Data-driven modeling of low-altitude turbulence

A method comprising:

• determining information regarding a first mission requiring a first aerial vehicle to fly from an origin to a destination within an environment;
• identifying a first plurality of positions within the environment, wherein each of the first plurality of positions is above a ground surface within the environment;
• determining a first time series of data regarding the environment, wherein the first time series comprises data regarding wind velocities at each of the first plurality of positions;
• predicting average velocities at each of the first plurality of positions;
• selecting normal distributions of white noise for each of the first plurality of positions;
• providing at least the normal distributions of the white noise for each of the first plurality of positions as inputs to an autoregressive filter characteristic polynomial, wherein the autoregressive filter characteristic polynomial is of a predetermined order, and wherein the autoregressive filter characteristic polynomial is configured to determine a stochastic wind velocity component for each of the plurality of positions based at least in part on the first time series;
• generating a second time series of data regarding the environment based at least in part on the average velocities at each of the first plurality of positions and outputs received from the autoregressive filter characteristic polynomial in response to the inputs, wherein the second time series comprises data regarding wind velocities at each of the first plurality of positions;
• and
• determining whether the first aerial vehicle may perform the first mission based at least in part on the second time series.

A method comprising:

• identifying a first time series of wind velocities, wherein each of the wind velocities of the first time series is a velocity of wind at one of a first plurality of positions at a first time;
• determining components of each of the wind velocities of the first time series about each of a plurality of orthogonal axes;
• normalizing the first time series of wind velocities about each of the plurality of orthogonal axes;
• fitting a first autoregressive process to the normalized first time series;
• generating tuples of values based at least in part on the first autoregressive process, wherein each of the tuples of values is generated for one of the first plurality of positions, and wherein each of the tuples of values comprises the one of the first plurality of positions, mean velocities along each of the plurality of orthogonal axes, standard deviations of velocities along each of the plurality of orthogonal axes, and coefficients of the first autoregressive process corresponding to each of the velocities of the first time series;
• training a copula to determine dependencies between each of the coefficients of the first autoregressive process and the first plurality of positions;
• constructing a second autoregressive process, wherein the second autoregressive process comprises a plurality of coefficients selected based at least in part on the copula;
• and
• predicting a second time series of wind velocities by the second autoregressive process, wherein each of the wind velocities of the first time series is a velocity of wind at one of a second plurality of positions at a second time.