In a series of papers written over the last few years [1-4], the authors introduced the concept of space-time integration (STI) to the problem of source detection and localization for narrowband targets in the oceanic waveguide. Traditionally, in narrowband processing for an array of hydrophones, a two-dimensional Fourier, or FRAZ (FRequency / AZimuth), spectrum of the data is computed. For a source with a sufficiently strong signal it is possible to detect the signal and to estimate the received frequency and azimuth of the  source from the FRAZ for a single integration period, or snapshot. Thus a sequence of FRAZs  yields a series of azimuth (bearing) and  frequency estimates which will change with respect to time for a moving source. These data can be used with traditional target motion analysis (TMA) algorithms to estimate the location and velocity of the target [5]. Another processing method which has been used more recently with array data is matched field processing (MFP) [6,7]. In this approach the signal model is based on more accurate waveguide propagation model than the conventional beamformer, or plane-wave model. The modelled signal field is correlated with the array data to yield estimates of the target’s range, depth, and azimuth for a single data snapshot.

However, in many situations the signal received at an array is so weak that for many or all of the Fourier transform or MFP integration periods it is not possible to detect the signal. This, of course, also implies that over such time periods it is not possible to track the target. The method of space time integration avoids many of the problems caused by weak signals. In this method a target track is hypothesized and then a signal model is used to predict the hydrophone data as a function of time which should be observed for this target. The model/data correlations from many consecutive integration periods are summed for the entire observation time of interest. This procedure is repeated for many hypothesized target tracks. The track which yields the largest sum is taken to be estimate of the target track. Because of the batch processing nature of this algorithm, the problems associated with tracking fading signals are avoided. In fact, because of the long-time sum of the data/model correlation, is possible to detect a target on the basis of this statistic when the target is not detectable using any single data snapshot.

Much of our research with the STI algorithm has been in implementing different signal and target track models. Our earliest work [1] considered constant-velocity target tracks and used a harmonic, plane-wave model signal in the waveguide. The application of an iterative Newton method to space-time integration was described in [2]. We then considered a multi-leg model for the target track [3] in order to tackle the localization problem for a manoeuvring target. In this case we still used the plane-wave for the model for the signal. Finally in [4] we considered an efficient implementation of the STI algorithm when the signal in an oceanic waveguide is modelled realistically with modes. This last algorithm may be considered a combination of TMA and MFP.

In this paper we start by describing the detection and localization problem in terms of general data model correlations over time. We then consider in more detail the computational aspects of implementing specific target track and signal models. In many of the cases the data / model correlations discussed above are simply implemented by using standard two-dimensional fast Fourier transforms (FFT) of the data.