The advantages of Seagnal's approach are manifold:

• Scalability :Supports a large number of sensors, ensuring high-resolution data acquisition and processing.

• Compact Design: Facilitates easy deployment in space-constrained environments.

• Performance: Offers scalable performance for more demanding applications.

• Time-to-Market: Significantly reduces the time-to-market for new deployments, providing a rapid and cost-effective path to implementation.

With Seagnal, users benefit from cutting-edge technology that is both robust and adaptable, meeting the needs of modern sonar systems with unparalleled efficiency and ease of integration. For more detailed information and to explore how Seagnal can meet your specific needs, please feel free to contact our sales team.

Here are the functionalities of the SW suite, ready to design Active and Passive Sonar: 

• Beamforming

  • Conventional Beamforming: Uses fixed weights for both transmission and reception to steer the beam.

  • Adaptive Beamforming: Adjusts weights dynamically to optimize echo detection in noisy environments.

  • MUSIC (MUltiple SIgnal Classification): Enhances resolution of direction-of-arrival estimation for received echoes.

• Detection Methods

  • Matched Filtering: Detects targets by correlating received signals with a known transmitted signal.

  • Pulse Compression: Improves range resolution and signal-to-noise ratio using modulated pulses.

  • Doppler Processing: Detects and estimates target velocity by analyzing Doppler shifts in echoes.

• Tracking Methods

  • Kalman Filtering: Provides efficient computational means to estimate the state of a linear dynamic system from a series of noisy measurements.

  • Interacting Multiple Model (IMM): Uses multiple models to represent different motion behaviors of a target, improving tracking accuracy in complex scenarios.

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BEAM FORMING

Conventional Beamforming

Conventional beamforming applies weights to the signals received at each sensor in an array. The output of the beamformer at time t is calculated as:

y(t) = w1 * x1(t) + w2 * x2(t) + ... + wN * xN(t)

Here:

• y(t) is the beamformer output at time t.

• x_i(t) is the signal received at the i-th sensor at time t.

• w_i is the weight applied to the i-th sensor.

• N is the number of sensors in the array.

The weights w_i are chosen to steer the beam in a particular direction θ and are typically set as:

w_i = exp(-j * (2π/λ) * (P_i • U_θ))

Where:

• λ is the wavelength of the signal.

• P_i is the relative position of the i-th sensor in vector form.

• U_θ is the pointing angle of the beam θ .

• j is the imaginary unit.

• • is the dot product

Adaptive Beamforming

Adaptive beamforming dynamically adjusts the weights to optimize the array's response. The goal is to minimize the mean square error (MSE) between the beamformer output and a reference signal. This optimization problem can be written as:

minimize_w E[|y(t) - d(t)|^2]

Where:

• d(t) is the reference signal at time t.

• E[.] denotes the expectation operator.

The solution to this problem is given by:

w = R^(-1) * p

Where:

• w is the vector of weights.

• R is the covariance matrix of the received signals.

• p is the cross-correlation vector between the received signals and the reference signal.

MUSIC (MUltiple SIgnal Classification) Beamforming

MUSIC is a high-resolution technique for direction-of-arrival (DOA) estimation. It involves decomposing the covariance matrix of the received signals into signal and noise subspaces. The covariance matrix R is given by:

R = E[x(t) * x(t)']

Where:

• x(t) is the vector of received signals at time t.

• x(t)' is the Hermitian transpose of x(t).

The covariance matrix is decomposed into eigenvalues and eigenvectors:

R = U_s * Λ_s * U_s' + U_n * Λ_n * U_n'

Where:

• U_s and U_n are the matrices of signal and noise subspace eigenvectors, respectively.

• Λ_s and Λ_n are the diagonal matrices of signal and noise subspace eigenvalues, respectively.

The MUSIC spectrum is computed as:

P_MUSIC(θ) = 1 / (a(θ)' * U_n * U_n' * a(θ))

Where:

• a(θ) is the steering vector for direction θ.

The directions of arrival are estimated by finding the peaks in the MUSIC spectrum.

These formulations provide a mathematical foundation for understanding how each beamforming technique operates in sonar systems.