Transfer alignment, quasi-stationary alignment, fine alignment, and ZUPT implementation.
An INS must know its initial attitude before it can navigate. Specifically, it needs to know the orientation of the body frame relative to the navigation frame (the rotation matrix Cnb). If this initial attitude is wrong, the INS will misrotate the specific force, causing errors that grow rapidly with time.
How rapidly? An initial attitude error of 1° causes:
• A velocity error that grows at ~0.17 m/s per second (0.17 m/s × t)
• A position error that grows quadratically: ~0.085 m × t²
• After just 60 seconds: velocity error ~10 m/s, position error ~300 m
Alignment is the process of determining this initial attitude to the required accuracy. There are several scenarios:
• Stationary alignment: Vehicle is not moving (on the ground, at the dock). Leveling + gyrocompassing gives roll, pitch, and heading.
• In-motion alignment: Vehicle is already moving. Uses GNSS or another reference navigation system.
• Transfer alignment: A subordinate INS is aligned from a nearby reference navigation system. Used for weapons launched from aircraft.
Transfer alignment initializes, aligns, and calibrates an INS while in motion, using measurements from a nearby reference navigation system (typically a better INS or integrated INS/GNSS on the host platform).
The scenario: A guided weapon or UAV is mounted on an aircraft wing pylon. It contains an INS that must be aligned before launch. The aircraft carries a reference INS/GNSS in its body. Transfer alignment uses the reference system to calibrate the weapon's INS.
Three phases:
• One-shot initialization: The aligning INS is initialized with the reference system's position, velocity, and attitude, corrected for the lever arm and relative orientation. This gives a rough starting point (attitude accuracy ~2° due to wing flexure and vibration).
• Measurement-matching phase: The aligning INS runs its own navigation equations. A Kalman filter compares the aligning-INS and reference-system solutions over time, estimating attitude corrections and IMU biases. Duration: 2 seconds to several minutes.
• Reinitialization: Just before launch, the position is reset from the reference system and the error covariance matrix is reset to account for inherited reference-system errors.
The measurement-matching phase uses a Kalman filter to compare the aligning-INS and reference solutions. The standard approach uses velocity matching:
The lever arm from the reference to the aligning INS must be accounted for, as the two systems experience different velocities due to the angular motion of the host vehicle.
Why velocity matching, not position matching?
• Velocity measurements lead to faster estimation of attitude and IMU errors, because velocity is one fewer integration step from them than position
• At low measurement rates (~1 Hz), position matching can perform better due to averaging of lever-arm vibration noise
• Time-averaged velocity measurements combine the benefits of both
Observability and maneuvers: The same observability considerations as INS/GNSS integration (Chapter 12) apply. The heading error is only observable during turns. An S-weave alignment maneuver is typically performed to provide heading observability. Without turns, only the roll and pitch errors and vertical accelerometer biases can be well determined.
The measurement noise arises mainly from lever-arm vibration and time-synchronization errors. These depend on the host aircraft type and the mounting position of the aligning INS.
Rapid transfer alignment adds attitude-measurement matching to the velocity matching of conventional transfer alignment. This directly observes the attitude errors, enabling alignment within 10 seconds instead of several minutes.
The attitude-matching measurement innovation is:
where Ĉnr is the reference attitude, Ĉrb is the estimated relative orientation (with flexure model), and Cbn comes from the aligning INS.
Benefits:
• Alignment in ~10 seconds (vs minutes for conventional)
• Reduced maneuver requirement — a wing rock (pair of rolls) suffices; turns are not strictly necessary
• Prevents subsequent degradation of the heading alignment after the maneuver
The flexure challenge: Wing flexure changes the relative orientation differently during rolls, turns, and level flight. If the filter assumes a constant relative orientation, the attitude and bias estimates can be severely biased. The solution is to model the flexure as a function of the specific force acting on the wing, estimating the flexure coefficients as additional Kalman filter states.
For heading-only attitude matching (which is less affected by flexure), the flexure model can be omitted, simplifying the algorithm while still providing the most valuable component of rapid alignment.
When a vehicle is stationary (or nearly so), the INS can be aligned without an external reference. This uses two natural references:
1. Gravity for roll and pitch (leveling): When stationary, the accelerometers measure only gravity. Roll and pitch are computed from the gravity direction in the body frame. This is the same as the AHRS leveling described in Chapter 10, but with higher precision for navigation-grade accelerometers.
2. Earth rotation for heading (gyrocompassing): The Earth rotates at 15.04°/hr. When stationary, the gyroscopes measure only the Earth's rotation vector, projected onto the body axes. By comparing the measured components with the known Earth rotation rate and latitude, the heading can be determined:
where ωx and ωy are the body-frame components of Earth rotation and L is the latitude.
Gyrocompassing limitations:
• Requires gyro bias stability much better than 15°/hr. This limits gyrocompassing to navigation-grade and tactical-grade IMUs. MEMS gyros (bias ~10–1000°/hr) cannot gyrocompass.
• At the poles, the horizontal component of Earth rotation vanishes, making gyrocompassing impossible.
• Alignment time depends on the gyro noise: typically 5–20 minutes for navigation-grade, longer for tactical-grade.
Fine alignment refines the attitude solution beyond what coarse alignment (leveling + gyrocompassing) provides. It uses a Kalman filter with zero velocity measurements.
Since the vehicle is stationary, the true velocity is zero. The INS computes a velocity from integrating the (noisy, biased) accelerometer outputs through the (imperfect) attitude. Any non-zero INS velocity is an error. The measurement innovation is:
This is a zero velocity update (ZUPT). The Kalman filter uses it to estimate:
• Attitude errors (which cause misrotation of gravity into horizontal velocity)
• Accelerometer biases
• Gyro biases (through their effect on attitude propagation)
The mechanism: An attitude error δθ about the east axis misrotates a component of gravity into the north direction, producing a north velocity error that grows as g · δθ · t. The ZUPT observes this growing velocity and the filter infers the pitch error. Similarly for roll. Heading errors produce cross-coupling effects during turns of the Earth frame, though these are much weaker and require long alignment times.
Fine alignment performance: With a navigation-grade IMU, fine alignment over 10–20 minutes achieves heading accuracy of ~0.05° and tilt accuracy of ~0.003°. With a tactical-grade IMU, heading accuracy of ~0.5–1° may be achieved with a longer alignment period, though gyrocompassing may not converge at all.
The Zero Velocity Update (ZUPT) is one of the most powerful tools in inertial navigation. Whenever the vehicle is known to be stationary, the true velocity is zero, and this information can be used as a Kalman filter measurement.
ZUPT applications:
• Fine alignment (Chapter 5): Determines attitude and calibrates sensor biases while stationary
• Pedestrian navigation: Foot-mounted IMU applies a ZUPT during each stance phase (~0.3 s per step), bounding position drift to ~1–2% of distance traveled
• Land vehicle at stops: At traffic lights and stop signs, a ZUPT corrects the INS velocity and calibrates sensor biases
• Submarine at periscope depth: When surfacing briefly, the velocity is nearly zero and GNSS can be acquired
ZUPT measurement model: The velocity measurement is simply:
The measurement noise covariance should reflect any residual motion (vibration, settling) during the "stationary" period.
ZUPT detection: The system must determine when the vehicle is actually stationary. Methods include thresholding the accelerometer and gyro outputs (looking for near-gravity acceleration and near-zero angular rate), monitoring odometer speed, or using an external trigger.
This simulation shows a pedestrian INS with zero velocity updates. The foot-mounted IMU accumulates velocity error during each step. At each stance phase (foot on ground), a ZUPT resets the velocity error. Compare with uncorrected INS drift.