A system for determining a heading angle of a vehicle or an implement connected to the vehicle, the system comprising: a first antenna associated with the vehicle, the first antenna configured to receive first signals comprising global positioning system data; a second antenna associated with the vehicle, the second antenna configured to receive second signals comprising global positioning system data; a receiver front-end for receiving the first and second signals; a real-time kinematic search engine with an electronic data processor capable of receiving the global position data from the receiver front-end, the electronic data processor configured or programmed to: measure carrier phases of carriers associated with the first signals and second signals; determine ambiguity solution sets for the measured carrier phases using a known baseline length between the first antenna and the second antenna to satisfy constant length and attitude constraints in a search process within the real-time kinematic search engine by applying an ambiguity search process; apply an error-reduction filter to the measured carrier phrases in ambiguity solution sets associated with the first and second signals using the known baseline length between the first antenna and second antenna as a virtual measurement in the filter, where a weight of the virtual measurement in the error-reduction filter is proportional to a position variance; estimate locations of the first and second antennas (12, 14) using the filtered carrier phases and filtered ambiguity solution sets of the first and second signals; and determine the heading angle of the vehicle or its implement based on the estimated locations of the first antenna and the second antenna. a first antenna associated with the vehicle, the first antenna configured to receive first signals comprising global positioning system data; a second antenna associated with the vehicle, the second antenna configured to receive second signals comprising global positioning system data; a receiver front-end for receiving the first and second signals; a real-time kinematic search engine with an electronic data processor capable of receiving the global position data from the receiver front-end, the electronic data processor configured or programmed to: measure carrier phases of carriers associated with the first signals and second signals; determine ambiguity solution sets for the measured carrier phases using a known baseline length between the first antenna and the second antenna to satisfy constant length and attitude constraints in a search process within the real-time kinematic search engine by applying an ambiguity search process; apply an error-reduction filter to the measured carrier phrases in ambiguity solution sets associated with the first and second signals using the known baseline length between the first antenna and second antenna as a virtual measurement in the filter, where a weight of the virtual measurement in the error-reduction filter is proportional to a position variance; estimate locations of the first and second antennas (12, 14) using the filtered carrier phases and filtered ambiguity solution sets of the first and second signals; and determine the heading angle of the vehicle or its implement based on the estimated locations of the first antenna and the second antenna. measure carrier phases of carriers associated with the first signals and second signals; determine ambiguity solution sets for the measured carrier phases using a known baseline length between the first antenna and the second antenna to satisfy constant length and attitude constraints in a search process within the real-time kinematic search engine by applying an ambiguity search process; apply an error-reduction filter to the measured carrier phrases in ambiguity solution sets associated with the first and second signals using the known baseline length between the first antenna and second antenna as a virtual measurement in the filter, where a weight of the virtual measurement in the error-reduction filter is proportional to a position variance; estimate locations of the first and second antennas (12, 14) using the filtered carrier phases and filtered ambiguity solution sets of the first and second signals; and determine the heading angle of the vehicle or its implement based on the estimated locations of the first antenna and the second antenna.