How do you estimate a target's course and speed from two radar sweeps?

How do you estimate a target's course and speed from two radar sweeps?

• A. Compare the target's color on the display.
• B. Use ambient noise to estimate.
• C. Compare the target's successive positions and compute the rate of change of range and bearing to derive course and speed.
• D. Guess based on previous sightings.

Answer: (C)

When you have two radar sweeps, you have two position fixes for the same target at known times. The way to estimate course and speed is to track how its position changes between those scans. Convert each sweep’s range and bearing into Cartesian coordinates (x, y) with the radar at the origin: x = r cos θ, y = r sin θ. Let the times be t1 and t2, with Δt = t2 − t1. The target’s velocity components are vx = (x2 − x1)/Δt and vy = (y2 − y1)/Δt. The speed is sqrt(vx^2 + vy^2), and the course (direction of travel) is arctangent of vy over vx (the angle of the velocity vector). In short, compare successive positions, turn them into velocity components over the time between sweeps, and from those you obtain both speed and course. The other options don’t provide a method for extracting motion from position data.

When you have two radar sweeps, you have two position fixes for the same target at known times. The way to estimate course and speed is to track how its position changes between those scans.

Convert each sweep’s range and bearing into Cartesian coordinates (x, y) with the radar at the origin: x = r cos θ, y = r sin θ. Let the times be t1 and t2, with Δt = t2 − t1. The target’s velocity components are vx = (x2 − x1)/Δt and vy = (y2 − y1)/Δt. The speed is sqrt(vx^2 + vy^2), and the course (direction of travel) is arctangent of vy over vx (the angle of the velocity vector).

In short, compare successive positions, turn them into velocity components over the time between sweeps, and from those you obtain both speed and course. The other options don’t provide a method for extracting motion from position data.