Cumulative Probability of Detection Solution

STEP 0: Pre-Calculation Summary
Formula Used
Cumulative Probability of Detection = 1-(1-Detection Probability of Radar)^N Scans
pc = 1-(1-pdetect)^n
This formula uses 3 Variables
Variables Used
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.
Detection Probability of Radar - Detection Probability of Radar is defined as the probability of finding or surveilling the object inside the radar.
N Scans - N scans refers to the total number of scans run during radar detection.
STEP 1: Convert Input(s) to Base Unit
Detection Probability of Radar: 0.25 --> No Conversion Required
N Scans: 2 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
pc = 1-(1-pdetect)^n --> 1-(1-0.25)^2
Evaluating ... ...
pc = 0.4375
STEP 3: Convert Result to Output's Unit
0.4375 --> No Conversion Required
FINAL ANSWER
0.4375 <-- Cumulative Probability of Detection
(Calculation completed in 00.004 seconds)

Credits

Created by Shobhit Dimri
Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat
Shobhit Dimri has created this Calculator and 900+ more calculators!
Verified by Urvi Rathod
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

Cumulative Probability of Detection Formula

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

What is meant by probability of detection?

Probability of detection is 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.The older term “Blip Scan Ratio” was renamed to as “Probability of Detection”.

How to Calculate Cumulative Probability of Detection?

Cumulative Probability of Detection calculator uses Cumulative Probability of Detection = 1-(1-Detection Probability of Radar)^N Scans to calculate the Cumulative Probability of Detection, The Cumulative Probability of Detection formula 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 is denoted by pc symbol.

How to calculate Cumulative Probability of Detection using this online calculator? To use this online calculator for Cumulative Probability of Detection, enter Detection Probability of Radar (pdetect) & N Scans (n) and hit the calculate button. Here is how the Cumulative Probability of Detection calculation can be explained with given input values -> 0.4375 = 1-(1-0.25)^2.

FAQ

What is Cumulative Probability of Detection?
The Cumulative Probability of Detection formula 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 and is represented as pc = 1-(1-pdetect)^n or Cumulative Probability of Detection = 1-(1-Detection Probability of Radar)^N Scans. Detection Probability of Radar is defined as the probability of finding or surveilling the object inside the radar & N scans refers to the total number of scans run during radar detection.
How to calculate Cumulative Probability of Detection?
The Cumulative Probability of Detection formula 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 is calculated using Cumulative Probability of Detection = 1-(1-Detection Probability of Radar)^N Scans. To calculate Cumulative Probability of Detection, you need Detection Probability of Radar (pdetect) & N Scans (n). With our tool, you need to enter the respective value for Detection Probability of Radar & 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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