By Jay Farrell

There is not anything particularly unsuitable with this publication. The format is logical. The chapters are good organised, even supposing there's a few to-and-fro among the self-alignment and AHRS chapters. there's instance code that turns out to paintings (except, after all, for the fairly very important chapters).

The challenge is, Groves (Principles of GNSS, Inertial, and Multi-Sensor built-in Navigation structures (GNSS expertise and Applications)) does it larger, extra logically and, as a practitioner, extra helpful in enforcing a GPS/INS system.

It does perform a little issues higher than Groves: it introduces Doppler radar, barometric measurements and different sensors and indicates how they are often placed into the framework. It additionally does quaternions, anything slightly addressed in Groves.

However, from a practitioner's standpoint, the "advantage" of leaving the rotation description as impartial makes the presentation tougher to stick with. Groves sticks to DCM for the sake of readability and it pulls off.

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The method can best be understood in relation to a speciﬁc example system. The system is intentionally simple and low dimensional to focus on the main theoretical ideas without large amounts of algebra. The intent of the discussion is to motivate the theoretical coverage in Part I and the general approach used in Part II. The realistic systems of Part II are considerably more complex. Most readers will not be familiar with all of the ideas presented in the following discussion, for example, diﬀerential equations with random inputs.

Since all engineering students take ordinary diﬀerential equations, physics, and some dynamics courses, the underlying concepts should be familiar; however, not all such courses are formulated within the state variable framework. Therefore, the two main goals of that chapter are to review state space analysis and state estimation. 3 Stochastic Processes By their senior year at college, most students are fairly comfortable with modeling continuous-time deterministic systems. The idea that we integrate acceleration to ﬁnd velocity and integrate velocity to ﬁnd position is now rather innate.

Although the direction cosine matrix has nine elements, due to the three orthogonality constraints and the three normality constraints, there are only three degrees of freedom. 5 and Appendix D. Analogous to eqn. 13) v2 = I2 x2 + J2 y2 + K2 z2 where [v2 ]2 = [x2 , y2 , z2 ] Therefore, 1 [v2 ] ⎡ and by eqn. 14) ⎡ ⎤ I1 1 [v2 ] = ⎣ J1 ⎦ v2 . 4. REFERENCE FRAME TRANSFORMATIONS 39 2 = R12 [v2 ] . 17) Point Transformation When eqn. 17) is substituted into eqn. 15) it yields the desired equation for the transformation of the coordinates of P with respect to frame 2, as represented by [v2 ]2 , to the coordinates of P with respect to frame 1, as represented by [v1 ]1 : ⎤1 x1 ⎣ y1 ⎦ z1 ⎡ [v1 ]1 ⎤1 xO 2 = ⎣ yO ⎦ + R12 [v2 ] zO ⎡ 2 = [O12 ]1 + R12 [v2 ] .