How do I implement an adaptive thresholding algorithm for underwater sonar

Question

I want to implement an adaptive thresholding algorithm in MATLAB for filtering data received by an underwater sonar receiver. The data received has an interactive noise component resulting from underwater noise and specular reflection. CFARD method is close, but it does not serve my purpose. I have to image the data so that i am able to see the object, on a screen, that is placed underwater within the scandepth of the sonar. Any help will be greatly appreciated.

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EDIT:

It is an underwater environment. I am trying to threshold a signal that has been received from a sonar transducer after it has been reflected by a solid target, that is situated in the same environment as the transducer. The problems belongs to Underwater Acoustic Imaging sonar domain. Problem is, I haven't been able to model the underwater environmental noise. From what I have read till now about this topic, the noise model follows a $K$-distribution. Also the environmental noise is not additive in nature, rather it's interactive. Hence the threshold has to be adaptive. I also mentioned CFARD method in my question. That is useful for signal processing in radar applications as we're just interested in finding a single point in a large area which has high energy. Same cannot be said about underwater acoustic imaging sonar, where we try to display the target on the screen as a video. I hope I have made it more clear now.

Answer 1

Your question has received quite few contributions, probably because of a lacking content. During a recent conference , I came across the PhD thesis: Détection en Environnement non Gaussien (Detection in a non-Gaussian environment). Since it is in French, I reproduce the abstract here:

For a long time, radar echoes coming from the various returns of the transmitted signal on many objects of the environment (clutter) have been exclusively modelled by Gaussian vectors. The related optimal detection procedure was then performed by the classical matched filter. Then, the technological improvement of radar systems showed that the true nature of the clutter could not be considered as Gaussian any more. Though the optimality of the matched filter is no more valid in such cases, CFAR techniques (Constant False Alarm Rate) were proposed for this detector in order to adapt the value of the detection threshold to the multiple local variations of the clutter. In spite of their diversity, none of these techniques turned to be either robust or optimal in these situations. With the modelling of the clutter by non-Gaussian complex processes, such as SIRP (Spherically Invariant Random Process), optimal structures of coherent detection have been found. These models describe many non-Gaussian laws, like K-distribution or Weibull laws, and are acknowledged in the literature to model many experimental situations in a relevant way. To identify the law of their characteristic component (namely the texture) without statistical a priori on the model, we propose, in this thesis, to tackle the problem by a Bayesian approach. Two new estimation methods of the texture law emerge from this proposition: the first one is a parametric method, based on a Padé approximation of the moment generating function, and the second one results from a Monte Carlo estimation. These estimations are carried out on reference clutter data and lead to two new optimal detection strategies, respectively named PEOD (Padé Estimated Optimum Detector) and BORD (Bayesian Optimum Detector Radar). The asymptotic expression of the BORD (convergence in law), called the "Asymptotic BORD", is established together with its law. This last result gives access to the optimal theoretical performances of the Asymptotic BORD, and may also applied to the BORD if the data correlation matrix is non-singular. The detection performances of BORD and those of Asymptotic BORD are evaluated on experimental ground clutter data. We obtained results that validate both the relevance of SIRP model for the clutter, the optimality of the BORD and its adaptability to any type of environment.

The math should be readable. If it is of any help, you can track English reference by the author or PhD thesis committee.