In this paper, the data wipe-off (DWO) algorithm is incorporated into the vector tracking loop of the Global Positioning System (GPS) receiver for improving signal tracking performance. The navigation data, which contains information that is necessary to perform navigation computations, are binary phase-shift keying (BPSK) modulated onto the GPS carrier phase with the bit duration of 20 ms (

The Global Positioning System (GPS) [

As the most vulnerable parts of a receiver, the carrier and code tracking loops play a key role in a GPS receiver. Traditional GPS receivers utilize the scalar tracking loop (STL) to track signals from different satellites independently. The STL consists of correlator, discriminator, loop filter, and numerically control oscillator (NCO) in each channel. The intermediate frequency (IF) signal is correlated with internally generated replica signal, and the output of correlator consists of in-phase (I) and quadrature-phase (Q) components

The vector tracking loop (VTL) [

The data wipe off (DWO), also referred to as the data bit wipe-off, or data wiping approach [

This paper presents the vector tracking loop performance improvement of a GPS receiver using the data wipe-off techniques. The paper is organized as follows. In Section 2, preliminary background on the signal processing for the GPS receiver tracking loop is reviewed. The data wipe-off approach is introduced in Section 3. In Section 4, the navigation filter processing is introduced. In Section 5, simulation experiments are carried out to evaluate the performance and effectiveness. Conclusions are given in Section 6.

A typical functional diagram of the GPS receiver signal processing is shown as in

GPS receivers utilize an omni-directional antenna to receive the GPS signals. These are passed through a band-pass filter and low noise amplifier before being down-converted to an intermediate frequency (IF) by a mixer. Many GPS receivers use two down-conversions to reach baseband, where the analog signal is sampled and converted into digital in-phase and quadrature-phase channels by multiplication by sine and cosine versions of the local oscillator (mixing) frequency. Some receivers sample at an intermediate frequency, before down-converting to baseband. The down-conversion from RF to IF is achieved by mixing the RF signal with a local oscillator (LO),

The signal at IF plus the noise at IF, and the upper band can be represented as

which, after low pass filtering, yields

The in-phase (I) component is realized by mixing ^{o} phase-shifted with respect to one another. Due to the fact that

with the noises in the in-phase and quadrature-phase components, respectively, given by

Signals sampled using analog-to-digital conversion, the in-phase and quadrature-phase components, respectively, at time,

with the corresponding noises

The Doppler shift can be removed from the signal

which can be multiplied with the digital reference C/A code at time

The expected value of the accumulated correlated in-phase signal component is shown to be

where

An approximation of the accumulated in-phase signal component can be shown to be

The integral in the above equation can be approximated and simplified as follow

and the accumulated in-phase signal component

Assuming the noise

with variance

Since the Fourier transform of the two-sided bandwidth Gaussian white noise is

with the variance given by

In order to normalize the noise variance, the in-phase component is multiplied by the factor

Since

Similarly, the ith accumulated quadrature-phase component at time

The signal energy for a given pair of accumulated I and Q is computed as

Correlation integration intervals generally do not exceed the duration of a navigation data bit (20 ms) for those cases where the receiver operates in open sky conditions. If the integration interval is extended longer than the period of data bit, the loss of the correlation values will occur due to the data bit transmission. A DWO algorithm is commonly employed for performance improvement on the basis of pre-detection method to detect data bit sign reversal every 20 ms.

Employed to extend the integration interval of the correlator, there are two commonly used DWO algorithms: (1) an energy-based bit estimation algorithm; (2) a carrier phase discriminator based algorithm, to remove the data bit in I and Q correlation values. The DWO method in this paper utilizes the energy-based bit estimation algorithm, shown as in

For illustration purpose, we assume that the correlator integration interval is 100 ms, which is five times of data bit transition. The initial point of navigation data bit is known due to acquisition process. We start tracking from this point. For the example of 100 ms interval, there are five 20 ms accumulated I values and five 20 ms accumulated Q values. The signal energy for a given pair of accumulated I and Q is computed as

Each row of

where

A sign combination and a sequence of bit combinations that maximize the signal energy over tracking integration interval are chosen:

The discriminator input signals are as follow:

As an example, the energy of possible sequential combinations is provided in

The GPS VTL differs from the traditional STL in that the task of navigation solutions, code tracking and carrier tracking loops for all satellites are combined into one loop. The central part of a VTL is an estimator, which is usually a Kalman filter to provide an estimation of signal parameters for all satellites in view and user PVT solutions based on both current and previous measurements from all satellites. The discriminator outputs of each channel are passed to the navigation filter. The DWO method using carrier phase discriminator is incorporated into the GPS VTL to remove the navigation data bit in I and Q correlation values.

The nonlinear filters deal with the case governed by the nonlinear stochastic difference equations:

where the state vector

where

When selecting EKF as the navigation state estimator in the GPS receiver, using

Information for the receiver dynamic includes the pseudorange, range-rate and Doppler frequency, discussed as follows. Mathematical model for the pseudorange observable is given by

and the satellite-to-antenna range rate is given by

where

The code phase error (in chip) can be written as

and the Doppler frequency error (in Hz) can be found as

where

where

and

In the above equation,

The normalized amplitude of the GPS signal amplitude

where

where the notations

and

respectively.

If the measurement equation for the navigation filter is composed of pseudorange and range-rate observables,

where (

Several tests have been carried out for confirmation of the effectiveness and justification of the performance. Simulation was conducted using a personal computer. The computer codes were developed by the authors using the Matlab® software. The commercial softwares Satellite Navigation Toolbox (SatNav) [

The following discussion presents performance comparison for the design with DWO algorithm involved when various integration intervals are involved.

PRN Number | 3 | 4 | 6 | 7 | 9 | 16 | 18 | 19 | 21 |
---|---|---|---|---|---|---|---|---|---|

C/No (dB-Hz) | 25 | 28 | 31 | 34 | 37 | 40 | 41 | 44 | 47 |

To overcome the problem of loss of lock when the signal is weak, the DWO approach is applied to mitigate the influence of navigation data on I and Q. Increase of the integration interval can effectively increase the energy in the

As an example on the weak signal environment, the performance for PRN 3 is illustrated.

Integration interval (ms) | East (m) | North (m) | Altitude (m) |
---|---|---|---|

20 | 1.7374 | 1.6262 | 2.3437 |

60 | 1.3012 | 0.8357 | 1.5551 |

100 | 1.1083 | 0.7264 | 1.2157 |

This paper employs the data wipe-off algorithm for the GPS receiver to improve the tracking and navigation accuracy. Conventional GPS receivers use scalar tracking loop and satellite signals from each channel are processed independently. On the vector tracking loop, signals in these channels can be shared with each other for improved tracking performance under the low-quality signal environment. The accumulated energy might be decreased by the possible data bit sign reversal every 20 ms to the integration interval. To resolve the problem, a data wipe off algorithm is presented on the basis of pre-detection method to detect data bit sign reversal every 20 ms. The data wipe-off method based on the energy-based bit estimation algorithm is employed to avoid energy loss due to bit transitions. The integration interval of the correlator can be extended over 20 ms in low C/No levels.

Examples have been presented for illustration. The method presented in this paper has an advantage to continuously estimate the navigation data bit and achieves improved tracking performance. Tracking accuracy of a weak GPS signal is increased by extending the coherent integration interval. In the weak signal environment, it is especially useful by extending integration interval. The coherent integration interval has been extended over 20 ms. Position errors based on various integration intervals, including 20, 60 and 100 ms, are presented. The results show that the tracking accuracy increases when longer integration interval is utilized. The simulation results show that the vector tracking loop with data wipe-off module enables improved tracking and navigation accuracy and demonstrates good potential in dealing with degraded signals.