GNSS Attitude Determination for Remote Sensing: On the Bounding of the Multivariate Ambiguity Objective Function

Global Navigation Satellite Systems (GNSS)-based attitude determination is a viable alternative for traditional methods such as gyroscopes. Precise attitude determination using multiple GNSS antennas mounted on a remote sensing platform relies on successful resolution of the integer carrier phase ambiguities. The Multivariate Constrained (MC-) LAMBDA method has been developed for the multivariate quadratically constrained GNSS attitude model that incorporates the known antenna geometry. In this contribution, it is demonstrated that the currently used easy-to-compute MC-LAMBDA bounding functions are relatively loose bounds that may result in too large integer search times. To mitigate this problem, we develop alternative bounding functions and compare their performance using simulated as well as real data. As a result we are able to identify tighter bounding functions that improve the search algorithms for instantaneous GNSS attitude determination.