Real Time Kinematic GPS in an Urban Canyon Environment




Signal to Noise Ratio (SNR)
The power of a GPS signal is the basic measure of its quality. The power levels of GPS signals are usually specified in terms of decibels with respect to 1 watt of power (dBw). The minimum received power levels of the GPS signals for the users on Earth are {160 dBw and {166 dBw for L1 and L2, respectively (NAVSTAR GPS, 1995). The most common signal quality measures that can be used for weighting are the signal-to-noise ratio (SNR) and the carrier-to-noise power density ratio (C/N0).

The SNR is the ratio of the amplitude of the desired signal to the amplitude of noise signals at a given point in time. The SNR is generally used as a measure of the noise level that can contaminate a GPS observation. This value can be compared with the power of a GPS signal. The ratio of the power of a received signal, S, and the noise power, Ns, can be considered a measure of strength.

A high SNR value is highly desirable. The C/N0 in GPS receivers is the ratio of the power level of the signal carrier to that of the noise in a 1 Hz bandwidth. Nominal GPS receiver C/N0 values often are in the 30 to 60-dB-Hz range. The C/N0 describes the ratio of the power level of the signal carrier to the noise level in an influence on the C/N0 value. It is a key parameter in analyzing GPS receiver performance and directly affects the precision of the receiver's pseudorange and carrier phase observations.

Quality Control
In handling various alternative hypothesis, the Detection, Identification and Adaptation (DIA) method as described by (Teunissen, 1998) was implemented in the software used in processing the observed data. The DIA-procedure consists of the followings steps (de Jong, 1998):
  • Detection: In the detection step, a global overall model test is performed on the whole observation set at a given epoch in other to check weather unspecified model errors have occurred.
  • Identification: After detecting of model errors, identification of the potential source of these errors is required. After identification, the detected bias is compared with the Minimal Detectable Biases (MDB) value that is a threshold value used to identify biases. If the bias candidate’s value is less than the MDB value, the observation is accepted.
  • Adaptation: After identification of the alternative hypothesis, adaptation of the recursive filter is needed to eliminate the presence of biases in the state estimation.
How well observations are controlled is a function of the redundancy in the observations. Redundancy numbers could be defined as elements of the principal diagonal of matrix . The redundancy of the ith observation can be expressed as


where the subscripts indicates the ith diagonal element of the matrix and is the covariance of the residual. The trace of Rd is the observation redundancy , since Rd is idempotent (unchanged in value following multiplication by itself) and the trace of an idempotent matrix equals its rank (Leick, 1995). Each diagonal element of Rd corresponds to that observation’s contribution to the overall redundancy. Assuming that the observation is uncorrelated (that is the observation covariance matrix is diagonal), the diagonal elements is


(24) The MDB is the smallest error on a particular observation which the model or system will be able to detect. The MDB for the ith observation can be expressed as (Lachapelle and Ryan, 2000)



Experiments
The elevation angle information is often used in the construction of the stochastic model. The reason for using the satellite elevation angle is because each satellite has a different precision and it is known that low elevation angle satellite tends to be noisier than the higher elevation angle satellite.

Figure 1: Shows elevation angles, C/N0 and number of satellites tracked during the experimental period. During the observation period, some satellites dropped out of view while some were reacquired shortly after an example of this is PRN 2 and PRN 15. The increase in C/N0 variations for descending and rising satellites illustrates the increase multipath on these signals at lower elevation angles.




Figure 1: Depicts Elevation angles, C/N0 and the number of satellites tracked during the observation period. Some satellites orbited out of view while new ones were tracked. The minimum number of satellites tracked was four, and the maximum tracked was 10.

During the observation period PRN 17 and PRN 30 orbited out of view, while there was constant loss of lock with PRN 15 during this period. Figure 2 depicts the multipath error of the satellites tracked on L1.


Figure2 shows the multipath error on L1 for all the tracked satellites, from the plot it could be seen that there were loss of lock in some of the satellites during the observation period. The most affected PRN is 15 which happened frequently.

Figure 3, shows the estimation of the multipath parameters with the implementation of an extended Kalman filter, the initial results were not too bad. In the EKF process, each new estimate is re-linearised as it becomes available, hence the filter worked well as it is near their true values.


Figure 3: Double difference multipath error on L1 (left) and L2 (right). The filtered multipath errors are in dotted lines. Only a portion of the observation is shown here. The filtered value did not deviate too much from their true values.

Figure 4 shows the north, east and the height position errors over time, The GPS error becomes noisy and it is expected that the error should drop with increasing satellite number, however the overall results show an improved position coordinates.


Figure 4: Positioning error showing the north (red), east (blue) and height (green) components. The data recording for this test was at the rate of 1 sample every 10seconds. The height components showed some strange characteristics, this is due to the measurement noise. The fact that multipath of such magnitude might be present in the carrier phase measurements limits the accuracy of the positioning. More so, it is known that multipath shows periodic behaviour, the periods can be in the order of minutes and also depends on the reflecting object.

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