Abstract: Systems and methods are provided for sequentially updating a Kalman filter in a navigation system. Respective signals from a plurality of transmitters containing range-finding data are received at a plurality of antennas. For each of the plurality of transmitters, a single differenced observable is calculated between a given pair of the plurality of antennas. A common bias, stored as a state in a Kalman filter, is subtracted from the calculated single differenced observable for each of the plurality of transmitters to provide respective double differenced residual values. A plurality of states stored in the Kalman filter are updated using the double differenced residual values.

Abstract: Systems and methods are provided for sequentially updating a Kalman filter in a navigation system. Respective signals from a plurality of transmitters containing range-finding data are received at a plurality of antennas. For each of the plurality of transmitters, a single differenced observable is calculated between a given pair of the plurality of antennas. A common bias, stored as a state in a Kalman filter, is subtracted from the calculated single differenced observable for each of the plurality of transmitters to provide respective double differenced residual values. A plurality of states stored in the Kalman filter are updated using the double differenced residual values.

Abstract: A force balanced instrument system and method for mitigating errors is provided. The system and method mitigate errors in measurement readings caused by charge buildup in force balanced instruments that employ charge pulses to generate an electrostatic force to null an inertial proof mass disposed between opposing electrodes. The system and method mitigate charge buildup by applying positive charge pulses alternately to each opposing electrode for a given charge cycle time period followed by negative charge pulses alternately to each opposing electrode for a second given charge cycle time period. The negative charge pulses remove any residual charge on the electrodes caused by the positive charge pulses. As a result the net residual charge left on the electrodes is reduced on the average.