Improving the filter performance with EGNOS

In this section, it is presented a new strategy that allows improving the estimation filter accuracy through the modification in real-time of the Kalman matrices using the integrity parameters calculated through the EGNOS’ integrity signals.

The accuracy and behavior of a Kalman filter rely on the values placed in the different covariance matrices. These values have to be found through a process that leads to an optimal result, and this is called tuning. The behavior of the filter as a result of the adjustment of the 𝑸_𝑖𝑛𝑖 and 𝑹_𝑖𝑛𝑖 matrices is the following:

 The system noise or state covariance matrix Q provides the statistical description of the error model. A large value in Q indicates increased

parameter uncertainty and implies noisy estimations. During the prediction, if the uncertainty in the IMU data grows, the GNSS+EGNOS position estimation will correct the INS at a higher level. In other words, a large value in Q will cause the INS to closely follow the GPS position estimations. This, in turn, can lead to an inaccurate navigation solution, if the GPS estimations are noisy.

 How well the measurement noise is modeled is determined by the measurement noise covariance matrix R. Imperfect modeling of the noise of the measurement observables leads to a bad estimation quality. Choosing a large value for R reflects inaccurate and noisy measurements and might not correct the INS sufficiently. Otherwise, a small value implies an accurate measurement and it will cause the system to rely more on the measured data than on the model.

The uncertainty in the covariance parameters of Q and R has a significant impact on the performance of the Extended Kalman Filter (Salychev, 2004). These matrices directly influence the weight that the filter applies between the existing process information and the latest measurements. Errors in any of them may result in the filter being suboptimal or even cause it to diverge. In practice, the Q and R values are generally fixed and applied during the whole operation of the vehicle. Due to the process noise and measurement errors are dependent on the application environment and process dynamics, settings of the stochastic parameters have to be conservative in order to stabilize the filter for the worst-case scenario, which leads to performance degradation.

Here, the innovation of the system developed in this thesis is based on the utilization of the vertical and horizontal protection levels calculated from the EGNOS integrity messages for weighting the Q and R parameters. These levels can provide information to the fusion algorithm and be used for tunning their matrix gains. In this way, these protection levels perform a real-time adaptation of the matrices and, in this way, to change the behavior of the filter depending on the quality and accuracy information that EGNOS provides concerning the GPS satellites.

For using this new procedure in the estimation algorithm, the first step consists of performing the tuning of the 𝑹𝑖𝑛𝑖 and 𝑸𝑖𝑛𝑖 matrices in the usual way. These

Once these preliminary matrices have been chosen, it is possible to start using the EGNOS integrity information by weighting the values of 𝑹𝑖𝑛𝑖 and 𝑸𝑖𝑛𝑖. In this way,

we obtain two new matrices (𝑹𝐸𝑔𝑛𝑜𝑠 and 𝑸𝐸𝑔𝑛𝑜𝑠) which depend on the protection

and the alarm levels.

𝑹 = 𝑹𝑖𝑛𝑖 ∗ 𝑹𝐸𝑔𝑛𝑜𝑠 (4-84)

𝑸 = 𝑸𝑖𝑛𝑖 ∗ 𝑸𝐸𝑔𝑛𝑜𝑠 (4-85)

Where the new matrices have the following form:

𝑹𝐸𝑔𝑛𝑜𝑠= ( 𝐻𝑃𝐿 𝐻𝑈𝐿∗ 𝑟𝑥𝑦 0 0 0 0 0 0 0 𝐻𝑃𝐿 𝐻𝑈𝐿∗ 𝑟𝑥𝑦 0 0 0 0 0 0 0 𝑉𝑃𝐿 𝑉𝑈𝐿∗ 𝑟𝑧 0 0 0 0 0 0 0 𝐻𝑃𝐿 𝐻𝑈𝐿∗ 𝑟𝑥𝑦𝑣 0 0 0 0 0 0 0 𝐻𝑃𝐿 𝐻𝑈𝐿∗ 𝑟𝑥𝑦𝑣 0 0 0 0 0 0 0 𝑉𝑃𝐿 𝑉𝑈𝐿∗ 𝑟𝑧𝑣 0 0 0 0 0 0 0 1) (4-86) 𝑸𝐸𝑔𝑛𝑜𝑠= ( 𝐻𝑈𝐿 𝐻𝑃𝐿∗ 𝑞ℎ 0 0 0 0 0 0 𝐻𝑈𝐿 𝐻𝑃𝐿∗ 𝑞ℎ 0 0 0 0 0 0 𝑉𝑈𝐿 𝑉𝑃𝐿∗ 𝑞𝑎 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1) (4-87) Where:

 HUL is the Horizontal User Level, it is a constant that the user imposes to the filter.

 HPL is the Horizontal Protection Level

 VUL is the Vertical User Level,it is a constant that the user imposes to the filter

 VPL is the Vertical Protection Level.

 rxy, rz, rxyv, rzv, qh and qa allows to give more or less importance to the integrity parameters. These parameters are imposed by the designer and must fulfill the following conditions:

∀𝜏𝑖> 0 𝑟𝑥𝑦, 𝑟𝑧, 𝑟𝑥𝑦𝑣, 𝑟𝑧𝑣 = { 1 𝜏1𝑖𝑓 𝐻𝑃𝐿 𝐻𝑈𝐿≤ 1 𝜏2 𝑖𝑓 𝐻𝑃𝐿 𝐻𝑈𝐿> 1 (4-88) ∀𝜏𝑖> 0 𝑞ℎ, 𝑞𝑎 = { 1 𝜏3𝑖𝑓 𝐻𝑃𝐿 𝐻𝑈𝐿> 1 𝜏4 𝑖𝑓 𝐻𝑃𝐿 𝐻𝑈𝐿≤ 1 (4-89)

Depending on these matrices, the behavior of the filter is the following:

 If the signals of the GPS and EGNOS satellites are available and are offering a good accuracy (protection levels are lower than the xUL field), then the weights of the elements of the matrix 𝑹𝐸𝑔𝑛𝑜𝑠 are smaller and the

elements of the matrix 𝑸𝐸𝑔𝑛𝑜𝑠 become bigger. In this case, the filter relies

more in the measurement model than in the system model, so the outputs are corrected following the GPS+EGNOS measurements.

 If the protection levels are higher than the alarm xUL field, then the weights of the variances of the matrix 𝑹𝐸𝑔𝑛𝑜𝑠 are increased because the

confidence on the GPS+EGNOS signal decreases. In this situation, the values of 𝑸𝐸𝑔𝑛𝑜𝑠 become smaller, the inertial sensors gain importance in

the estimation and the measurement model corrects the outputs of the filter in a softer way.

 If the receiver is not receiving the EGNOS signals, then the matrix 𝑹𝐸𝑔𝑛𝑜𝑠

and the matrix 𝑸𝐸𝑔𝑛𝑜𝑠 remain constants with the weights calculated in the

Figure 4-7 shows a summary of the real-time tuning process.

Figure 4-7: New Tuning procedure using the EGNOS protection levels.

4.6. Conclusions

In this chapter, it has been presented the EIRE navigator system. This navigator is used for the take-off and waypoint navigation phases of the autonomous mission. Here, two fusion integrations strategies are presented: The Tighly Coupled and the Loosely Coupled schemes. From the characteristics of both of them, it is concluded that the Loosely Coupled scheme is the most appropriate architecture for the navigator developed in this thesis. This is due to the LC processing time is faster than the obtained with the TC architecture, and also, due to the implementation of the LC architecture is more straightforward than the TC one, making possible to

add more sensors to the fusion filter in a faster way.

Through this chapter, it is also derived the navigation and mechanization equations of the Inertial Navigation System. This derivation is done because the EKF that is running in the EIRE navigation algorithm has been built by perturbing the kinematics equations. In this filter it was decided to add the bias in the state vector by modeling this error as a Gaussian Markov process. Although the turn-on bias could be added also to this filter, it is concluded that this error can be removed from the navigational solution with an initial calibration stage and, in this way, the filter is reduced by 6 dimensions.

Finally, this chapter presents a new strategy that improves the performance of the fusion filter in real-time by using the protection level information provided by the EGNOS sensor.

69