Probability of Detection Solution

STEP 0: Pre-Calculation Summary
Formula Used
Detection Probability of Radar = 1-(1-Cumulative Probability of Detection)^(1/N Scans)
pdetect = 1-(1-pc)^(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
pdetect = 1-(1-pc)^(1/n) --> 1-(1-0.4375)^(1/2)
Evaluating ... ...
pdetect = 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)

Credits

Created by Shobhit Dimri
Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat
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Vishwakarma Government Engineering College (VGEC), Ahmedabad
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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
Target Height
Go Target Height = (Range Resolution*Range)/(2*Antenna Height)
Radar Antenna Height
Go Antenna Height = (Range Resolution*Range)/(2*Target 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
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
Effective Area of Receiving Antenna
Go Effective Area of Receiving Antenna = Antenna Area*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
Measured Runtime
Go Measured Runtime = 2*Target Range/[c]
Range of Target
Go Target Range = ([c]*Measured Runtime)/2

Probability of Detection Formula

Detection Probability of Radar = 1-(1-Cumulative Probability of Detection)^(1/N Scans)
pdetect = 1-(1-pc)^(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 pdetect 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 (pc) & 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 pdetect = 1-(1-pc)^(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 (pc) & 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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