Innovation: Comb Filtering

March 1, 2009 By: Andrew G. Dempster GPS World

Improving Acquisition and Tracking in GNSS Receivers

INNOVATION INSIGHTS with Richard Langley

Our world is inherently noisy. Of course, we are all familiar with the sounds that assault our ears when we're walking down a busy street or the vibration of a hotel air conditioner that might keep us awake on a hot summer evening. But the concept of noise can be extended to any process or activity if we think of it as something whose presence usually results in a less than ideal outcome. So we talk about the off-topic noise in an online discussion group, for example.

Richard Langley

In the electronic world, we are often faced with noisy signals. Fluctuating electrical currents or electromagnetic waves have two components: one of interest, called the desired signal, and one which is not, called the noise. The noise typically is unwanted and we usually seek ways to reduce its presence or level compared to that of the desired signal. The noise may or may not be random. The 50 or 60 Hz power-line hum picked up by an improperly grounded amplifier is an example of the latter, whereas the static on a weak radar return is an example of the former.

We can reduce an undesirable component in a signal, analog or digital, by using a filter. A filter enhances or attenuates a particular frequency or range of frequencies in the input signal to produce the desirable output signal. There are a wide variety of filters, each designed to operate on a given input to produce a desired output. Common generic filters are the lowpass, highpass, and bandpass filters where the designations indicate the frequency range of the output signal.

A special type of filter can be used where the desired signal or the noise has equally spaced frequency components. This filter has a frequency response with equally spaced passbands or stopbands resembling the teeth of a comb. Accordingly, it is called a comb filter. Comb filters are used in analog and digital televisions, for example, to reduce picture artifacts that otherwise result from incomplete separation of the luminance and chrominance signals in composite video. Comb filters have also been used to attenuate the power-line fundamental and its harmonics in audio signals and to separate solar and lunar variations in electron-content data.

The pseudorandom noise codes transmitted by GNSS satellites repeat in the time domain, which results in equally spaced spectral components in the frequency domain. So, could comb filters in GNSS receivers enhance acquisition and tracking of satellite signals? In this month's column, we find out.

"Innovation" is a regular column that features discussions about recent advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering at the University of New Brunswick, who welcomes your comments and topic ideas. To contact him, see the "Contributing Editors" section.

GNSS signals are all spread by pseudorandom sequences, often called pseudorandom noise (PRN). Each GPS satellite, for example, is known by its PRN number, which identifies the particular code, which that satellite is using to spread its data (the navigation message). The reason these codes are called pseudorandom (and not random) is that the chip sequences "look" random for the length of the code, but then they repeat. For the GPS C/A code, the code period is 1 millisecond. For most modernized signals, that period has been increased. Where the period hasn't been increased (for example, for the GPS L5 signal), the number of chips in each code period has been increased.

A GPS receiver estimates the range to a particular satellite by correlating the received signal with a replica of the satellite's PRN code. This procedure, which is carried out in the receiver's baseband processor, can be described in an equation as:

where s(t) is the received signal, c(t) is a replica or local version of the PRN code generated within the receiver, τ is a delay applied to that code, and T is the integration period (the time spent observing the signal). In plain English, a delayed version of the local code is multiplied by the incoming signal and integrated. This integration is usually carried out by a simple accumulator; that is, successive signal samples are added to each other for the integration period, which is often 1 millisecond, the code repetition period.

Where higher accuracy or sensitivity is required, the integration period is extended beyond 1 millisecond. This article examines a way of performing that longer integration that adds up samples that are 1 millisecond apart, prior to adding up consecutive samples. This method has been called comb filtering because the frequency response of such an action looks like the teeth of a hair comb. I will just overview the basic concepts in this article. For a more technical discussion, see the paper "Use of Comb Filters in GPS L1 Receivers" listed in Further Reading.