Table 3 Mathematical notation and variable definitions.
From: Advanced algorithms for UAV tracking of targets exhibiting start-stop and irregular motion
Symbol/Notation | Definition |
|---|---|
t | Time (seconds) |
\(\:{p}_{R}\left(t\right)\) | UAV (robot) position at time \(\:\:t\:\), typically \(\:{\left[{x}_{R}\left(t\right),{y}_{R}\left(t\right),{z}_{R}\left(t\right)\right]}^{T}\) |
\(\:{p}_{T}\left(t\right)\) | Target position at time t, typically [x_T(t), y_T(t), z_T(t)]^T |
\(\:D\left(t\right)\) | Tracking error at time t, D(t) = \(\:{p}_{R}\left(t\right)-{p}_{T}\left(t\right)\) |
\(\:x\left(t\right)\) | State vector (e.g., position, velocity, acceleration) at time t |
\(\:\dot{{p}_{T}}\left(t\right)\) | Target velocity at time t |
\(\:\ddot{{p}_{T}}\left(t\right)\) | Target acceleration at time t |
\(\:F\) | State transition matrix |
\(\:Q\) | Process noise covariance matrix |
\(\:H\) | Observation matrix |
\(\:R\) | Measurement noise covariance matrix |
\(\:z\left(t\right)\) | Measurement vector at time t |
\(\:{K}_{k}\) | Kalman gain at step k |
\(\:P\) | State estimation error covariance matrix |
\(\:U\left({x}_{R},{y}_{R},{z}_{R}\right)\) | Potential function for UAV control objective |
\(\:{V}_{max}\) | Maximum velocity of the UAV |
\(\:\:{\upalpha\:},\:{\upbeta\:},\:{\upgamma\:},\:{\updelta\:}\) | Parameters in adaptive tracking filters (e.g., α-β-γ-δ filter) |
\(\:IoU\) | Intersection over Union (tracking accuracy metric) |
\(\:HOTA\) | Higher Order Tracking Accuracy (tracking metric) |
\(\:MOTA\) | Multiple Object Tracking Accuracy (tracking metric) |
\(\:IDF1\) | Identification F1 Score (tracking metric) |
\(\:\:n\:\) | Number of time steps or data points |
\(\:w\left(t\right)\) | Process noise at time t |
\(\:v\left(t\right)\) | Measurement noise at time t |
\(\:m\left(t\right)\) | Motion mode index (for hybrid motion models) |
