T he tw o graphs in figure 6 -7 sh ow that the relative variability in the estim ate o f the sig n a l-to -n o ise ratio is higher at the low er o f the tw o sig n a l-to -n o ise ratios. Exam ination o f the relative variability at other sign al-to-n oise ratios sh o w ed that this w as indeed a trend. T his observation is in accordance with exp ectation . T he estim ate o f the n o ise p o w er ou tside the target is perform ed on several hundred ran ge-cells and hence w ill be c lo s e to the n o ise pow er selected to generate the synthetic n oise. H o w ev er, the signal p o w er is estim ated from the ten to one hundred ra n ge-cells com p risin g the target and h en ce w ill be subject to greater variability and inaccuracy. A s the sign a l-to -n o ise ratio falls the n o ise part o f the ran ge-cells that are d eem ed part o f the target increases. Thus
the variability in the noise power added to these range-cells as a part of the total power in these range-cells also increases. Thus the estimate of the signal power, which is taken to be the power in the range-cells after the mean of the range-cells outside the target is deducted, will also vary more. It can be seen that at both signal to noise ratios there is a tendency to overestimate the signal to noise ratio.
As expected, figures 6-8 to 6-10 all show a drop in the performance of all five classifiers as range to target increases and hence signal-to-noise ratio falls. It can be seen from figures 6-8 and 6-9 that both of the database methods significantly out performed both the basic and traditional methods. This difference falls in absolute terms as the signal-to-noise ratio decreases. The difference is even greater for the integrated data than the pseudo single pulse data. However, this larger difference can be explained by noting that the signal-to-noise ratio marked on the x-axis of figure 6-9 is the signal- to-noise ratio for a single pulse range profile, but the profile being classified is the sum of eleven of these plus beamweighting which is on average over seven times larger. Hence, the difference between the basic/traditional methods and the database methods for integrated range profiles should be compared to the difference between the methods on the pulse-to-pulse range profiles at a seventh of the signal-to-noise ratio. If this is done then the difference between the basic/traditional and database methods is approximately the same for both pulse-to-pulse and integrated range profiles. For example, the difference between the basic/traditional methods and the database methods on 12 signal-to-noise ratio integrated range profiles is about 15% which is approximately the same as the difference between the pair of methods at 72 signal-to- noise ratio on single-pulse range profiles.
It can also be seen from figures 6-8 and 6-9 that the database2 method has equal or better performance than the databasel method except at a signal-to-noise ratio of 10000. The principle of using information in the test range profile from range-cells outside those that correspond to the candidate template is thus supported by this observation. However, as noted earlier, the manner in which information outside the candidate template target was used was restricted to declaring whether a non-noise event had occurred, no information was used if the range-cells outside the template target were below the selected threshold and thus deemed to be noise. Further, it might be possible to improve the performance of the databaseZ method by selecting the threshold in a different manner or using a different or even varying fine factor as both the threshold and fine factor were selected in a fairly ad-hoc manner.
The poor performance of the databasel method at the very high signal-to-noise ratio is thought to be due to a problem with setting the threshold too low. Thus some low scatterers that are actually part of the target in the training data, but were not included in the template because they were so low, are still higher than the threshold. This problem could be avoided by setting a greater minimum threshold or by ensuring that the templates include all of the target scatterers including the low valued ones.
As stated in the implementation section the correlation classifier is known to be somewhat robust to changes in signal-to-noise ratio and that is confirmed by the results on this data set. The correlation classifier outperforms all the other classifiers except for the database2 method on the integrated data at signal-to-noise ratios between 100 and 33.
It can be seen from figure 6-8 that the traditional method of removing the noise mean gives even worse performance than the basic method of doing nothing in response
to changes in the signal-to-noise ratio on pulse-to-pulse range profiles. This is because the probability density functions of the corrupted signal following subtraction of the mean are even further away from the template probability density function than the corrupted signal distribution. This can be seen by examining figures 6-5 and 6-6. When classifying single-pulse range profiles, the large number of range-cells that will have a zero value following the subtraction is shown by the large spike against the y-axis in figure 6-6. All of these values will generate a zero likelihood for most of the range-cell templates in the database and hence be of no use in the classification decision. However, once the data have been integrated over the eleven pulses the standard deviation of the integrated noise will be a much smaller fraction of the average signal plus noise. Thus there is a lower probability that the signal plus noise is less than the noise mean, thus fewer zero valued range-cells will occur and the probability density function of the corrupted signal minus the noise mean will be closer to the template probability density function for that range-cell.
Random performance is calculated by dividing one hundred per cent by the number of training classes which in this case gives 14.3%. Although the performance of all the classifiers drops by a large amount at low signal-to-noise ratios, none of the classifiers drops to random performance. Hence, there is the possibility that overall performance could be increased by using confidence thresholds and unknown classes or by taking multiple looks at the target at different aspect angles and times. Confidence thresholds, unknown classes and multiple looks will be examined in detail in chapter 8.
By comparing figure 6-8 with 6-10 the effect of having to estimate the signal-to- noise ratio of the corrupted profile can be assessed. It can be seen that the database classifiers perform significantly better than the basic classifier at very low signal-to-
noise ratios if the signal-to-noise ratio is known but only comparably when the signal- to-noise ratio must be estimated. Additionally, when the signal to noise ratio is known, the database classifiers even outperform the correlation classifier at these low signal-to- noise ratios. Although, this difference in performance between the correlation and database classifiers at low signal to noise ratios may not be statistically significant, it can be seen that the estimation of the signal-to-noise ratio is a crucial part of the process.
For a calibrated radar it may be possible to more accurately estimate the signal-to- noise ratio by knowing the noise value from calibration tests and having recorded the target radar cross-section in the template. If this could be done the higher level of classification that is demonstrated in figure 6-10 could be achieved. Further, if the radar cross-section of the target were known this could be used as information to aid the discrimination between the targets and push the probability of correct classification even higher.