Probability of Detection Calculator

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Radar & Antenna Specifications

Radar Antennas Reception

Special Purpose Radars

✖Cumulative probability of detection is defined as the ratio of detected aims to the number of all possible blips on the radar screen, i.e. all possible targets in a given direction.ⓘ Cumulative Probability of Detection [p_c]			+10% -10%
✖N scans refers to the total number of scans run during radar detection.ⓘ N Scans [n]			+10% -10%

✖Detection Probability of Radar is defined as the probability of finding or surveilling the object inside the radar.ⓘ Probability of Detection [p_detect]

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Formula

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Probability of Detection

Formula

`"p"_{"detect"} = 1-(1-"p"_{"c"})^(1/"n")`

Example

`"0.25"=1-(1-"0.4375")^(1/"2")`

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Probability of Detection Solution

STEP 0: Pre-Calculation Summary

Formula Used

Detection Probability of Radar = 1-(1-Cumulative Probability of Detection)^(1/N Scans)
p_detect = 1-(1-p_c)^(1/n)
This formula uses 3 Variables

Variables Used

Detection Probability of Radar - Detection Probability of Radar is defined as the probability of finding or surveilling the object inside the radar.
Cumulative Probability of Detection - Cumulative probability of detection is defined as the ratio of detected aims to the number of all possible blips on the radar screen, i.e. all possible targets in a given direction.
N Scans - N scans refers to the total number of scans run during radar detection.

STEP 1: Convert Input(s) to Base Unit

Cumulative Probability of Detection: 0.4375 --> No Conversion Required
N Scans: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

p_detect = 1-(1-p_c)^(1/n) --> 1-(1-0.4375)^(1/2)

Evaluating ... ...

p_detect = 0.25

STEP 3: Convert Result to Output's Unit

0.25 --> No Conversion Required

FINAL ANSWER

0.25 <-- Detection Probability of Radar

(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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< 24 Radar & Antenna Specifications Calculators

Maximum Range of Radar

Go Target Range = ((Transmitted Power*Transmitted Gain*Cross Section Area of Radar*Effective Area of Receiving Antenna)/(16*pi^2*Minimum Detectable Signal))^0.25

Minimum Detectable Signal

Go Minimum Detectable Signal = (Transmitted Power*Transmitted Gain*Cross Section Area of Radar*Effective Area of Receiving Antenna)/(16*pi^2*Target Range^4)

N Scans

Go N Scans = (log10(1-Cumulative Probability of Detection))/(log10(1-Detection Probability of Radar))

Transmitted Gain

Go Transmitted Gain = (4*pi*Effective Area of Receiving Antenna)/Wavelength^2

Transmitted Frequency

Go Transmitted Frequency = Doppler Frequency*[c]/(2*Radial Velocity)

Power Density Radiated by Lossless Antenna

Go Lossless Isotropic Power Density = Maximum Radiated Power Density/Maximum Gain of Antenna

Maximum Power Density Radiated by Antenna

Go Maximum Radiated Power Density = Lossless Isotropic Power Density*Maximum Gain of Antenna

Maximum Gain of Antenna

Go Maximum Gain of Antenna = Maximum Radiated Power Density/Lossless Isotropic Power Density

Radar Antenna Height

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

Target Height

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

Probability of Detection

Go Detection Probability of Radar = 1-(1-Cumulative Probability of Detection)^(1/N Scans)

Cumulative Probability of Detection

Go Cumulative Probability of Detection = 1-(1-Detection Probability of Radar)^N Scans

Effective Area of Receiving Antenna

Go Effective Area of Receiving Antenna = Antenna Area*Antenna Aperture Efficiency

Antenna Aperture Efficiency

Go Antenna Aperture Efficiency = Effective Area of Receiving Antenna/Antenna Area

Antenna Area

Go Antenna Area = Effective Area of Receiving Antenna/Antenna Aperture Efficiency

Pulse Repetition Frequency

Go Pulse Repetition Frequency = [c]/(2*Maximum Unambiguous Range)

Maximum Unambiguous Range

Go Maximum Unambiguous Range = ([c]*Pulse Repetition Time)/2

Pulse Repetition Time

Go Pulse Repetition Time = (2*Maximum Unambiguous Range)/[c]

Target Velocity

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

Doppler Frequency

Go Doppler Frequency = Doppler Angular Frequency/(2*pi)

Doppler Angular Frequency

Go Doppler Angular Frequency = 2*pi*Doppler Frequency

Radial Velocity

Go Radial Velocity = (Doppler Frequency*Wavelength)/2

Range of Target

Go Target Range = ([c]*Measured Runtime)/2

Measured Runtime

Go Measured Runtime = 2*Target Range/[c]

Probability of Detection Formula

Detection Probability of Radar = 1-(1-Cumulative Probability of Detection)^(1/N Scans)
p_detect = 1-(1-p_c)^(1/n)

How do you find the probability of a false alarm?

False alarm is “an erroneous radar target detection decision caused by noise or other interfering signals exceeding the detection threshold”. In general, it is calculated by ratio of false targets per pulse repetition time to number of range cells.

How to Calculate Probability of Detection?

Probability of Detection calculator uses Detection Probability of Radar = 1-(1-Cumulative Probability of Detection)^(1/N Scans) to calculate the Detection Probability of Radar, Probability of Detection refers to the likelihood or probability that a radar system or antenna will correctly detect the presence of a target or signal of interest. It is a critical performance metric used to assess the effectiveness and reliability of a radar system or an antenna in detecting and tracking targets. Detection Probability of Radar is denoted by p_detect symbol.

How to calculate Probability of Detection using this online calculator? To use this online calculator for Probability of Detection, enter Cumulative Probability of Detection (p_c) & N Scans (n) and hit the calculate button. Here is how the Probability of Detection calculation can be explained with given input values -> 0.249667 = 1-(1-0.4375)^(1/2).

FAQ

What is Probability of Detection?

Probability of Detection refers to the likelihood or probability that a radar system or antenna will correctly detect the presence of a target or signal of interest. It is a critical performance metric used to assess the effectiveness and reliability of a radar system or an antenna in detecting and tracking targets and is represented as p_detect = 1-(1-p_c)^(1/n) or Detection Probability of Radar = 1-(1-Cumulative Probability of Detection)^(1/N Scans). Cumulative probability of detection is defined as the ratio of detected aims to the number of all possible blips on the radar screen, i.e. all possible targets in a given direction & N scans refers to the total number of scans run during radar detection.

How to calculate Probability of Detection?

Probability of Detection refers to the likelihood or probability that a radar system or antenna will correctly detect the presence of a target or signal of interest. It is a critical performance metric used to assess the effectiveness and reliability of a radar system or an antenna in detecting and tracking targets is calculated using Detection Probability of Radar = 1-(1-Cumulative Probability of Detection)^(1/N Scans). To calculate Probability of Detection, you need Cumulative Probability of Detection (p_c) & N Scans (n). With our tool, you need to enter the respective value for Cumulative Probability of Detection & N Scans 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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