DATA MINING

Data Mining and Machine Learning

Data Mining and Machine Learning

This meant to introduce the reader to the principles Sliding Correlators and how they are used to cerate a delay discriminator. Additionally the spread spectrum term “Processing Gain” is discussed. There are many other types of correlators but here we will focus on the Sliding Type. Before we dive right in on the sliding correlator we need some intro material on the Correlation operation.

One of the key operations that distinguish the GPS receiver from classic narrow band receivers is the use of a correlator. The correlation process in the GPS receiver is used to align the replica C/A code with the transmitted C/A code. Additional this results in recovery of timing signals that are ultimately used in the receiver TOA measurement process. But what is correlation and how does it work?

Fundamentally correlation is a statistical process that is it is related to averages and probabilities. We intuitively know that when we roll a pair of dice the outcome from one throw to another is not correlated, that is the previous throws have no effect on subsequent throws. When two events are in some way interrelated such that the outcome of one affects the other we could say the events had some sort of correlation.

There is another interpretation of correlation and that is as a measure of similarity. Particularly in electronics it would be desirable to compare various time signals to one another and see if they have anything in common. By having such a tool it should be possible to quantitatively determine how much and where two signals are correlated and where they are not correlated. It is this interpretation of correlation that is used in the GPS receiver correlation process. Finding the point in time where two signals are similar, or in GPS receiver where the receiver's replica C/A code is lined up with the received C/A code from the satellite, is the prime reason we need to understand the correlation process. We will see that correlation allows to us determine, to very high degree of accuracy, when we have C/A code alignment.

Before we discuss correlation in more depth we need to briefly examine a concept called “Time Average Value” of a time varying voltage or current signal.

Time Averaging

What is the “time averaging value” function? Lets look at the waveforms in figure A1 Figure A1-A shows a sinewave that has a max value of +1 volts and a minimum value of -1 volts. Its time average is zero volts. The reason is that the waveform spends as much time positive as it does negative and the magnitude of theses positive and negative excursions is identical. The waveform shown in figure A1-B is a square wave that goes from 0 to 1 volt. The average value would be 0.5 volts. Waveform A1-C is a sinewave that goes from zero volts to 5 volts maximum. The average value of this waveform is ...