Abstract: The present invention relates to an absolute target system intended to be incorporated in observation satellites. To establish an absolute target system provided with maximum accuracy, the present invention proposes coupling a star sensor (4) to an optical metrological system (5N, 5R). Since these two items of equipment are normally already on board the satellites, in particular for formation flight missions, this solution adds no extra weight or cost.

Abstract: A method of and apparatus for determining and controlling the inertial attitude of a spinning artificial satellite without using a suite of inertial gyroscopes. The method and apparatus operate by tracking three astronomical objects near the Earth's ecliptic pole and the satellite's and/or star tracker's spin axis and processing the track information.

Abstract: A control system of a spacecraft for controlling two or more sets of collinear control moment gyroscopes (CMGs) comprises an attitude control system. The attitude control system is configured to receive a command to adjust an orientation of the spacecraft, determine an offset for a momentum disk for each of the two or more sets of CMGs that maximizes torque, determine a momentum needed from the two or more sets of CMGs to adjust the orientation of the spacecraft, and calculate a total torque needed by taking the derivative of the momentum. The control system further comprises a momentum actuator control processor coupled to the attitude control system, the momentum actuator control processor configured to calculate a required gimbal movement for each of the CMGs in each of the two or more sets of collinear CMGs from total torque.

Abstract: A method for spacecraft power acquisition is provided using single-axis slit sun sensors for both wing-stowed and wing-deployed spacecraft configurations. The method for wing-deployed spacecraft includes initializing a solar wing of the spacecraft to search for sun; rotating the spacecraft about a search axis substantially parallel to a slit sun sensor field of view; monitoring the slit sun sensor for a time of arrival signal; and wherein, if the time of arrival signal occurs, the spacecraft is rotated along the search axis to an orientation where the time of arrival signal occurred and the spacecraft is placed in stable rotation about an axis substantially parallel to a solar wing longitudinal axis; and for a non-occurrence of the time of arrival signal, the spacecraft is slewed about a keyhole axis substantially perpendicular to the search axis to move the sun away from a keyhole.

Abstract: A method of controlling attitude of a spacecraft during a transfer orbit operation is provided. The method includes providing a slow spin rate, determining the attitude of the spacecraft using a unified sensor set, and controlling the attitude of the spacecraft using a unified control law. The use of a unified set of sensors and a unified control law reduces spacecraft complexity, cost, and weight.

Abstract: Methods and apparatus for assigning weighting coefficients to measurements of a succession of stars acquired by a star sensor connected to a client device in order to determine a spatial orientation, characterized in that higher or lower preference is given to refreshment of the positions of measurements with the highest weights and/or stars on which these measurements are made by the star sensor and/or its client device, so as to displace part of the power of the error associated with the set of star measurements within the frequency spectrum.

Abstract: A method of controlling attitude of a spacecraft during a transfer orbit operation is provided. The method includes providing a slow spin rate, determining the attitude of the spacecraft using a unified sensor set, and controlling the attitude of the spacecraft using a unified control law. The use of a unified set of sensors and a unified control law reduces spacecraft complexity, cost, and weight.

Abstract: A method of and apparatus for determining and controlling the inertial attitude of a spinning artificial satellite without using a suite of inertial gyroscopes. The method and apparatus operate by tracking three astronomical objects near the Earth's ecliptic pole and the satellite's and/or star tracker's spin axis and processing the track information.

Abstract: One or more fixed-orientation fanned laser beams and one or more displacement measurement devices to precisely measure the orientation of a payload platform are disclosed in a metrology system and method. The measurement devices may be distributed at locations across a payload platform such that displacement changes of these devices can be used to accurately determine platform pointing. Laser beam transmitters may be fixed in the same reference block to which a spacecraft attitude sensor is mounted. Fanned laser beams are transmitted from these sources to the measurement devices so that their displacements can be determined with respect to the plane of the fanned beams and thereby with respect to the spacecraft attitude sensor. Only a small number of fixed laser beams are needed to achieve precision measurements at a reduced cost, weight and power, and with increased system reliability and simplified system integration.

Abstract: A control moment gyroscope system for delivering a target torque to a spacecraft including a rotor assembly having a rotor and a motor to spin the rotor about a rotor axis. A gimbal assembly has a gimbal for supporting the rotor assembly and a gimbal torque motor to rotate the gimbal about a gimbal axis, which is normal to the rotor axis, to generate an output torque. A control system has a sensor for determining the output torque and a processor in communication with the rotor assembly, the gimbal assembly and the sensor. The processor requests the target torque and establishes a feedback control loop to generate a torque error signal based on the output torque for bringing the output torque within a predetermined range of the target torque.

Abstract: A system for providing precision thrust and sun tracking attitude control is provided. The system determines a proximity region and alternately engages either an ideal operational mode or a predictive operational mode based on whether a thrust trajectory vector is in the proximity region in order to provide attitude control. The proximity region is determined based on an angle between the thrust trajectory vector and a sun vector. For example, the angle is about 20-30 degrees. The system engages the predictive operational mode when the thrust trajectory vector enters the proximity region. When in the predictive operational mode, the system periodically re-calculates the thrust trajectory vector and determines where the thrust trajectory vector will exit the proximity region.

Abstract: A method and apparatus for controlling a gimbaled platform (108). The method comprises the steps of computing an acquisition phase gimbal angle rate command ?cmd—Acq (530) from a measured LOS angle error ??LOS (520) for an initial control period T while computing an estimated LOS angle rate {circumflex over (?)}LOS (524), computing a tracking phase gimbal angle rate command ?cmd—Trk (532) using a controller (512) having an output initialized with the estimated LOS angle rate {circumflex over (?)}LOS (524), and commanding the gimballed platform (108) according to an angle rate command ?cmd (522), wherein the angle rate command ?cmd (522) is the acquisition phase angle rate command ?cmd—Acq (530) during the initial control period T and the tracking phase gimbal angle rate command ?cmd—Trk (532) after the initial control period T.

Abstract: A method of determining the attitude of a spinning spacecraft is provided. The method includes stabilizing the spacecraft, initializing the attitude of the spacecraft using star tracker data, and estimating the attitude of the spacecraft.

Abstract: A method and system for degimbalization of sensor outputs is provided. Data output from an embedded GPS inertial navigation system (EGI), which is mounted within a gimbaled system on a vehicle, is processed to provide degimballed navigation data. Generally, motion of the EGI is due to the vehicle motion and the gimbal motion. To provide navigation information relating solely to the vehicle, effects of the gimbal motion within the EGI outputs can be removed.

Abstract: A method for spacecraft power acquisition is provided using single-axis slit sun sensors for both wing-stowed and wing-deployed spacecraft configurations. The method for wing-deployed spacecraft includes initializing a solar wing of the spacecraft to search for sun; rotating the spacecraft about a search axis substantially parallel to a slit sun sensor field of view; monitoring the slit sun sensor for a time of arrival signal; and wherein, if the time of arrival signal occurs, the spacecraft is rotated along the search axis to an orientation where the time of arrival signal occurred and the spacecraft is placed in stable rotation about an axis substantially parallel to a solar wing longitudinal axis; and for a non-occurrence of the time of arrival signal, the spacecraft is slewed about a keyhole axis substantially perpendicular to the search axis to move the sun away from a keyhole.

Abstract: A method and apparatus for maneuvering a satellite in orbit to alternately optimize the collection of solar energy and to take sensor data of terrestrial objects is disclosed The longitudinal axis of a large payload package is oriented perpendicular to the orbital plane to minimize the disturbance torque due to gravity gradient, and to allow simple rotation about the axis for attitude change between optimal Sun and optimal ground coverage.

Abstract: An spacecraft control system is provided that includes a tube and a plurality of microwheels. The plurality of microwheels is disposed within the tube. Each microwheel has a first stator wafer, a second stator wafer, and a rotor wafer disposed therebetween. The first and second stator wafers are configured to spin the rotor wafer.

Abstract: A method for modeling a structure deployed on a spacecraft. The method includes determining a geometric shape that resembles the structure in a fully deployed configuration; generating time functions for a change in shape of at least one structural component of the structure, the change in shape occurring as the structure expands into the fully deployed configuration; and calculating mass properties of the geometric shape as a function of the time functions.

Abstract: A flight instrument and associated method where vertical speed information is combined with gyro information to produce gyro enhanced vertical speed information that is displayed to a pilot. The gyro information may include a pitch rate gyro and may include an azimuth rate gyro. The pitch rate gyro and azimuth rate gyro may be combined to yield a corrected pitch rate in turns. In one embodiment, the display is an airplane symbol that moves relative to a horizon line responsive to the gyro enhanced vertical speed information. The horizon line may also tilt in response to the azimuth rate gyro.

Abstract: A system and method for assisting a pilot to recover the aircraft from a variety of dangerous situations involving one or more of the following: altitude, airspeed, attitude, roll rate, and a partial equipment failure in the control panel. In accordance with the invention, these factors are sensed automatically, and voice instructions are provided to the pilot to direct him or her to get the aircraft out of the dangerous situation sensed by this system.

Abstract: A system and associated method for compensating for thermal deformation of a spaced-based structure having a spacecraft payload. The system including a beacon source coupled to a first spacecraft for transmitting a first signal and a beacon sensor coupled to a second spacecraft for receiving the first signal and providing measurement data derived from the first signal. At least one attitude sensing device is coupled to the second spacecraft for determining estimated spacecraft attitude data for the second spacecraft. A processor on the second spacecraft is configured to process ephemeris data of the first and second spacecraft, beacon measurement data, estimated spacecraft attitude data, and gimbal angular position data to estimate spacecraft structural deformation.

Abstract: An apparatus for estimating attitude using an inertia measuring apparatus comprising: a Kalman filter 3 adapted to receive a quantity of state ?(t) from the inertia measuring apparatus 1, input the quantity of state into a predetermined system equation and a predetermined observation equation and execute time update processing and observation update processing with regard to the system equation and the observation equation; a processing section 4 adapted to generate an estimated value of a time differentiation of a modified Rodrigues parameter ?(t) based upon an output of the Kalman filter; an integral processing section 5 adapted to generate an estimated value of the modified Rodrigues parameter based upon an output of the processing section; a system propagation matrix generating section 6 adapted to update an observation sensitivity matrix based upon an initial value being given beforehand and an output of the integral processing section and supply the updated output to the Kalman filter; a transformed mat

Abstract: The present method provides a method for avoiding singularities in the movement of CMGs in an array of CMGs in a spacecraft. In a first step, a torque command representing a desired torque to produce an attitude adjustment for the spacecraft is received. Next, a range-space gimbal rate required to produce the desired torque based on the desired torque and a Jacobian matrix is calculated. Then, a null-space gimbal rate that assists in the avoidance of singularities is calculated. The total gimbal rate command is determined by summing the range-space gimbal rate and the null-space gimbal rate. Then, the total gimbal rate command is provided to the CMGs to produce the total gimbal rate.

Abstract: An integrated inertial stellar attitude sensor for an aerospace vehicle includes a star camera system, a gyroscope system, a controller system for synchronously integrating an output of said star camera system and an output of said gyroscope system into a stream of data, and a flight computer responsive to said stream of data for determining from the star camera system output and the gyroscope system output the attitude of the aerospace vehicle.

Abstract: A method of calibrating a gyro (42) of a spacecraft (14) may include determining a yaw attitude residual of the spacecraft. Roll gyro bias residual is determined in response to the yaw attitude residual. The gyro (42) is calibrated in response to the roll gyro bias residual. A method of calibrating a gyro (42) of a spacecraft (14) may alternatively include disabling gyro calibration, gain scheduling, or resetting attitude and gyro bias covariance, for selective axes, for a yaw transient period. The gyro (42) is calibrated in a nominal fashion after completion of the yaw transient period.

Abstract: A virtual sensor mast for a ground vehicle and a method for operating a ground vehicle using a virtual sensor mast are disclosed. The virtual sensor mast includes an unmanned airborne vehicle capable of lifting itself from the ground vehicle upon deployment therefrom; a sensor suite mounted to the unmanned airborne vehicle; and a tether between the unmanned airborne vehicle and the ground vehicle over which the sensor suite is capable of communicating sensed data upon deployment. The method includes elevating a tethered unmanned airborne vehicle from the ground vehicle to a predetermined height; sensing environmental conditions surrounding the ground vehicle; and terminating the deployment.

Abstract: A method and apparatus for estimating spacecraft momentum is disclosed. The method comprises the steps of generating a plurality of spacecraft momentum measurements, fitting the plurality of spacecraft momentum measurements to a parametric model of a spacecraft momentum profile having a time period of tp, determining the momentum of the spacecraft from the parametric model; and generating an estimate of the momentum to be removed from the spacecraft at least in part from the determined momentum of the spacecraft.

Abstract: A system and associated method for compensating for thermal deformation of a spaced-based structure having a spacecraft payload. The system including a beacon source coupled to a first spacecraft for transmitting a first signal and a beacon sensor coupled to a second spacecraft for receiving the first signal and providing measurement data derived from the first signal. At least one attitude sensing device is coupled to the second spacecraft for determining estimated spacecraft attitude data for the second spacecraft. A processor on the second spacecraft is configured to process ephemeris data of the first and second spacecraft, beacon measurement data, estimated spacecraft attitude data, and gimbal angular position data to estimate spacecraft structural deformation.

Abstract: A method and apparatus for estimating a slave payload attitude is disclosed. The method includes accepting a plurality of slave payload attitude measurements, deriving a model of the relative attitude of the slave payload and a master payload attitude at least in part from the plurality of slave attitude measurements, predicting the relative attitude between the slave payload attitude and the master payload attitude using the derived model, and estimating the relative attitude between the slave payload attitude and the master payload attitude at least in part from the predicted relative attitude between the slave payload attitude and the master payload attitude. Furthermore, the absolute attitude of the slave payload is computed using the relative attitude and the master payload attitude.

Abstract: A sensor alignment system and method is provided that facilitates the precise alignment determination of satellite sensors. The system and method utilizes an Inertial Measurement Unit (IMU) to facilitate alignment determination of multiples sensors on a satellite. The system and method performs a roll of the satellite around a preliminary sensor active axis, using the IMU to measure the rotation rate in both magnitude and direction. The sensor input is monitored by the IMU during the roll around the preliminary sensor axis. The data from sensor output obtained during the roll can be processed to calculate the difference between the preliminary sensor axis and the actual sensor axis. From this calculation the actual alignment of the sensor axis can be determined. Furthermore, by performing this alignment determination operation for multiple sensors the relative alignment between sensors can be determined.

Abstract: A method for determining azimuth and elevation angles of a radiation source or other physical objects located anywhere within an cylindrical field of view makes use of an omni-directional imaging system comprising of reflective surfaces, an image sensor and an optional optical filter for filtration of the desired wavelengths. The imaging system is designed to view an omni-directional field of view using a single image sensor and with no need for mechanical scan for coverage of the full field of view. Use of two such systems separated by a known distance, each providing a different reading of azimuth and elevation angle of the same object, enables classic triangulation for determination of the actual location of the object. The invention is designed to enable use of low cost omni-directional imaging systems for location of radiation sources or objects.

Abstract: An attitude determination system and method is provided that includes at least two sensor sets. Each sensor set is configured to detect electromagnetic radiation, such as light of a known frequency. Specifically, each sensor set is configured to detect electromagnetic radiation from a one of a plurality of point sources, where each of the plurality of point sources emits electromagnetic radiation of a different frequency. Each sensor set includes at least three sensors, with each of the three sensors having a different orientation. The three sensors in the sensor set are used to determine a relative orientation of the vehicle with respect to one of the point sources. The at least two sensor sets in the system determine the relative orientation with respect to at least two point sources. By placing the sensors on a vehicle and knowing the direction to the point sources in a reference frame coordinate system, the orientation of the vehicle with respect to this reference frame can be estimated.

Abstract: A system and associated method where a vertical flight dynamic sensor is stabilized using pitch rate gyro information combined with azimuth rate gyro information corrected by scaling the azimuth rate gyro information in accordance with feedback derived from the difference between the vertical flight dynamic sensor signal and the corrected vertical flight dynamic output. In one embodiment, the vertical flighy dynamic sensor may be a vertical speed sensor. In another embodiment, the vertical flight dynamic sensor may be a pitch attitude sensor derived from the difference between an inertial based acceleration signal and a velocity based acceleration signal. The velocity based acceleration signal may be based on airspeed or GPS velocity.

Abstract: A system for counteracting a disturbance in a spacecraft includes a biasing apparatus that is coupled to the spacecraft and a spacecraft controller within the spacecraft. The disturbance has a known sign, magnitude and time. The biasing apparatus controls the biasing apparatus to place the spacecraft in a first dynamic state or position as a function of the sign, magnitude, and time of the disturbance. The controller also controls the spacecraft to a second dynamic state as a function of the known sign, magnitude, and time so that the spacecraft is oriented in a position other than the desired orientation so that after the disturbance the spacecraft is oriented in the desired orientation in response to the disturbance. The biasing apparatus may comprise a momentum wheel and the disturbance may comprise thrusting firing used for controlling momentum dumping.

Abstract: Satellite earth sensors (ES) generate scan lines, areas of detected infrared information gathered across the view of the earth by the satellite. The length of these scan lines is utilized by the satellite Attitude Control Subsystem (ACS) to determine the satellite pointing in roll and pitch. There are areas on the earth during particular periods of the year that can cause earth radiance gradient disturbance effects, satellite attitude errors caused by the ACS-calculated length of the scan lines becoming faulted. This invention includes methods and systems for minimizing disturbances to the satellite attitude for satellites in inclined, elliptical orbits that use infrared earth sensors to determine pitch and roll angles. These include identifying areas where earth radiance gradient events cause such disturbances and the prediction of times of such occurrences and methods for mitigating the effect of such events.

Abstract: A method for increasing the roll offset operating range for a spacecraft using an earth sensor operating in single scan mode includes the steps of moving the spacecraft to a first roll position, which has a roll angle that will cause the earth sensor to have a desired standard chord, switching the earth sensor to single scan mode by deselecting one of the earth sensor scans, whereby switching the earth sensor to a single scan mode, the earth sensor standard chord is locked at or near the desired standard chord. After the desired standard chord is set, the spacecraft is moved to a second roll position, which is a desired roll offset operating position for the spacecraft, and the earth sensor roll output (generated by using the single scan mode) is used to calculate the spacecraft roll at the roll offset operating position.

Abstract: A satellite constellation system, including a plurality of satellites in relatively close proximity to each other so that line-of-sight communications can be maintained at all times between adjacent satellites. The satellites are in closely-spaced orbits with incremental offsets in their starting true anomalies to create a pattern of the satellites which is serpentine in nature, moving north and south through latitudes covered as a result of the selected inclination angle while moving also in a longitudinal direction so that the serpentine pattern moves across most ground regions of interest. The constellation is asymmetric in nature in order to maximize the continuous access time. It is also possible to have multiple symmetrically-located constellations of this type.

Abstract: A method, apparatus, article of manufacture, and a memory structure for compensating for optical sensor data corrupted by angular acceleration is disclosed. The method comprises the steps of determining an angular acceleration of the optical sensor and modifying the optical sensor data according to the determined angular acceleration of the optical sensor. The apparatus comprises a sensor for determining an angular acceleration of the optical sensor and a navigation system for modifying the optical sensor data according to the determined angular acceleration of the optical sensor.

Abstract: In general, a constellation of spacecraft is used to broadcast to a particular region with high angles of view in order to reduce blockage or shadowing. A constellation of a plurality of spacecraft is placed in 24-hour orbits having inclination of about 55°, eccentricity of about 0.32, semi-major axis of about 42,000 km, longitude of the ascending node of about 43° East, argument of perigee of about 270°, and longitude of the ground track at maximum latitude of about 7° East. The preferred number of spacecraft ranges from three to six. In a particular application of Digital Audio Broadcast to Europe in some embodiments, the most populous cities are provided with service from no more than about 10° from vertical, and broadcast takes place when the spacecraft are above at least 35° North latitude. The broadcast power is reduced during those portions of the orbit in which the ground track lies in the Southern hemisphere.

Abstract: The invention provides a system and method of providing protection against the effects of protons of solar origin, so as to make it possible for a start sensor to be reconfigured. The system detects the arrival of an eruption of solar origin protons, supplies a control signal and triggering operation of the second star sensor in tracking mode on the basis of attitude data supplied by the first star sensor.

Abstract: In one embodiment, a method for controlling an aircraft comprises providing an attitude error as a first input into a neural controller and an attitude rate as a second input into the neural controller. The attitude error is calculated from a commanded attitude and a current measured attitude, and the attitude rate is derived from the current measured attitude. The method also comprises processing the first input and the second input to generate a commanded servo actuator rate as an output of the neural controller. The method further comprises generating a commanded actuator position from the commanded servo actuator rate and a current servo position, and inputting the commanded actuator position to a servo motor configured to drive an attitude actuator to the commanded actuator position. The neural controller is developed from a neural network, wherein the neural network is designed without using conventional control laws, and the neural network is trained to eliminate the attitude error.

Abstract: For controlling the attitude of a satellite placed on a low earth orbit, components of a vector Bm of the earth's magnetic field along three measurement axes of a frame of reference bound with the satellite (typically by means of a three-axis magnetometer) are measured. The orientation of the earth's magnetic field in the frame of reference is computed and a derivative {dot over (B)}m of the vector is also computed. Magneto-couplers carried by the satellite are energized to create a torque for spinning the satellite at an angular frequency &ohgr;c about a determined spin axis of the satellite, where &ohgr;c is greater than an orbital angular frequency 2&ohgr;0 of the satellite.

Abstract: Systems and methods of controlling and correcting the attitude of a spacecraft or a spacecraft-based payload due to disturbances that cause attitude changes determined by a spacecraft attitude measurement sensor and one or more additional attitude measurement sensors on the spacecraft. The systems and methods measure the attitude of the spacecraft and measure relative attitude errors between the spacecraft and the payload. The measurements are processed to generate control signals that selectively control the pointing direction of the spacecraft or payload. Embodiments are disclosed wherein the additional attitude measurement sensor is disposed on a platform that is stable with respect to the spacecraft attitude measurement sensor, and wherein it is disposed on a platform that is not stable with respect to the spacecraft attitude measurement sensor.

Abstract: A method for correcting spacecraft pointing errors. An orbit frequency distortion angle between a rate sensor and at least one attitude sensor is estimated. An estimated attitude of the spacecraft is adjusted to correct for the distortion angle.

Abstract: An attitude detection system for an artificial satellite includes an interpolator for interpolating an angular-velocity signal to generate an interpolated angular-velocity signal, a sequential Kalman filter for generating a low-frequency attitude-angle signal, and an adder for adding the low-frequency attitude-angle signal and a high-frequency attitude-angle signal generated by a high-frequency angular sensor to generate a broad-band attitude-angle signal.

Abstract: A fault tolerant attitude control system for a zero momentum spacecraft. A zero momentum attitude control system is operable to control spacecraft attitude utilizing data received from an earth sensor, a sun sensor, and the inertial measurement unit. A gyroless attitude control system is operable to control spacecraft attitude without receiving data from the inertial measurement unit. A redundancy management system is operable to monitor an inertial measurement unit to detect faults and to reconfigure the inertial measurement unit if a fault is detected and operable to determine when an inertial measurement unit fault is resolved. A controller is operable to automatically switch the spacecraft from the zero momentum attitude control to the gyroless attitude control when a fault in the inertial measurement unit is detected and is operable to automatically switch the spacecraft from the gyroless attitude control to the zero momentum control upon resolution of the fault.

Abstract: A method for rapid earth reacquisition of a spacecraft. A three-axis inertial attitude of the spacecraft is determined by rotating the spacecraft about its pitch axis while measuring star patterns. A pitch axis of the spacecraft is aligned with earth's pole axis. The spacecraft is reoriented with respect to an earth-pointing reference frame.

Abstract: A method and apparatus for determining star tracker misalignments is disclosed. The method comprises the steps of defining a defining a reference frame for the star tracker assembly according to a boresight of the primary star tracker and a boresight of a second star tracker wherein the boresight of the primary star tracker and a plane spanned by the boresight of the primary star tracker and the boresight of the second star tracker at least partially define a datum for the reference frame for the star tracker assembly; and determining the misalignment of the at least one star tracker as a rotation of the defined reference frame.

Abstract: A three-axis attitude control for a low-orbiting satellite. A sensor which measures in two axes is a magnetometer, and a satellite is positioned on an inclined orbit at an inclination angle of approximately 25 degrees to approx. 90 degrees. The satellite has been provided with an overall spin by spin wheels, and actuators generate torque on all three axes of the satellite. Accordingly, this is applicable to three-axis attitude control of a low-orbiting satellite that includes a sensor which measures in two axes and that includes one or several spin wheels.

Abstract: Methods and structures are provided that enhance attitude control during gyroscope substitutions by insuring that a spacecraft's attitude control system does not drive its absolute-attitude sensors out of their capture ranges. In a method embodiment, an operational process-noise covariance Q of a Kalman filter is temporarily replaced with a substantially greater interim process-noise covariance Q. This replacement increases the weight given to the most recent attitude measurements and hastens the reduction of attitude errors and gyroscope bias errors. The error effect of the substituted gyroscopes is reduced and the absolute-attitude sensors are not driven out of their capture range. In another method embodiment, this replacement is preceded by the temporary replacement of an operational measurement-noise variance R with a substantially larger interim measurement-noise variance R to reduce transients during the gyroscope substitutions.