[.uk] The Global Positioning System & Inertial Navigation (ISBN 007022045X)

Another Reader:
First let me point out that the "error" mentioned by couple of reviewers are not errors. Perhaps the reviewers misunderstood or missed something. The NY reviewer wrote " dot{/bf{R}}_{b2a}(t) = - /Omega /bf{R}_{b2a}(t) whic is fine. but then it is concluded that /bf{R}_{b2a}(t) = exp(-/int_{t0}^t /Omega dt) /bf{R}_{b2a}(t_0) which is wrong because $/Omega$ is a function of time. " Actually this last line is in fact correct. I am not sure why reviewer think there is a problem. Perhaps the dummy integration variable t in the integral should have been denoted by a different letter, but I think this is understood to be the dummy variable and not related to independent variable t. At any rate this equations is perfectly correct. Also the "errors" pointed out by reviewers with title "Mixed Results" are not errors. Matrix multiplication representation of the cross product has the right sign per convention that it is representing angular velocity of "a" frame relative to b frame. Multiplying this by -1, would represent angular velocity of b frame relative to "a" frame. The mappings from the quaternions to the Euler angles (Chapter 2 equations 2.47 through 2.49) are all correct. Perhaps the reviewer uses a different convention for the signs relative to reference and rotating frame. The book itself is probably one of the better books if one is not afraid of mathematical rigor (of course Mathematical rigor itself is relative). It does a nice job of blending the inertial navigational with system theory and Kalman filtering methods.

An aerospace engineering student:
This is a great book for the student. It goes over the basics of GPS and inertial navigaion. I found the development of the equations and models of the systems invaluable. I have used this book as the basis of many useful functions for transforming from latitude/longitude/altitude to ECEF and others. Overall, a great book for the beginner, although, a bit weak on advanced topics.

There are fundamental mistakes in the book:
Page 45 equation 2.60 is wrong. I write in latex form for those who read the book carefully. In the book it is given /dot{/bf{R}}_{b2a}(t) = - /Omega /bf{R}_{b2a}(t) which is fine. But then it concludes that /bf{R}_{b2a}(t) = exp(-/int_{t0}^t /Omega dt) /bf{R}_{b2a}(t_0) which is wrong because $/Omega$ is a function of time. This mistake is propagated. I have used the book but I corrected the mistakes. Response to critic of this review (for the benefit of readers): The first thing you learn in linear system theory is that if /( /dot{/bf x}(t) = A(t) {/bf x}(t) /) then /( {/bf x}(t) /ne e^{A(t)} {/bf x}_0 /) unless $A(t)$ is constant, which both the authors and the critic are not paying attention to.

There's a fundamental error in Chapter 2:
I thought that a time varying matrix diffeq, xdot = A(t)x, had an integrating factor iff the time-varying system matrix A(t) commuted with int(A(s): 0 -> t) for all t. Then the solution is x(t) = exp(int(A(s);0->t)x(0) For the rotation R, Omega clearly does not commute with its integral in this way. Is the closed form solution still valid? I don't know! It's obviously valid for small delta_t = t(k+1) - t(k), since then the relevant matrices are approximately constant.

Not what I expected:
I am an electrical engineer and was looking for an insight into INS. From what I had read, I had the impression that this book would be at a level I could understand with relative ease - not the case. I have now purchased an alternative. This is what happens when you only have a limited review capability before purchasing.