Complex-Domain DSLA Spatial-Temporal Four-Dimension Matched Field Localization

Detection and Estimation found the basis of signal processing. Therefore, the target localization in underwater environment is supposed to involve two aspects, where the first is to make assure whether the target exists and the second is to estimate the corresponding parameters of target position if existed. According to their close relationship, this paper derives the matched field processing method for underwater target localization in detail, initialized from the optimal detector and estimator. This matched field processing methods is the extension from spherical/plane wave beamforming in free field to underwater waveguide, whose essence is the correlation calculation with data and replica vectors.Ocean environment is bounded by surface and bottom, resulting in the cylindrical wave propagation. The acoustic field in underwater environment is spatial-temporal four-dimension, constituted by three spatial dimensions and one temporal dimension. Therefore, the target localization in waveguide is spatial-temporal four dimensional localization with joint spatial three-dimension localization and temporal one-dimension wave localization. The joint three dimensional localization means that we estimate the bearing, depth and ranging simultaneously. If we are interested in one or two of these dimensions, we can get it from sections or marginalization. Practical localization is four-dimensional with three-dimensional information contained in mobile curve and the recovered received signals.The acoustic field in waveguide is spatial-temporal wide banded. Spatial wide band means multi-wave-number, while temporal wide band means multi-frequency. In spatial domain, the cylindrical wave propagation can models as normal mode model, the cylindrical wave is decomposed into a standing wave and a propagating wave. Each mode corresponds to a up-going plane wave and a down-going plane wave, each up-going plane wave or down-going plane wave corresponds a spatial wave number such multi-mode propagation forms spatial wide band. In time domain, signals emitted from the target are wideband. Spatial-temporal wide band is good for localization, for the very first reason, different targets at different three-dimension location motivate different sound field, which could be explored to three-dimension localization; secondly, the temporal wide band could be used to fight against fading,for frequency diversity could decrease variance.In order to fully use the spatial-temporal wide band of the acoustic field, it is necessary to design spatial-temporal wide band array, that is, large time-bandwidth product and large space-bandwidth product, which can exploit spatial-temporal wide band properties since signals with large time-bandwidth product has close temporal and Doppler spread directivity and array with large space-bandwidth product has good three dimensional directivity, then result in good performance when against interference.The Double Spiral Linear Array (DSLA) designed in this paper is constituted by two spiral linear arrays. The heights of two arrays starts are separated by several intervals. Moreover, the bearing of the two arrays is differed by nearly180degree. These two arrays go down clockwise spirally. Each of the eastern and western hemispheres corresponding to each of the northern and southern hemispheres has elements with complex spatial orientations with no replication. Therefore, DSLA is spatially wide banded array.The matched field localization faces the challenge from the environmental uncertainty in practice, which will induce the weighting vector of model predication is not matched with the practical data. This will cause the error diverging and system unstable, then accordingly the performance of matched field localization will degenerate and even collapse. Therefore, we need robust modeling and robust signal processing methods.This paper takes the environmental parameters and target parameters as the state vector of systems, whose spatial-temporal evolution follows the basic laws of dynamics. We can treat it as one common existing AR processing and then construct state equations correspondingly. Later, we can establish the measurement equation from the acoustic propagation model and received data. Until now, the state-space model is constructed finally by state equation and measurement equation. In state-space model, we can take the posterior estimation of the current state as the prior of the next state and get the MMSE estimation for the data measured and the next state according to the state equation. Then, the innovation can be extracted from data to revise the prior estimation as feedback, which achieve the posterior estimation. This process is conducted sequentially and finally the posterior PDF of the state will converge, which enable the reliable localization.The matched field localization is essentially the least-squares estimation problems for target position. In practical process, we need pay attention to whether the signal is proper or not and circular or not. This paper has developed the previous work from the proper case to the improper case by discarding the previously underlying proper assumption of signals. We process the improper signals in augmented complex domain by exploiting the complementary correlation of improper signals to achieve better performance. The numerical simulations and experiments have validated the better performance of such a method when processing the improper signals compared to the regular method. In proper case, the complex signal processing is reduced to the regular method. Thus, the proper is the special case of the improper and the improper signal processing contains the proper signal processing.