Time between Observations Calculator

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Special Purpose Radars

Radar & Antenna Specifications

Radar Antennas Reception

✖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.ⓘ Velocity Smoothing Parameter [β]			+10% -10%
✖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.ⓘ Smoothed Velocity [v_s]			+10% -10%
✖(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.ⓘ (n-1)th Scan Smoothed Velocity [v_s(n-1)]			+10% -10%
✖Measured position at Nth scan is the measured or actual position of target at the nth scan by the track-while-scan surveillance radar.ⓘ Measured Position at Nth Scan [x_n]			+10% -10%
✖Target Predicted Position is the predicted or estimated position of target at the nth scan by the track-while-scan surveillance radar.ⓘ Target Predicted Position [x_pn]			+10% -10%

✖Time between observations is the time taken between two successive observations made by the track-while-scan surveillance radar.ⓘ Time between Observations [T_s]

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Formula

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Time between Observations

Formula

`"T"_{"s"} = ("β"/("v"_{"s"}-"v"_{"s(n-1)"}))*("x"_{"n"}-"x"_{"pn"})`

Example

`"320s"=("8"/("9.3m/s"-"11m/s"))*("6m"-"74m")`

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Time between Observations Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time between Observations = (Velocity Smoothing Parameter/(Smoothed Velocity-(n-1)th Scan Smoothed Velocity))*(Measured Position at Nth Scan-Target Predicted Position)
T_s = (β/(v_s-v_s(n-1)))*(x_n-x_pn)
This formula uses 6 Variables

Variables Used

Time between Observations - (Measured in Second) - Time between observations is the time taken between two successive observations made by the track-while-scan surveillance radar.
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.
Smoothed Velocity - (Measured in Meter per Second) - 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.
(n-1)th Scan Smoothed Velocity - (Measured in Meter per Second) - (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.
Measured Position at Nth Scan - (Measured in Meter) - Measured position at Nth scan is the measured or actual position of target at the nth scan by the track-while-scan surveillance radar.
Target Predicted Position - (Measured in Meter) - Target Predicted Position is the predicted or estimated position of target at the nth scan by the track-while-scan surveillance radar.

STEP 1: Convert Input(s) to Base Unit

Velocity Smoothing Parameter: 8 --> No Conversion Required
Smoothed Velocity: 9.3 Meter per Second --> 9.3 Meter per Second No Conversion Required
(n-1)th Scan Smoothed Velocity: 11 Meter per Second --> 11 Meter per Second No Conversion Required
Measured Position at Nth Scan: 6 Meter --> 6 Meter No Conversion Required
Target Predicted Position: 74 Meter --> 74 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_s = (β/(v_s-v_s(n-1)))*(x_n-x_pn) --> (8/(9.3-11))*(6-74)

Evaluating ... ...

T_s = 320

STEP 3: Convert Result to Output's Unit

320 Second --> No Conversion Required

FINAL ANSWER

320 Second <-- Time between Observations

(Calculation completed in 00.004 seconds)

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Created by Shobhit Dimri

Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat

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< 21 Special Purpose Radars Calculators

Amplitude of Signal Received from Target at Range

Go Amplitude of Signal Received = Echo Signal Voltage/(sin((2*pi*(Carrier Frequency+Doppler Frequency Shift)*Time Period)-((4*pi*Carrier Frequency*Range)/[c])))

Echo Signal Voltage

Go Echo Signal Voltage = Amplitude of Signal Received*sin((2*pi*(Carrier Frequency+Doppler Frequency Shift)*Time Period)-((4*pi*Carrier Frequency*Range)/[c]))

Velocity Smoothing Parameter

Go Velocity Smoothing Parameter = ((Smoothed Velocity-(n-1)th Scan Smoothed Velocity)/(Measured Position at Nth Scan-Target Predicted Position))*Time between Observations

Time between Observations

Go Time between Observations = (Velocity Smoothing Parameter/(Smoothed Velocity-(n-1)th Scan Smoothed Velocity))*(Measured Position at Nth Scan-Target Predicted Position)

Smoothed Velocity

Go Smoothed Velocity = (n-1)th Scan Smoothed Velocity+Velocity Smoothing Parameter/Time between Observations*(Measured Position at Nth Scan-Target Predicted Position)

Phase Difference between Echo Signals in Monopulse Radar

Go Phase Difference between Echo Signals = 2*pi*Distance between Antennas in Monopulse Radar*sin(Angle in Monopulse Radar)/Wavelength

Predicted Position of Target

Go Target Predicted Position = (Smoothed Position-(Position Smoothing Parameter*Measured Position at Nth Scan))/(1-Position Smoothing Parameter)

Amplitude of Reference Signal

Go Amplitude of Reference Signal = CW Oscillator Reference Voltage/(sin(2*pi*Angular Frequency*Time Period))

Reference Voltage of CW Oscillator

Go CW Oscillator Reference Voltage = Amplitude of Reference Signal*sin(2*pi*Angular Frequency*Time Period)

Measured Position at Nth Scan

Go Measured Position at Nth Scan = ((Smoothed Position-Target Predicted Position)/Position Smoothing Parameter)+Target Predicted Position

Position Smoothing Parameter

Go Position Smoothing Parameter = (Smoothed Position-Target Predicted Position)/(Measured Position at Nth Scan-Target Predicted Position)

Smoothed Position

Go Smoothed Position = Target Predicted Position+Position Smoothing Parameter*(Measured Position at Nth Scan-Target Predicted Position)

Distance from Antenna 1 to Target in Monopulse Radar

Go Distance from Antenna 1 to Target = (Range+Distance between Antennas in Monopulse Radar)/2*sin(Angle in Monopulse Radar)

Distance from Antenna 2 to Target in Monopulse Radar

Go Distance from Antenna 2 to Target = (Range-Distance between Antennas in Monopulse Radar)/2*sin(Angle in Monopulse Radar)

Efficiency of Cross Field Amplifier(CFA)

Go Efficiency of Cross Field Amplifier = (CFA RF Power Output-CFA RF Drive Power)/DC Power Input

CFA DC Power Input

Go DC Power Input = (CFA RF Power Output-CFA RF Drive Power)/Efficiency of Cross Field Amplifier

CFA RF Power Output

Go CFA RF Power Output = Efficiency of Cross Field Amplifier*DC Power Input+CFA RF Drive Power

CFA RF Drive Power

Go CFA RF Drive Power = CFA RF Power Output-Efficiency of Cross Field Amplifier*DC Power Input

Range Resolution

Go Range Resolution = (2*Antenna Height*Target Height)/Range

Doppler Frequency Shift

Go Doppler Frequency Shift = (2*Target Velocity)/Wavelength

Peak Quantization Lobe

Go Peak Quantization Lobe = 1/2^(2*Mean Lobe)

Time between Observations Formula

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. The Smoothed Velocity as in spite of some inherent limitations, smooth models are well adapted to run reflection tomography coupled with migration velocity analysis for the imaging.

How to Calculate Time between Observations?

Time between Observations calculator uses Time between Observations = (Velocity Smoothing Parameter/(Smoothed Velocity-(n-1)th Scan Smoothed Velocity))*(Measured Position at Nth Scan-Target Predicted Position) to calculate the Time between Observations, The Time between Observations formula is defined as the total time taken between the observation in the velocity as by the prediction of the target. Time between Observations is denoted by T_s symbol.

How to calculate Time between Observations using this online calculator? To use this online calculator for Time between Observations, enter Velocity Smoothing Parameter (β), 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) and hit the calculate button. Here is how the Time between Observations calculation can be explained with given input values -> -272 = (8/(9.3-11))*(6-74).

FAQ

What is Time between Observations?

The Time between Observations formula is defined as the total time taken between the observation in the velocity as by the prediction of the target and is represented as T_s = (β/(v_s-v_s(n-1)))*(x_n-x_pn) or Time between Observations = (Velocity Smoothing Parameter/(Smoothed Velocity-(n-1)th Scan Smoothed Velocity))*(Measured Position at Nth Scan-Target Predicted Position). 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, 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, (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, Measured position at Nth scan is the measured or actual position of target at the nth scan by the track-while-scan surveillance radar & Target Predicted Position is the predicted or estimated position of target at the nth scan by the track-while-scan surveillance radar.

How to calculate Time between Observations?

The Time between Observations formula is defined as the total time taken between the observation in the velocity as by the prediction of the target is calculated using Time between Observations = (Velocity Smoothing Parameter/(Smoothed Velocity-(n-1)th Scan Smoothed Velocity))*(Measured Position at Nth Scan-Target Predicted Position). To calculate Time between Observations, you need Velocity Smoothing Parameter (β), 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). With our tool, you need to enter the respective value for Velocity Smoothing Parameter, Smoothed Velocity, (n-1)th Scan Smoothed Velocity, Measured Position at Nth Scan & Target Predicted Position and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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