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Technical report | Development of GPS Receiver Kalman Filter Algorithms for Stationary, Low-Dynamics, and High-Dynamics Applications


This report presents algorithms that can be utilized in a GPS receiver to convert satellite-to-receiver pseudo-ranges to receiver position estimates. The report discusses a method that is used to determine instantaneous estimates of receiver position and then goes on to develop three Kalman filter based estimators, which use stationary receiver, low dynamics, and high dynamics models for the receiver motion, respectively. These particular dynamic models are utilized because they are commonly used in actual GPS receivers, and cover a wide range of applications. While the standard form of the Kalman filter, of which the three filters just mentioned are examples, is theoretically correct, it can be susceptible to numerical round-o_ errors, which can in some cases result in poor performance or, in the worst case, filter divergence. This issue, and its solution, is investigated, and another version of the high dynamics filter, which addresses this problem, is presented. Matlab code was developed to test the performance of each of the filters and simulations were performed. The results of the simulations are also presented.  

Executive Summary

The Global Positioning system (GPS) is the primary source of information for a broad range of positioning, navigation and timing systems. It is an all-weather, satellite-based radio-navigation system which provides world-wide coverage. The objective of this report is to present algorithms used in a central component of the system's receiver position calculation, viz., to convert the satellite-to-receiver pseudo-ranges to receiver position estimates. This report is one outcome of recent efforts to expand our knowledge base for this important component of GPS receiver technology; this increased knowledge will facilitate our capabilities to provide scientifically based advice to the Australian Defence Force.

The report first describes a method for determining instantaneous estimates of receiver position, and then goes on to develop three Kalman filter based receiver position estimators, i.e., a stationary receiver, low dynamics, and high dynamics estimator. As is implied by their names, the three types of filters incorporate dynamic models that are optimized for situations where the receiver is stationary, is subjected to small accelerations, and to large accelerations, respectively. These estimators are designed to optimize performance for commonly occurring applications, as is done in many GPS receivers.

The development of the three types of Kalman filter, as well as the instantaneous estimator is presented in Section 2. Section 3 then presents the results of testing by simulation. It is found that the simulations give indications of performance degradation, resulting from errors associated with numerical round-off, in the case of the high dynamics Kalman filter. This is then further investigated in Section 4 and an alternate form of the high dynamics filter is then developed to overcome the problem. The filter was implemented in Matlab and tested by simulation. The results of the simulations are also in Section 4. Finally, concluding remarks are presented in Section 5.

While this report deals specifically with GPS algorithms, the work covered forms part of a larger effort to develop algorithms for fusing GPS measurements with other sensor data, particularly measurements from inertial navigation systems (INS), to support R&D into multisensor positioning and navigation performance in non-benign environments. The algorithms presented in this report, and software developed for this work, will be required for future research into deep integration of GPS with other sources of position data. The software will also be useful as a component of future modelling software that may need to be developed for performance prediction of current or future systems that incorporate GPS. The ultimate aim is to help inform future capability requirements through the outcomes of this research.

Key information


Peter W. Sarunic

Publication number


Publication type

Technical report

Publish Date

June 2016


Unclassified - public release


Kalman lters, GPS, GNSS, Global Positioning System