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(11173)

By the law of Coriolis, for a vehicle rotating relative to navigation frame with angular rate n , the velocity of the navigation system and aiding nb source are related according to

Table 25-1

(11174)

Frequency designation Very Low (VLF) Low (LF) Medium (MF) High (HF) Very High (VHF) Ultra High (UHF) Super High (SHF) Extremely High (EHF)

The navigation system predicts the velocity aiding output according to ya = = h a vn h n vn + n r nb Rn b b (11175) (11176)

n nb where vn , n , and Rn are directly computable from the navigation state b The residual aiding error, used to drive the Kalman lter, is computed as ya which has the error model ya = = =

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Frequency range 3 kHz 30 kHz 30 kHz 300 kHz 300 kHz 3 MHz 3 MHz 30 MHz 30 MHz 300 MHz 300 MHz 3 GHz 3 GHz 30 GHz 30 GHz 300 GHz Wavelength range 100 km 10 km 10 km 1 km 1 km 100 m 100 m 10 m 10 m 1 m 1 m 100 mm 100 mm 10 mm 10 mm 1 mm

n n r n h vn vn + n rn nb n + nb n r n h vn vn + Rn b rb Rn nb b + b nb b n h vn + PRn b rb + Rn ( b b ) + Rn b rb + b nb b b nb nb r b

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The factor b could be further expanded The nal equation provides nb a linear relationship, suitable for Kalman lter processing, between the measurement residual and the INS error state Inertial Measurement Aiding Inertial measurement matching would require another derivative which would introduce terms involving b The nb fact that measurements of this term are not typically available limits the implementability of inertial measurement matching procedures in situations were the angular rate has signi cant variation This approach is limited to master-slave implementations Master-slave initialization uses one accurate, previously initialized INS to calibrate a second INS The second INS may have been recently turned on or of low enough quality that signi cant drift is expected to have occurred since the last calibration For example, this scenario is applicable for the initialization of the INS state in weapon applications, where an expensive INS may not be warranted on the weapon due to the short span of time over which accurate post-launch navigation is required and due to the expectation that the INS will be destroyed with the weapon Master-slave initialization may take a variety of forms In one-shot alignment (or transfer alignment) the

state of the master INS is used to initialize the state of the slave INS at a particular instant of time Alternatively, the position, velocity, or inertial measurements of the master INS could be di erenced with the same quantities of the slave INS The resulting residual measurements driving a Kalman lter based error estimator [20] The master INS speci c force and angular rate vectors are processed to provide a correct navigation frame version of these vectors at the slave INS location This statement implies that the processing accounts for lever arm, ex, and non-common mode disturbance e ects This is of course not completely possible The slave INS processes the corrected master INS vectors denoted f n and n in a manner similar to that described for analytic gyro-compassing Inertial measurement matching can theoretically outperform analytic gyro-compassing, since the master-slave system is capable of maneuvering Due to the maneuvers, the observability properties of the system are enhanced However, in practice, the lever arm, ex, and disturbance e ects can make inertial measurement matching techniques di cult to implement

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