Feature Articles—November 2009 Issue
Countering the Torpedo Threat Through Detection and 3D TrackingThe Development of a Sonar System to Detect and Track Torpedoes as Part of a Sensor Weapon and Control System
By Nico Roosnek
Director
Roosnek Research & Development
The Hague, Netherlands
Ship torpedo-defense systems are ideally based on 3D information about incoming torpedoes, so a torpedo detection and location (TDL) sonar system has been designed that would use a transmitting transducer, two receiving arrays and optimal signal processing with 3D tracking capabilities.
The system’s hardware and almost all of its software are equivalent to that used in acoustic tracking systems for offshore surveying of pipelines at the seafloor.
Torpedoes can be tracked by active and/or passive acoustic means. In the latter case, the distance is estimated by measuring the curvature of the wave front with three hydrophones or hydrophone arrays, instead of using the propagation time.
The curvature is estimated by correlating the hydrophone signals with optimal estimation so that statistical errors are minimized. However, considerable system errors remain, making such systems almost useless.
This is not the case for active systems. These systems, known as sonar, use beamformers with hydrophone signals and a transmitting transducer, the latter eventually with beamforming capability.
The transmitting transducer might have a receiving mode. Beamforming is an extensive computing process that produces a relatively small amount of extracted information about the objects of interest.
Another approach is to identify the reflections in the hydrophone signals. When one or more events correlate in time over a large number of hydrophones, detection of a reflecting object has occurred, and tracking can begin.
By using more than one suitably oriented receiving array, the 3D position and velocity of the object relative to the sensor platform can be obtained.
With the position of the sensor platform obtained by a global positioning system and a motion reference unit, the absolute position of the torpedo can be derived.
Reflections from the environment and reverberation can interfere with detection and tracking. Interference from other sound sources does not depend on the transmitted pulse energy.
From these parameters and receiving operating characteristics, a 3D torpedo detection system with a range of up to 400 meters in an ocean environment is feasible, according to the work of Robert J. Urick and others.
To test the capabilities of such a system, an equivalent one has been developed to work in the atmosphere, and trials in the air have shown it to be a success.
The system’s range in air must be increased before full-scale system development for the ocean can begin, however.
Active System Detection Method
In an active system, four types of pulses can be transmitted: the frequency-modulated continuous wave (FMCW) pulse, the continuous wave (CW) pulse and the linear-frequency modulated (FM) or period-modulated (PM) chirp pulse. While the FMCW and CW pulses have well-known advantages, they will not be discussed in this article.
The strength of the ambiguity function—the output of the correlation process of the linear PM chirp—is invariant. This is not the case for the linear FM pulse.
The strength of the ambiguity function of this pulse will not change when BTv/c is much less than 1, where B, T, v and c are the frequency bandwidth, chirp duration, relative object velocity and sound velocity, respectively. With a transducer, an acoustic chirp pulse is transmitted into the water and reflected or scattered by objects.
The length of the propagation path from the transmitting transducer to an object and from the object to the lth hydrophone of the kth array are respectively rtr and rk,l (α), with α being the declination angle of the propagation path to the middle of the arrays.
The total propagation path and time are shown in equations 1 and 2, respectively.
Equation 2 is used for the detection of reflecting objects. By using a closure error in a least-square sense with the propagation times of all array hydrophones, one obtains a likelihood figure for object identification in the signals with noise.
In the tracking process, all hydrophone signals, Sk,l, are combined in the cost function (Equation 3), with the propagation time defined by Equation 4, with r, rtr and rk,l representing the 3D coordinates of the object, the transducer and the (k,l)th hydrophone, respectively, and with Wk,l,j as the weight of the Jth sample of the (k,l)th hydrophone signal and φklj as the phase function of the hydrophone signal, Skl.
By minimizing the cost function χ2, the most likely position, r, for the torpedo is obtained.
This type of estimation is most efficient and gives the same results for Gaussian distributed errors as the maximum likelihood and moment methods.
The parameter ω is equal to the momentary or mean radial frequency of the reflected signal and thus may be omitted from the estimation procedure, since the v/c is much less than 1.
For small changes in r and ω, the cost function can be linearized as shown in Equation 5, obtaining a system of simultaneous equations with the unknown δr and eventually δω.
The obtained δr and δω values are used to iterate toward the best estimates.
With the history, system and observations known and with errors taken into account, the least-square procedure is transformed into an optimal estimation or extended Kalman filter procedure.
Trials in Air
The hardware and software of the pipeline detection and tracking system were used to test the feasibility of such a system in the atmosphere. All distances and signal frequencies were scaled down a factor of five, the ratio between sound’s velocity in water vs. air.
Each of the two arrays consists of 16 electret microphones with the microphone signals summed per pair (the analog to digital-digital to analog hardware had 16 channels). For transmission, a double array of two by four small tweeters was used. The hydrophone arrays were oriented vertically.
The spacing between the microphones was six centimeters, and the base of the microphone arrays was one meter. For the tweeters, spacing was 10.5 centimeters. The tweeter double array can be located anywhere, but for the test it was placed between the microphone arrays.
The transmitted pulse was a Hanning windowed linear FM-chirp pulse with a mean frequency, bandwidth and pulse duration of 10 kilohertz, 10 kilohertz and 30 milliseconds, respectively.
The dynamic range of the complete system was found to be sufficient.
Conclusions
In simulation mode, the system was found to work correctly and with a very low signal-to-noise ratio. Reverberation has not been simulated, however.
In real-time mode, the system also works correctly in the air, but the range is limited to 25 meters. The detection and tracking capability should be increased to at least 80 meters in the air before starting the development of a real TDL system such as this for the underwater environment. In this way, the risk and the costs of developing such a system can be minimized.
Figures about the performance of the system as a function of the system parameters, the maneuvering of a torpedo, signal-to-noise ratio, reverberation or other environmental parameters should be obtained to figure out the operational characteristics.
References
For a full list of references, please contact nico@roosnek.nl.
Nico Roosnek is an experimental physicist who specializes in the field of underwater acoustics, sonar and related fields, like electronics and signal processing. He is the director of Roosnek Research & Development.
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