GLRT Detector

Perform generalized likelihood ratio test detection

Since R2023b

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Libraries:
Phased Array System Toolbox / Detection

Description

The generalized likelihood ratio test detector (GLRT) performs detection of signals with unknown parameters in the presence of noise. Unknown parameters include signal amplitude, phase, frequency, and arrival times. The detector replaces unknown parameters by their maximum likelihood estimates under the signal absent and H₀ and the alternative signal present H₁ hypotheses. Then, the binary detector chooses between the null hypothesis H₀ and the alternative hypothesis H₁ based on the measurements. If the H₀ hypothesis best accounts for the data, the detector declares that a target is not present. If the H₁ hypothesis best accounts for the data, the detector declares that a target is present.

Ports

Input

X — Input data

real-valued N-by-1 vector | complex-valued N-by-1 vector | real-valued N-by-M matrix | complex-valued N-by-M matrix

Input data, specified as a real-valued or complex-valued N-by-1 vector, or an N-by-M real-valued or complex-valued matrix. N is the signal length and M is the number of data channels. Detection is performed along the columns of X. The size of each row M cannot change during simulation. When M = 1, X represents a single channel of data. When M > 1, X can represent N samples from M data channels. Data streams can later be combined, for example, by the beamforming.

The input data has a general interpretation. For example, the data can be interpreted as:

• Time series – N samples of a time series

• Sensor - N represents a snapshot of data samples from a set of sensors

Data Types: single | double
Complex Number Support: Yes

Hyp — Augmented linear equality constraint matrix

real-valued R-by-(P + 1) matrix | complex-valued R-by-(P + 1) matrix

Augmented linear equality constraint matrix, specified as a real-valued or complex-valued R-by-(P + 1) matrix. The matrix takes the form [A,b] and represents the equation:

$$A\Theta =b$$

where the unknown parameters are represented byϴ. A has the rank R ≥ 1. The augmented linear equality constraint matrix expresses the null hypothesis H₀.

For this signal model, the GLRT detector determines whether to reject the null hypothesis which is expressed in the form A*ϴ = b where A is an R-by-P matrix with R ≤ P and rank R ≥ 1, and b is an R-by-1 vector. A and b are carried in the augmented linear equality constraint matrix hyp = [A,b]. Because there are D signal models, the GLRT detector outputs D detection results for each column of X

Data Types: single | double
Complex Number Support: Yes

Obs — Observation matrix

N-by-P-by-D array

Observation matrix for the linear deterministic signal model, specified as an N-by-P-by-D array N > p and rank P, D is the number of signal models, and the white Gaussian noise is a N-by-1 vector determined by the covariance ncov argument. The observation matrix is defined by X = obs*param + noise,

Example: 20.0

Data Types: single | double
Complex Number Support: Yes

Ncov — Known noise power

positive scalar

Known noise power, specified as a scalar or a row vector of length D. When ncov is a scalar, it represents equal known noise power for D models. When ncov is a row vector of length D, it represents the known noise power for the D models, respectively.

Example: 20.0

Dependencies

To enable this argument, set the NoiseInputPort property to true.

Data Types: single | double

Output

Y — Detection results

D-by-M logical-valued vector | 1-by-L integer-valued vector | 2-by-L integer-valued matrix

Detection results of D models for M independent data samples returned as a D-by-M logical-valued vector pr . The format of Y depends on how the OutputFormat property is specified. By default, the OutputFormat property is set to 'Detection result'.

When OutputFormat is 'Detection result', Y is a D-by-M matrix containing logical detection results, where D is the number of signal models and M is the number of columns of X. For each row, Y is true in a column if there is a detection in the corresponding column of arg. Otherwise, Y is false.

When OutputFormat is 'Detection index', Y is a 1-by-L vector or a 2-by-L matrix containing detection indices, where L is the number of detection found in the M data samples and D models. When X is a column vector, Y is a 1-by-L vector and contains the index of the detections found in the D models. When X is a matrix, Y is a 2-by-L matrix, and each column of Y has the form [detrow;detcol], where detrow is the index of the model, and detcol is the column index of X.

Stat — detection statistic

N-by-M (default) | 1-by-L

Detection statistics, returned as a N-by-M matrix or 1-by-L vector. The format of stat depends on the OutputFormat property.

• When OutputFormat is 'Detection result', stat has the same size as Y.

• When OutputFormat is 'Detection index', stat is a 1-by-L vector containing detection statistics for each corresponding detection in Y.

Dependencies

To enable this port, select the Output detection statistics and threshold check box.

Th — Detection threshold

scalar

Detection threshold, returned as a scalar.

Dependencies

To enable this port, select the Output detection statistics and threshold check box.

Param — Maximum likelihood estimates of signal parameters

P-by-M-by-D array

Maximum likelihood estimates (MLE) of unknown signal parameters, returned as a P-by-M-by-D array.

Dependencies

To enable this port, select the Output MLEs of unknown signal parameters check box.

N — Estimated noise power

positive scalar

Estimated noise power, returned as a positive scalar. When the OutputFormat property is 'Detection result', estnoise has the same size as Y. When OutputFormat property is 'Detection index', estnoise returns a noise power estimate of size 1-by-L for each corresponding detection in Y.

Dependencies

To enable this port, select the Output estimated noise power check box.

Parameters

Probability of false alarm — Probability of false alarm

0.1 (default) | nonnegative scalar

Probability of false alarm, specified as positive scalar between 0 and 1, inclusive.

Programmatic Use

Block Parameter:ProbabilityFalseAlarm

Type:double, single

Values:scalar |

Default:0.1

Data Types: single | double

Output format — Format of output data

Detection result (default) | Detection index

Format of output data, specified as Detection result or Detection index. Output data is returned in the Y port.

Example: Detection index

Programmatic Use

Block Parameter:OutputFormat

Type:char, string

Values:Detection result | Detection index

Default:Detection result

Data Types: char | string

Output detection statistics and threshold — Output detection statistics and threshold

0 (default) | 1

Select this checkbox to output detection statistics and detection threshold using the Stat and Th ports.

Programmatic Use

Block Parameter:ThresholdOutputPort

Type:check box

Values:0 | 1

Default:0

Enable known noise power input — Enable known noise power input

1 (default) | 1

Select this checkbox to allow input of noise power using the NCov port.

Dependencies

To select this check box, deselect the Output estimated noise power checkbox.

Programmatic Use

Block Parameter:NoiseInputPort

Type:check box

Values:0 | 1

Default:0

Output MLEs of unknown signal parameters — Output MLEs of unknown signal parameters

0 (default) | 1

Select this check box to output maximum likelihood estimate of signal parameters using the Param port.

Programmatic Use

Block Parameter:SignalParamterOutputPort

Type:check box

Values:0 | 1

Default:0

Output estimated noise power — Output estimated noise power

0 (default) | 1

Select this check box to output estimated noise power using the N port.

Programmatic Use

Block Parameter:NoisePowerOutputPort

Type:check box

Values:0 | 1

Default:0

Simulate using — Block simulation method

Interpreted Execution (default) | Code Generation

Block simulation, specified as Interpreted Execution or Code Generation. If you want your block to use the MATLAB^® interpreter, choose Interpreted Execution. If you want your block to run as compiled code, choose Code Generation. Compiled code requires time to compile but usually runs faster.

Interpreted execution is useful when you are developing and tuning a model. The block runs the underlying System object™ in MATLAB. You can change and execute your model quickly. When you are satisfied with your results, you can then run the block using Code Generation. Long simulations run faster with generated code than in interpreted execution. You can run repeated executions without recompiling, but if you change any block parameters, then the block automatically recompiles before execution.

This table shows how the Simulate using parameter affects the overall simulation behavior.

When the Simulink^® model is in Accelerator mode, the block mode specified using Simulate using overrides the simulation mode.

Acceleration Modes

Block Simulation	Simulation Behavior
	Normal	Accelerator	Rapid Accelerator
Interpreted Execution	The block executes using the MATLAB interpreter.	The block executes using the MATLAB interpreter.	Creates a standalone executable from the model.
Code Generation	The block is compiled.	All blocks in the model are compiled.

For more information, see Choosing a Simulation Mode (Simulink).

Programmatic Use

Block Parameter:SimulateUsing

Type:enum

Values:Interpreted Execution, Code Generation

Default:Interpreted Execution

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2023b