(Color online) General geometrical configuration for an array of N acoustic sensors located above flat ground (xy-plane) and the linear trajectory of an airborne sound source (aircraft) as it transits past the array in a straight line at constant speed and constant altitude.
(Color online) Direct paths and ground-reflected paths for the signal emitted by the source at time arriving at a pair of sensors and ( ), and the mirror images ( and ) of the two sensors about the ground surface (xy-plane).
Projection of source trajectory and sensors onto the xy-plane.
(Color online) CRLBs on error standard deviations of flight parameter estimates obtained with the small aperture L-shaped array using the proposed method and conventional time-delay based method for four different observation times T = 14, 28, 56, and 112 s, assuming white Gaussian measurement noise with standard deviation σ = 0.1 ms. Simulation results are for T = 14 s only.
(Color online) CRLBs on error standard deviations of flight parameter estimates obtained with the small aperture linear array using the proposed method for four different observation times T = 14, 28, 56, and 112 s, assuming white Gaussian measurement noise with standard deviation σ = 0.1 ms. Simulation results are for proposed method with T = 14 s only.
Sensor configuration of the large planar microphone array used in the field experiment.
Normalized correlogram for the second sensor pair (microphones 13 and 14) of the 13th small aperture linear array for a particular aircraft transit (transit 10).
Time sequences of time delay and intersensor multipath delay estimates (small circles) from the two sensor pairs of the 13th small aperture linear array for the same aircraft transit considered in Fig. 7 , and LS fit of the delay model to these sequences of delay measurements (solid lines).
Mean values (circles) and ±1 standard deviation (error bars) in the estimates of the aircraft's (a) velocity, (b) altitude, (c) CPA ground range, and (d) CPA azimuth angle for each of the ten aircraft transits. Note that all mean values shown in (a) and (d) are absolute values and the signs of all velocity and CPA azimuth angle estimates are correct. The squares in (a) and (b) represent the nominal speed and altitude of the aircraft during each transit.
Mean values and ±1 standard deviation in the estimates of the aircraft's (a) speed and (b) altitude, obtained by applying the single-sensor cepstrum NLS method in turn to each of the 15 sensors (1–15), for each of the 10 aircraft transits.
Comparison of variability in aircraft speed and altitude estimates for the proposed method and single-sensor cepstrum NLS method. First entry: Average standard deviation. Second entry: Average relative standard deviation.
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