Smoothed Velocity Calculator

Smoothed Velocity Formula:

\[ v_s = v_{s(n-1)} + \frac{\beta}{T_s} \times (x_n - x_{pn}) \]

(n-1)th Scan Smoothed Velocity:

m/s

Velocity Smoothing Parameter (β):

Time between Observations (Tₛ):

Measured Position at Nth Scan (xₙ):

Target Predicted Position (xₚₙ):

Smoothed Velocity (vₛ):

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1. What is Smoothed Velocity?

Smoothed Velocity is the smoothed estimate of target's present velocity on the basis of the past detections by the track-while-scan surveillance radar. It provides a more stable and accurate velocity estimation by filtering out measurement noise.

2. How Does the Calculator Work?

The calculator uses the Smoothed Velocity formula:

\[ v_s = v_{s(n-1)} + \frac{\beta}{T_s} \times (x_n - x_{pn}) \]

Where:

\( v_s \) — Smoothed Velocity (m/s)
\( v_{s(n-1)} \) — (n-1)th Scan Smoothed Velocity (m/s)
\( \beta \) — Velocity Smoothing Parameter
\( T_s \) — Time between Observations (s)
\( x_n \) — Measured Position at Nth Scan (m)
\( x_{pn} \) — Target Predicted Position (m)

Explanation: The formula calculates the smoothed velocity by combining the previous smoothed velocity estimate with a correction term based on the difference between measured and predicted positions.

3. Importance of Velocity Smoothing

Details: Velocity smoothing is crucial in radar tracking systems to provide stable and accurate velocity estimates, reduce measurement noise, and improve target tracking performance in track-while-scan surveillance systems.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Time between observations must be greater than zero. The calculator provides the smoothed velocity estimate in meters per second.

5. Frequently Asked Questions (FAQ)

Q1: What is the purpose of the velocity smoothing parameter (β)?
A: The velocity smoothing parameter is a tuning parameter used to control the balance between responsiveness to new measurements and smoothing of noisy data.

Q2: How does time between observations affect the calculation?
A: The time between observations determines the weighting of the correction term - shorter intervals give more weight to position differences.

Q3: What are typical values for the smoothing parameter?
A: Typical values range from 0.1 to 0.3, but optimal values depend on specific radar characteristics and measurement noise levels.

Q4: When should this smoothing technique be used?
A: This technique is particularly useful in track-while-scan radar systems where measurements are noisy and stable velocity estimates are needed for accurate target tracking.

Q5: How does this compare to other smoothing techniques?
A: This is a simple recursive smoothing technique that provides good performance with minimal computational requirements, making it suitable for real-time radar systems.