transitions smoothly from foundational single-variable concepts to advanced multivariable topics. Students will explore everything from standard differentiation and integration to spatial vectors, multi-dimensional derivatives, and complex vector fields. By breaking down abstract coordinate systems, infinite series, and spatial motion, this structured approach builds the robust analytical skills and advanced mastery essential for STEM success.

calculus

Estimating Altitude Changes with Linearization

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