検出

ターゲット検出、CFAR、2-D CFAR、ROC 曲線、ソナー方程式

Phased Array System Toolbox™ には、整合フィルター処理、1 次元または 2 次元での定偽警報率 (CFAR) 検出、ストレッチ処理パルス圧縮、およびコヒーレント/非コヒーレントパルス積分を実行するための System object と Simulink^® ブロックが含まれています。ユーティリティ関数を使用すると、さまざまな S/N 比 (SNR) レベルまたは偽警報の確率に対する受信者動作特性 (ROC) 曲線を計算して可視化できます。一連の関数やアプリを使用することで、レーダー方程式を使用してレーダー解析を実行できます。たとえば、受信 SNR や最大ターゲット検出レンジを推定できます。ソナー方程式についても同様の機能セットが提供されます。ブレイクチャートを使用することで、レーダーカバレッジを可視化できます。

オブジェクト

`phased.AlphaBetaFilter`	Alpha-beta filter for object tracking
`phased.CFARDetector`	Constant false alarm rate (CFAR) detector
`phased.CFARDetector2D`	Two-dimensional CFAR detector
`phased.GLRTDetector`	Generalized likelihood ratio detector (R2023b 以降)
`phased.LRTDetector`	Likelihood ratio test detector (R2023b 以降)
`phased.MatchedFilter`	Matched filter
`phased.StretchProcessor`	Stretch processor for linear FM waveform
`phased.TimeVaryingGain`	Time varying gain control

ブロック

2-D CFAR Detector	Two-dimensional constant false alarm rate (CFAR) detector
CFAR Detector	Constant false alarm rate (CFAR) detector
Dechirp Mixer	Dechirping operation on input signal
GLRT Detector	Perform generalized likelihood ratio test detection (R2023b 以降)
LRT Detector	Likelihood ratio test detector (R2023b 以降)
Matched Filter	Matched filter
Pulse Integrator	Coherent or noncoherent pulse integration
Stretch Processor	Stretch processor for linear FM waveforms
Time Varying Gain	Time varying gain (TVG) control

関数

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ROC 推定

`albersheim`	Albersheim の方程式を使用した必要な SNR
`dechirp`	Perform dechirp operation on FMCW signal
`npwgnthresh`	Detection SNR threshold for signal in white Gaussian noise
`pulsint`	Pulse integration
`rocpfa`	Receiver operating characteristic curves by false-alarm probability
`rocsnr`	Receiver operating characteristic curves by SNR
`shnidman`	Required SNR using Shnidman’s equation

レーダーパフォーマンス

`bw2rangeres`	Convert bandwidth to range resolution (R2021a 以降)
`coincidence`	Coincidence algorithm (R2021a 以降)
`crt`	Chinese remainder theorem (R2021a 以降)
`freq2wavelen`	Convert frequency to wavelength (R2021a 以降)
`iscoprime`	Check coprime relation (R2021a 以降)
`physconst`	物理定数
`rangeres2bw`	Convert range resolution to bandwidth (R2021a 以降)
`wavelen2freq`	Convert wavelength to frequency (R2021a 以降)

ソナーパフォーマンス

`bw2rangeres`	Convert bandwidth to range resolution (R2021a 以降)
`freq2wavelen`	Convert frequency to wavelength (R2021a 以降)
`physconst`	物理定数
`rangeres2bw`	Convert range resolution to bandwidth (R2021a 以降)
`range2tl`	Compute underwater sound transmission loss from range
`sonareqsl`	Compute source level using the sonar equation
`sonareqsnr`	Compute SNR using the sonar equation
`sonareqtl`	Compute transmission loss using the sonar equation
`tl2range`	Compute range from underwater transmission loss
`wavelen2freq`	Convert wavelength to frequency (R2021a 以降)

SAR イメージ形成

`rangeMigrationSFM`	Range migration image formation algorithm for stepped FM waveform (R2022a 以降)
`rangeMigrationLFM`	Range migration image formation algorithm for linear FM waveform (R2022a 以降)
`rangeMigrationFMCW`	Range migration image formation algorithm for frequency-modulated CW waveform (R2022a 以降)
`rangeDopplerImagerLFM`	Range Doppler image formation algorithm for linear FM waveform (R2022a 以降)

アプリ

ソナー方程式計算機	Estimate maximum range, SNR, transmission loss and source level of a sonar system
センサーアレイアナライザー	線形、平面、3D、および任意のセンサーアレイのビームパターンとパフォーマンス特性の解析

トピック

検出と推定

Neyman-Pearson Hypothesis Testing
In phased-array applications, you sometimes need to decide between two competing hypotheses to determine the reality underlying the data the array receives. For example, suppose one hypothesis, called the null hypothesis, states that the observed data consists of noise only. Suppose another hypothesis, called the alternative hypothesis, states that the observed data consists of a deterministic signal plus noise. To decide, you must formulate a decision rule that uses specified criteria to choose between the two hypotheses.
Constant False-Alarm Rate (CFAR) Detectors
CFAR detectors apply the Neyman-Pearson criterion to target detection. The detectors estimate noise statistics from data.
Receiver Operating Characteristics
Receiver operating characteristic (ROC) curves describe a detector’s performance by relating probability of false alarm to probability of detection.
整合フィルター処理
整合フィルター処理により、SNR が向上し、検出が改善されます。
Stretch Processing
Stretch processing, also known as deramping or dechirping, is an alternative to matched filtering.
FMCW Range Estimation
FMCW range estimation dechirps the received signal, extracts beat frequencies, and computes the target range.
レンジ-ドップラー応答
レンジ-ドップラー処理を実行し、レンジ-ドップラーマップを可視化する。

フェーズドアレイ規則

Standards and Conventions
This section introduces the concept of baseband signals and defines the local and global coordinate systems used in the toolbox.
Units of Measure and Physical Constants
Phased Array System Toolbox uses the International System of Units (SI).

ソナー方程式

Sonar Equation
The sonar equation is used in underwater signal processing to relate received signal power to transmitted signal power for one-way or two-way sound propagation. The equation computes the received signal-to-noise ratio (SNR) from the transmitted signal level, taking into account transmission loss, noise level, sensor directivity, and target strength. The sonar equation serves the same purpose in sonar as the radar equation does in radar. The sonar equation has different forms for passive sonar and active sonar.
Doppler Effect for Sound
The Doppler effect is the change in the observed frequency of a source due to the motion of either the source or receiver or both. Only the component of motion along the line connecting the source and receiver contributes to the Doppler effect. Any arbitrary motion can be replaced by motion along the source-receiver axis with velocities consisting of the projections of the velocities along that axis. Therefore, without loss of generality, assume that the source and receiver move along the x-axis and that the receiver is positioned further out along the x-axis. The source emits a continuous tone of frequency, f₀, equally in all directions. First examine two important cases. The first case is where the source is stationary and the receiver is moving toward or away from the source. A receiver moving away from the source will have positive velocity. A receiver moving toward the source will have negative velocity. If the receiver moves towards the source, it will encounter wave crests more frequently and the received frequency will increase according to

$f^{'} = f_{0} (\frac{c - v_{r}}{c})$
Frequency will increase because v_r is negative. If the receiver is moving away from the source, the v_r is positive and the frequency decreases. A similar situation occurs when the source is moving and the receiver is stationary. Then the frequency at the receiver is

$f^{'} = f_{0} (\frac{c}{c - v_{s}})$
The frequency increases when v_s is positive as the source moves toward the receiver. When v_s is negative, the frequency decreases. Both effects can be combined into

$f^{'} = f_{0} (\frac{c - v_{r}}{c}) (\frac{c}{c - v_{s}}) = f_{0} (\frac{c - v_{r}}{c - v_{s}}) = f_{0} (\frac{1 - \frac{v_{r}}{c}}{1 - \frac{v_{s}}{c}}) .$

検出