Target Tracking with Multi Acoustic Array Sensors Data

Acoustic array sensor along with Root-MUSIC algorithm is used to estimate the direction of arrival of the acoustic signal emitted by an acoustic target. Three architectures are used to track the target in Cartesian coordinates: (i) digital filter with least square estimation, (ii) linear Kalman filter with least square estimation, and (iii) extended Kalman filter. A comparative evaluation of the three architectures in terms of performance metrics is presented.

λ

Wavelength

i^th DoA angle

Perturbation step size

Noise variance

Vandermode matrix

Steering vector

Butterworth filter's denominator coefficients

Butterworth filter's numerator coefficients

Rate of propagation

Spacing between sensors

Expectation operator

Complex envelope of additive Gaussian noise at j^th sensor

State transition matrix

Process noise gain matrix

Measurement matrix

Filter transfer function

Identity matrix

Index numbers

Kalman gain

i^th direction vector

Number of targets

Number of samples

Number of sensors

Number of snapshots

Indexes

State error covariance

Process noise covariance matrix

Measurement noise covariance matrix

Correlation matrix

Singular value decomposition operator

Innovation covariance matrix

i^th sensor

i^th target signal waveform

Sampling interval

Continuous time index

Eigenvector

Noise subspace

Signal subspace

Measurement noise sequence

Process noise sequence

State vector

Estimated X

Predicted X

True state vector

i^th sensor output

Position in x-axis

True x-position

Target x-position

Velocity in x-axis

Array output

Position in y-axis

True y-position

Target y-position

Velocity in y-axis

j^th sensor position

Measurement vector

Transpose of matrix A

i^th Eigen value