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The Global Positioning System & Inertial Navigation
Download The Global Positioning System & Inertial Navigation
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From the Back Cover
With GPS and INS hardware becoming ever smaller and less expensive, innovative opportunities for commercial, military, and scientific navigation systems are everywhereÑand continue to arise. Integrated GPS/INS systems have some real advantages, in terms of output rate, reliability, and accuracy. The Global Positioning System and Inertial Navigation is the first-ever reference to provide engineers and scientists with a detailed, top-to-bottom look at GPS and INS in a single volume. Features include: Integrated practical examples; In-depth case studies; Detailed theoretical derivations; Guidelines for building integrated GPS/INS systems; Advanced GPS and INS techniques presented in a unifying format; Comparison of alternative implementation techniques; A systematic engineering design approach. This in-depth text provides navigation system designers comprehensive and accurate coverage of such topics as coordinate frames and transformations...Kalman filtering techniques...navigation system performance analysis...GPS receiver ephemeris and pseudo-range processing... differential GPS, carrier phase processing, and attitude determination. Extensively cross-referenced to the literature on advanced navigation system design, this superb engineering reference is ideal for navigation systems designers, analysts, and project managers.
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About the Author
Jay A. Farrell (Riverside, CA) is Professor of Electrical Engineering at the University of California, Riverside.
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Product details
Hardcover: 340 pages
Publisher: McGraw-Hill Professional; 1 edition (December 31, 1998)
Language: English
ISBN-10: 007022045X
ISBN-13: 978-0070220454
Product Dimensions:
7.7 x 0.9 x 9.5 inches
Shipping Weight: 1.6 pounds
Average Customer Review:
3.3 out of 5 stars
5 customer reviews
Amazon Best Sellers Rank:
#2,483,203 in Books (See Top 100 in Books)
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.
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 beendenoted 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.
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 thatif\[\dot{\bf x}(t) = A(t) {\bf x}(t)\] 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.
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.
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.
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