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Smoothed Velocity Formula

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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. Check FAQs

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

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

Smoothed Velocity Example

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With units

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Here is how the Smoothed Velocity equation looks like with Values.

Here is how the Smoothed Velocity equation looks like with Units.

Here is how the Smoothed Velocity equation looks like.

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

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

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

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Smoothed Velocity Solution

Follow our step by step solution on how to calculate Smoothed Velocity?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

v s = 11 + \frac{8}{320} \cdot (6 - 74)

LAST Step Evaluate

∴

v s = 9.3m/s

Smoothed Velocity Formula Elements

Variables

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

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

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

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

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 Smoothed Velocity?

Smoothed Velocity evaluator uses Smoothed Velocity = (n-1)th Scan Smoothed Velocity+Velocity Smoothing Parameter/Time between Observations*(Measured Position at Nth Scan-Target Predicted Position) to evaluate the Smoothed Velocity, The Smoothed Velocity formula is the smoothed estimate of target's present velocity on the basis of the past detections by the track-while-scan surveillance radar. Smoothed Velocity is denoted by v_s symbol.

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

FAQs on Smoothed Velocity

What is the formula to find Smoothed Velocity?

The formula of Smoothed Velocity is expressed as Smoothed Velocity = (n-1)th Scan Smoothed Velocity+Velocity Smoothing Parameter/Time between Observations*(Measured Position at Nth Scan-Target Predicted Position). Here is an example- 9.3 = 11+8/320*(6-74).

How to calculate Smoothed Velocity?

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

Can the Smoothed Velocity be negative?

Yes, the Smoothed Velocity, measured in Speed can be negative.

Which unit is used to measure Smoothed Velocity?

Smoothed Velocity is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Smoothed Velocity can be measured.

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Smoothed Velocity Formula

Smoothed Velocity Example

Smoothed Velocity Solution

Smoothed Velocity Formula Elements

Other formulas in Special Purpose Radars category

How to Evaluate Smoothed Velocity?

FAQs on Smoothed Velocity

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