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Velocity Smoothing Parameter Formula

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Velocity Smoothing Parameter is the tuning parameter which is used to improve the quality of smoothed velocity estimated by the track-while-scan surveillance radar to avoid noisy measurements. Check FAQs

β = (\frac{v s - v s(n-1)}{x n - x pn}) \cdot T s

β - Velocity Smoothing Parameter?v_s - Smoothed Velocity?v_s(n-1) - (n-1)th Scan Smoothed Velocity?x_n - Measured Position at Nth Scan?x_pn - Target Predicted Position?T_s - Time between Observations?

Velocity Smoothing Parameter Example

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Here is how the Velocity Smoothing Parameter equation looks like with Values.

Here is how the Velocity Smoothing Parameter equation looks like with Units.

Here is how the Velocity Smoothing Parameter equation looks like.

8 = (\frac{9.3 - 11}{6 - 74}) \cdot 320

8 = (\frac{9.3m/s - 11m/s}{6m - 74m}) \cdot 320s

8 = (\frac{9.3 - 11}{6 - 74}) \cdot 320

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Velocity Smoothing Parameter Solution

Follow our step by step solution on how to calculate Velocity Smoothing Parameter?

FIRST Step Consider the formula

β = (\frac{v s - v s(n-1)}{x n - x pn}) \cdot T s

Next Step Substitute values of Variables

∴

β = (\frac{9.3m/s - 11m/s}{6m - 74m}) \cdot 320s

Next Step Prepare to Evaluate

∴

β = (\frac{9.3 - 11}{6 - 74}) \cdot 320

LAST Step Evaluate

∴

β = 8

Velocity Smoothing Parameter Formula Elements

Variables

Velocity Smoothing Parameter

Velocity Smoothing Parameter is the tuning parameter which is used to improve the quality of smoothed velocity estimated by the track-while-scan surveillance radar to avoid noisy measurements.

Symbol: β

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Velocity Smoothing Parameter

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.

Symbol: v_s

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Smoothed Velocity

(n-1)th Scan Smoothed Velocity

(n-1)th Scan Smoothed Velocity is the smoothed estimate of target's velocity at the n-1 th scan by the track-while-scan surveillance radar.

Symbol: v_s(n-1)

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find (n-1)th Scan Smoothed Velocity

Measured Position at Nth Scan

Measured position at Nth scan is the measured or actual position of target at the nth scan by the track-while-scan surveillance radar.

Symbol: x_n

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Measured Position at Nth Scan

Target Predicted Position

Target Predicted Position is the predicted or estimated position of target at the nth scan by the track-while-scan surveillance radar.

Symbol: x_pn

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Target Predicted Position

Time between Observations

Time between observations is the time taken between two successive observations made by the track-while-scan surveillance radar.

Symbol: T_s

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time between Observations

Other formulas in Special Purpose Radars category

Go Doppler Frequency Shift

Δf d = \frac{2 \cdot v t}{λ}

Go Reference Voltage of CW Oscillator

V ref = A ref \cdot \sin (2 \cdot π \cdot ω \cdot T)

Go Amplitude of Reference Signal

A ref = \frac{V ref}{\sin (2 \cdot π \cdot ω \cdot T)}

Go Amplitude of Signal Received from Target at Range

A rec = \frac{V echo}{\sin ((2 \cdot π \cdot (f c + Δf d) \cdot T) - (\frac{4 \cdot π \cdot f c \cdot R o}{[c]}))}

How to Evaluate Velocity Smoothing Parameter?

Velocity Smoothing Parameter evaluator uses Velocity Smoothing Parameter = ((Smoothed Velocity-(n-1)th Scan Smoothed Velocity)/(Measured Position at Nth Scan-Target Predicted Position))*Time between Observations to evaluate the Velocity Smoothing Parameter, The Velocity Smoothing Parameter formula is used to calculate the tuning parameter which is used to improve the quality of smoothed velocity estimated by the track-while-scan surveillance radar to avoid noisy measurements due to factors like clutters or noise in radar system. Velocity Smoothing Parameter is denoted by β symbol.

How to evaluate Velocity Smoothing Parameter using this online evaluator? To use this online evaluator for Velocity Smoothing Parameter, enter Smoothed Velocity (v_s), (n-1)th Scan Smoothed Velocity (v_s(n-1)), Measured Position at Nth Scan (x_n), Target Predicted Position (x_pn) & Time between Observations (T_s) and hit the calculate button.

FAQs on Velocity Smoothing Parameter

What is the formula to find Velocity Smoothing Parameter?

The formula of Velocity Smoothing Parameter is expressed as Velocity Smoothing Parameter = ((Smoothed Velocity-(n-1)th Scan Smoothed Velocity)/(Measured Position at Nth Scan-Target Predicted Position))*Time between Observations. Here is an example- -9.411765 = ((9.3-11)/(6-74))*320.

How to calculate Velocity Smoothing Parameter?

With Smoothed Velocity (v_s), (n-1)th Scan Smoothed Velocity (v_s(n-1)), Measured Position at Nth Scan (x_n), Target Predicted Position (x_pn) & Time between Observations (T_s) we can find Velocity Smoothing Parameter using the formula - Velocity Smoothing Parameter = ((Smoothed Velocity-(n-1)th Scan Smoothed Velocity)/(Measured Position at Nth Scan-Target Predicted Position))*Time between Observations.

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Velocity Smoothing Parameter Formula

Velocity Smoothing Parameter Example

Velocity Smoothing Parameter Solution

Velocity Smoothing Parameter Formula Elements

Other formulas in Special Purpose Radars category

How to Evaluate Velocity Smoothing Parameter?

FAQs on Velocity Smoothing Parameter

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