# Improving Real-Time Position Estimation Using Correlated Noise Models +
## 6 Discussion and Future Work  
We developed algorithms for the sequential inference of the location of a GPS receiver, taking into account the correlated nature of the GPS noise. We found that the DOP parameters do not help in uncertainty quantification of the GPS positioning. This noise, which may be attributable to atmospheric and multipath effects, as well as the satellite configuration, is found to be correlated in time and can be modelled as an OU process. The AUKF algorithm using an OU noise model provides an accurate series of posterior distributions for GPS position with improved uncertainty quantification compared to inference assuming iid Gaussian noise provided a large enough value is assumed for the OU noise variance. The improved posterior distributions offer many practical advantages in applications in which knowledge of the correct uncertainty is important, e.g., automated navigation, where one must be very confident of avoiding obstacles. The algorithm is also easily extendible to incorporate data from additional sensors, e.g., accelerometers and gyroscopes to inform the inference (so-called sensor fusion). We expect that using a correlated model for the GPS noise in a sensor fusion application will extend its potential to improve accuracy, as a well-quantified position uncertainty will allow position corrections from other sensors to be accepted.  
There are clear avenues for further improvement of the techniques in this paper. An algorithm similar to Algorithm 1 may be used to simultaneously estimate the OU variance \(\sigma^{2}\) during the inference process, by including \(\sigma^{2}\) as a state parameter. However, such an algorithm requires a different choice of sigma points from that in Algorithm 1. Additional sigma point should be added to the scheme with mixed components from \(\sigma^{2}\) and the process noise, such that the mean and co-variance of the sigma points does not change. Furthermore, since we have earlier showed that more sophisticated noise models, e.g., the higher order AR processes and ARMA processes could be superior to the OU model, we expect that upgrading the noise models will lead to further improved position inference. The AUKF algorithm presented could be straightforwardly upgraded to use the higher order AR processes, taking care to parametrise the model such that it represents a stationary process. The forward map of an ARMA process also includes multiplicative noise, so to use such a forward map, similar care must be taken with the choice of sigma points.  
We mention an extension of our current work to engineering applications. The effect of time-correlated noise on the applicability of classical Kalman filters has been previously analysed to a certain degree [42]. The noise models proposed here, however, can be seamlessly incorporated into a Kalman filter or Bayesian inference algorithm providing both an estimate for the location and the associated uncertainty quantified. Although such extensions require extra numerical calculation, the computational load is acceptable and provides seamless integration for sensor fusion, treating all sensors on equal footing. Incorporating the aforementioned noise models into such algorithms is in preparation.  
Finally, although for the sake of transparency and simplicity, we modelled latitude, longitude and altitude separately as one-dimensional time-series, a more natural approach could be to combine them into one vector quantity. Building an inference algorithm similar to that in Section 3.2 would lead to a compact model that calculates and takes into account the covariances between these coordinates. This could further improve the algorithm performance.  
Figure 9: Estimates of the OU rate parameter \(\theta\) for the (a) latitude, (b) longitude and (c) altitude time-series of a stationary receiver at Port Douglas.