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The strapdown INS integrates eqn (1125) to compute va (t) and pa (t) The vehicle attitude is represented by Ra b This chapter will focus on strapdown inertial navigation Throughout the presentation, the direction cosine representation of attitude will be assumed Other representations exist (eg, Euler angles, quaternions) Readers are encouraged to consider the quaternion representation (see Appendix D) It may have a steeper learning curve, but provides a computationally e cient and singularity-free attitude representation approach The error modeling approach presented in this chapter is applicable to any of the attitude representations Equations for speci c choices of the a-frame will be considered in the following subsections For each frame, a di erential equation will be derived for each of the position, velocity, and attitude

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In the common gate circuit (Fig 23-12), the gate is placed at signal ground The input is applied to the source The illustration shows an N-channel JFET For other types of FETs, the same considerations apply as previously described for the common source circuit Enhancement-mode devices would require a resistor between the gate and the positive supply terminal (or the negative terminal if the MOSFET is P-channel) The dc bias for the common gate circuit is basically the same as that for the common source arrangement But the signal follows a different path The ac input signal enters through C1 Resistor R1 keeps the input from being shorted to ground Gate bias is provided by R1 and R2 Capacitor

The accelerometer and position measurements occur simultaneously f2 = 1 times per second For these instances, the Kalman gain and update are computed using H= 1 0 0 0 0 1 0 1 0 1 0 a and R=

2 2 0

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C 2 places the gate at signal ground In some common gate circuits, the gate is directly grounded, and R2 and C 2 are not necessary The output signal leaves the circuit through C3 Resistor R3 keeps the output signal from being shorted through the power supply The common gate arrangement produces less gain than its common source counterpart But a common gate amplifier is not likely to break into unwanted oscillation, making it a good choice for power-amplifier circuits, especially at RF The output is in phase with the input

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