Kalman Filtering Consultant Associates

PO Box 17224

Anaheim, CA 92817

ph: 714-281-4619

fax: 714-281-4619

KFCAS

**Provided a concise, but practical approach to applying Kalman filtering to relevant real-world applications. This will directly transfer to the work I do as a professional...I now have the tools and have an idea of how to start applying the course info to new problems. **

*Participant*

**"Grewal is a GPS Superstar. It was an honor to be in this class." "This was a good course--Thanks--We need more like this." "Great course!" "The Instructor's clear expertise made the lectures very enjoyable." "Excellent course, excellent instructor. He literally 'wrote the book' on a lot of this stuff." "Best short course I have taken."***Participants, Edwards AFB "On-Site Course***“Thanks to Professor Grewal for a great series of lectures!” “He is certainly knowledgeable and well-prepared.” “Very informative. Excellent book and software has been provided. Excellent visuals also.” (Most valuable aspects of course) “The algorithms and the potential errors and how to mitigate them...” “So much useful information.” “Excellent.” “Very good--easy to understand--took time to answer questions and explanations were helpful.” “It was clear, concise.” “Having the man who wrote the book--teach the class is great.” “Enjoyed the teacher. There are two types--instructors and teachers. Professor Grewal is (in my opinion) a teacher, who takes much pride in his work and students.”****Participants from an on-site course at China Lake Naval Air Weapons Station****“Lots of examples with well-organized materials… Hands on experience from instructor and relaying this to class…The professor’s willingness to answer questions and his ability to answer them was great. Also, the books and notes seem to be very complete and useful…Excellent, experienced, and friendly instructor…Materials were thorough. Instructor is very knowledgeable of material presented…”****Participants from an on-site course at NASA Dryden****“Course was excellent. Give this course the highest rating. Very well structured and moves at a good pace. Professor Grewal makes the course material understandable and deserves a high rating as an instructor. The ‘value added’ to this course is the talent of Professor Grewal to open up the complexities of this material and provide tools for self study following the course.”***Participant, BAE Systems***“The course was above and beyond my expectations and I am very glad I decided to take it. In addition, I plan on recommending the course to my colleagues..(the book and the notes) are very thorough and**__very__useful for the applications I originally had taken the course for. Thank you for your time and all the useful knowledge provided.”*Participant, SAIC*Excellent. It is a pleasure to learn the material from someone that is not just a mathematician, but a practicing, experienced veteran. The practical insights and intuition were invaluable and made the whole course.

*Participant, Sensor Platforms, Inc.*

(Most useful will be) “help in model and noise formulations and advice on different implementations, and advice on how to use metrics (K, P, innovation)...” *(Participant, Chevron )*

(Most useful will be) “knowing how solutions got derived and the applications to real world problems. I wish I took this course many years ago. (General comments) “Excellent. I definitely plan to recommend especially to practitioners of GPS. Dr. Grewal is an excellent teacher, did not bore me, kept the class interesting.” *(Participant )*

"The course was more than I expected. A+ ...The Kalman filter is a simple concept, but implementation is not straightforward if you have never done it before. I feel I will be able to design and implement a Kalman filter to solve my current problem."* (Participant, ITT)*

(General comments) “...It was great how the presentation is tied to the textbook. Therefore, it allows you a reference for more detail to work through on your own. (Most useful) The Kalman filter design with GPS aided INS examples...It was very helpful to walk through actual calculations and examples. Plus the MATLAB illustrations give you better insight, rather than just looking at equations and numbers.” *(Participant, DRS Sensors & Targeting Systems )*

(Most useful will be) “understanding how to use the covariance matrix and residues to monitor filter performance…” *(Participant )*

(Most useful will be) “Data fusion/two sensors tight coupling, UDU^{T} algorithm, suggestions from the experience of Dr. Grewal. Very complete and interesting. Good notes.” *(Participant )*

(Most useful will be) “GPS clock modeling, linearization technique, GPS history and description…” *(Participant )*

“Now I have a precise understanding of the different DOPs…” *(Participant )*

(Most useful will be)* *“GPS clock modeling, linearization technique, GPS history and description. Well done.” *(Participant)*

(Most useful will be)* *“the equation representation on the MATLAB feed into the application. The course is understandable (explains) by using equations to represent the application and shows it in the MATLAB code and output. This course (increased) my knowledge of understanding what the manufacturers are looking into and testing.” *(Participant)*

(Most useful will be)* *“INS-GPS integration. Very helpful.” *(Participant)*

*Was the course what you expected?* * *“Yes. In fact, the material was more in depth than expected and covered more applications than expected.” *(Most useful will be)* Understanding the design of the KF will help me better integrate systems which use KFs. I enjoyed listening to Dr. Grewal. His deep understanding of the subject commands your attention.” *(Participant, Northrop Grumman Corporation)*

*Was the course what you expected?* * *“Yes, it was a good overview of Kalman filters and provided the base to implement Kalman filter designs.” *(Most useful will be)* the MATLAB examples and reference material for future use. Although a lot of information was presented, I feel I absorbed enough to be able to implement a Kalman filter design.” *(Participant)*

“Course was excellent. Give this course the highest rating. Very well structured and moves at a good pace. Professor Grewal makes the course material understandable and deserves a high rating as an instructor. The ‘value added’ to this course is the talent of Professor Grewal to open up the complexities of this material and provide tools for self study following the course.” *(Participant, BAE Systems)*

“The course was above and beyond my expectations and I am very glad I decided to take it. In addition, I plan on recommending the course to my colleagues..(the book and the notes) are very thorough and very useful for the applications I originally had taken the course for. Thank you for your time and all the useful knowledge provided.” *(Participant, SAIC-CA)*

“Pace and level fit well. The way the instructor handled individual questions proved to be useful...Great. Good instruction, best I’ve had at the professional level.” *(Participant, ARINC-MD)*

“Dr. Grewal is both an expert and an excellent teacher. I highly recommend the course.” *(Participant, ARINC-UT)*

*Was the course what you expected?* “Yes. This training absolutely benefits... engineers involved in GPS/INS Navigation. The instructor used a step-by-step approach to explain a complex GPS/INS Kalman filter modeling system...Job well done! *(Participant, Edwards AFB)*

*Was the course what you expected?* “More than expected. Excellent introduction to Kalman filtering. (Most useful was)--in depth understanding of basic concepts. Many examples that demonstrate the concepts presented in clear way.” *(Participant, TRW)*

“The texts and lecture notes will be an outstanding reference (extremely complete coverage of the topics.” *(Participant, Eglin AFB)*

*Was the course what you expected?* "Much more than I expected!! Dr. Grewal is an outstanding instructor--very, very accomplished and knowledgeable in the subjects. Fantastic!!" *(Participant, Edwards AFB)*

"A great balance of technical insight with practical considerations. Extremely well taught. Good emphasis on 'important to remember' concepts. Good mix of the practical with the theoretical. One of the best taught classes I've had in fifteen years." *(Participant)*

“Excellent instruction, excellent visual aids. Very good course material organization.” *(Participant, NAWCWD)*

*Was the course what you expected?* "It was everything I expected and more. Very professionally conducted with a level of detail that stimulated my interest. I can now address the subject well enough to appreciate what my people are doing, recognize their performance and respond to their technical needs. Outstanding. Worth every minute!" *(Participant, Veridian)*

*What will be most useful to you from this course? *"Knowledge of differing Kalman filtering implementations. Algorithmic differences between the extended Kalman filter implementations of predictors and corrections." *(Participant)*

*What will be most useful to you from this course? *"Descriptions and solutions to the real world implementations (Chapter 7 in Kalman Filtering book). Additionally, methods to fix problems...Great information-great presentation. Just the right amount of detail." *(Participant, Boeing)*

"Great class! Excellent professor." *(Participant)*

"I think the last three days will prove to be invaluable to my work. I will finally be able to put all of the GPS puzzle pieces together." *(Participant, Computer Sciences Corporation)*

*What will be most useful to you from this course? *"General knowledge of Kalman filtering techniques and examples of how to apply them. Also found the discussion of GPS, navigation and WAAS to be very useful." *(Participant)*

*What will be most useful to you from this course?* "The introduction and application of the Kalman filter, especially with GPS. The course gives a distinction of continuous and discrete system equations, and is well-defined."* (Participant)*

*What will be most useful to you from this course?* "UDU^{T} Kalman filtering implementation and other algorithms in MATLAB. I got a lot out of this class. The MATLAB algorithms will be extremely useful. Also, useful were methods of characterizing sensor noise and methods for checking that the Kalman filter design is good." *(Participant, Honeywell)*

"This is an outstanding course." *(Participant, Edwards AFB)*

"The course is very interesting and enjoyable. It was a course worth the time."* (Participant)*

"Valuable course. The Kalman filtering part clarified several issues for me." *(Participant)*

*What will be most useful to you from this course?* "Being able to apply concepts to existing designs (aircraft) for the purpose of test validation." *(Participant)*

*Was the course what you expected?* "Yes. It was even more than I expected. I felt the applications were extremely effective and instructive...This course is an exceptional course. The balance between theory and practical application gives the student familiarization and confidence with this difficult subject. I found the GPS/INS instruction particularly instructive and informative...I would highly recommend the course." *(Participant, TRW)*

"Awesome, awesome training, and well represented. Good teaching technique." *(Participant, SPAWAR)*

"...The intuition provided by this class into the filter behavior and tuning process is irreplaceable!* (Most useful)* The examples, approaches, and intuition. The examples included in this course will be extremely beneficial tomorrow, next month, or even next year. The course has left me with a roadmap with which I can perform filter evaluations and designs...Enjoyed class format. Good presentation and presentation pace." *(Participant)** *

*What will be most useful to you from this course?* "The insight I got into designing Kalman filters in the real world. I feel a lot more comfortable with Kalman filters, even though I have designed and implemented them before." *(Participant) *

*What will be most useful to you from this course?* "...examples of KF implementation (supported by MATLAB files) will make it easy to 'practice' developing KFs after the course...Very worthwhile course." *(Participant, Meggitt Avionics)*

*What will be most useful to you from this course?* "Overall insight into the analysis of systems and design of KFs to match those systems. Insight into KF performance testing...An extremely good course, providing both conceptual and practical insights and explanations of the subject." *(Participant, Meggitt Avionics) *

"I really enjoyed the course!" *(Participant, Kongsberg Defence and Aerospace) *

*What will be most useful to you from this course?* "Instructor insights from practical experience, MATLAB source examples." *(Participant)*

*Was the course what you expected?* "Yes, I got more than I expected. It is an excellent KF course. I not only learned the concept and theory of KF, but also got hands on experience." *(Participant, SPAWAR)*

"This course was an excellent way to learn about Kalman filtering. I enjoyed the specific applications presented, as well as the instructor's enthusiasm toward the subject matter." *(Participant, Raytheon) *

"Excellent instructor. Materials in course and book complement each other. Excellent software examples. Have everything we need to start our own development." *(Participant, Trak-Tech Corporation) *

"This course was excellent. It met my every expectation...Thank you for your most responsive comments and answers..." *(Participant, SPAWAR)*

Most useful from course-- "The basics will be very useful for me when I start designing my own Kalman filter. Also, the special advice I received from Dr. Grewal on the problems I will be facing in my work will be very useful." *(Participant, TERN Systems, Inc.) *

Most useful from course-- "Lots of examples and useful MATLAB programs." *(Participant) *

Most useful from course-- "How the H matrix is utilized in the K.F. problem was enlightening." *(Participant) *

"Dr. Grewal addresses perfectly the main aspects of Kalman filtering with emphasis on the physical meaning of mathematical models. This demystification of a "fit-for-a-guru" subject is by far the most attractive aspect of the course. The material provided to participants is complete and well-structured."** (Participant, Dept. of Aerospace Engineering, 2nd University of Naples, Italy)**

Most useful from course-- "Better understanding of GPS and latest developments in applications of Kalman filters, for example, square root filters." *(Participant, TRW) *

"The course turned out to be more than I expected. The course content was comprehensive and parts on GPS implementations were particularly interesting. The instructor was well prepared and quite knowledgeable in this specialty." *(Participant, Dept. of the Navy) *

"I was surprised how well instructor brought students who were lacking in background up to speed...Excellent overview of estimation theory and application. Lots of examples to clarify ideas and formulations." *(Participant, Boeing)*

"Most helpful were the practical discussions on when to use one technique in preference to another, computer demos to gain a feel for Kalman filtering, concrete examples of Kalman filtering in action. A very practical course." *(Participant, U.K. Meteorological Serv.)*

"Most helpful was the explanation of how Kalman filtering works and its limitations. Application of extended Kalman filter to non-linear systems. Practical examples and a clear style to teach." ** (Participant, Magnetic Marelli TecMobility, FIAT, **Italy )

"Most helpful was the emphasis in implementation issues and "how to" approach. This was very much appreciated. Thank you for doing an excellent job." *(Participant, Boeing Space Systems)*

"Information on Kalman filters, step by step process from development of model to checking accuracy of the filter. This was excellent... M. Grewal did an excellent job on the instructing." *(Participant) *

"Most helpful were the extensive examples in notes; the real software source code to take home; textbook that follows course." ** (Participant**)

"The course was as advertised, very well-organized and thorough. I enjoyed the class very much. I thought Dr. Grewal was very organized and thorough and patient with our questions. I will definitely recommend this class to my colleagues." *(Participant, Jet Propulsion Laboratory) *

"Good, thorough, comprehensive course. Provides the basics of probability, matrix math, system modeling, random processes for a good qualitative understanding of the advantages/disadvantages of Kalman filtering techniques." *(Participant)*

*(Affiliations are given for reference and do not imply endorsement by participant's company.)** *

(most useful) The description of the different methods for evaluating a Kalman filter. Also, the practical considerations of "bad data" and if the filter is not converging...The course was very useful. It was good to hear examples of applications of Kalman filtering. ** (Participant)**

(most useful) I learned mathematical tricks for onboard implementation of Kalman filters--practical implementations on MATLAB. ** (Participant)**

(most useful) KF and EKF theory and MATLAB examples. ** (SPAWAR)**

(most useful) ...better understanding of the Kalman filter subject in my business. The limits about how to use and some applications were great too. *(Participant, Castro Leite Consulting)*

(most useful) The notes and textbooks as reference material. (most challenging) I already knew about Kalman filters, but not a lot of the tricks (coning, skulling, Cholesky factorization, Schuler, tightly vs loosely coupled). ** (Participant)**

(most useful) Implementation of the Kalman filter. ** (Participant, Tubitak Uzay)**

**(most useful) I really understand mathematical background behind Kalman filter. This will help me on future work. Also, in GPS part, I have benefited from position determination. **** (Participant, Tubitak Uzay)**

(most useful) The tips on solving the Ricatti in a numerically stable way, particularly the iterative inverse and UDU^T; INS equations, EKF estimation techniques, GPS/INS error modelling. *(Participant)*

Very well organized! Excellent course! If you need to use a KF in any complicated manner, you need to take this course! *(Participant, John Deere)*

The only KF course I had that focuses on practical use of KF rather than on theory. Thank you Prof. Grewal! (Most useful) Tips about the KF practical implementation; the GPS/INS integration process; all the performance monitoring part. *(Participant, French German Research Institute)*

(most useful) Day 4 material on GPS/INS and the EKF implementation; new KF implementation with no matrix inversion. **(Participant, Simon Fraser University)**

(most useful) Pseudorange/tightly coupled navigation; unscented Kalman filter formulations; sigmaRho formulation for limited word length and fixed point implementation; filter health monitoring techniques; receiver clock modeling...very good course on the details of KF and GPS integration. The material presented was clear and concise and I now feel ready to dive deeper and start implementing *(Participants, Space Dynamics Laboratory, USU)*

Very comprehensive and intensive. Professor is so experienced and subject matter expert. *(Participant, JHU Applied Physics Laboratory)*

I didn't previously have any practical experience with Kalman filtering, but I have done a lot of work with max.likelihood parameter estimation. The KF machinery will give me another tool to apply to the system identification work I do**...(Participant, Sandia National Laboratories)**

Expansive coverage of the topics, issues & methods for GPS/INS navigation. Covers the ideas & methods without bogging down in the math. The INS navigation & correction methods were presented well. The complete coverage of the indivudal components of GPS/INS navigation was helpful. (P*articipant, Applied Research Labs, University of Texas*)

(most useful) Latest implementation methods, as well as enhanced knowledge of GPS. Practical implementation of Kalman filter and sensor modeling was extremely useful... **(Participant)**

(most useful) Practical aspects of applying KF to real world problems. Excellent! *(Participant, NEC Corp)*

(most useful) Learning the GPS/INS filter with error states. How to handle colored noise. How to handle modeling errors. *(Participant, Autonomous Solutions)*

(most useful) Discussion of integration of INS with other sensors; an appreciation for just how difficult the GPS position estimation problem is, and how easy the industry makes it appear. (general comments) Outstanding. I really enjoyed it...*(Participant, Applied Research Labs, University of Texas)*

(most useful) Wasy to identify when the filter is working. Tools learned in the developing the KF. *(Participant, Dexcom)*

(Most useful) Kalman filtering information and how to fix problems with it. How to combine KF and GPS, also hot to set up a state transition matrix etc. for a GPS. Very good pace, probably the best short course I have taken. *(Participant, JHU Applied Physics Laboratory)*

(Most useful) Understanding what GPS/Kalman filtering hardware is doing under the hood...Great course. Instructor is very knowledgable. *(Participant, Collision Analysis)*

(Most useful) The basic Kalman filter design and implementation. The software we use is already built to handle almost everything we need, but to maintain that software, I needed to understand the underlying principles...The course was very thorough and highly educational. Dr. Grewal definitely knew what he was talking about. *(Participant)*

Good briefing on KF and GNSS/INS with lot of things to do later on to build on this course. (Most useful).. implementation details/ error analysis of KF, GPS overview, a very good tutorial.* **(Participant)*

"Excellent...(most useful) Kalman filtering theory and implementation/engineering--tricks of the trade, things to watch out for, various approaches..." *(Participant)*

"Excellent depth of coverage of the theory and good breadth of application examples." *(Participant, Trimble)*

"The high level summary and introduction on Kalman filter and its applications on GPS and INS related projects are very beneficial in lighting up the directions for future potential applications."** (Participant)**

(Most useful) "Concept of continuous and discrete KF; KF tuning technique; tightly coubled INS/GPS system integration." *(Participant)*

Better than expected. Great discussion of fundamentals of KF and covariance analysis. Discussion of mitigation for numerical precision type errors (UDU^T, sigmaRho, etc.) and avoidance of matrix inversion in the KF algorithm was very helpful. *(Participant, MTSI)*

I learned more than expected...This course was an excellent intro to the KF, its variations and applications. Highly recommended. Dr. Grewal has extensive experience which comes through in the lectures and addressing questions that arise. *(Participant)*

Dr. Grewal has an excellent teaching style--you can tell he's an expert in his field, yet he's still able to break things down to a level that others can learn and understand. *(Participant, MTSI)*

The course provided me with excellent ideas about KF evaluation, difference between linear KF, linearized KF, EKF, and Weiner filter...(and) what mistakes people usually do when they design KF. *(Participant, Ag Leader)*

Most useful--The details about different kind of noise types, and how we must model them in the filter design; the details in the implementation of the filter to sensor fusion. The details about noise characteristics and how the KF designer must deal with that problem is very important for us. *(Participant)*

It gave me great insight to implement IMUs in my project and will greatly help my work out. (*Participant, US Army Picatinny Arsenal)*

The different Kalman (filtering) applications will be very helpful regarding implementation and processing time... Very informative! *(Participant)*

I was very pleased with the course and believe that this information will come in handy down the line...*(Participant)*

It was better than expected! *(Participant)*

The instructor is thoroughly grounded in the practical real life application of the Kalman filter... *(Participant, National Research Council of Canada)*

(most useful) Using Kalman filters in the application of geo-locating where a gimbaled camera is "looking" when mounted in an aircraft. Liked the recommendations of best methods to use in real-time applications, considering available processor speed, memory and available sensors (gyros, accels., etc.) *(Participant, Innovative Intuitive Technology, Inc.)*

Excellent. It is a pleasure to learn the material from someone that is not just a mathematician, but a practicing, experienced veteran. The practical insights and intuition were invaluable and made the whole course. *(Participant, Sensor Platforms, Inc. )*

Great course, great approach to real world problem. This approach is really missing in many Kalman filter courses. …*(Participant, NAVCOM Technology )*

This was by far the best professional development technical training course I have ever attended. I now understand intuitively how a KF works and what are the various techniques for testing their performance……*(Participant, MTSI )*

Dr. Grewal presents the material with clarity and insight. *(Participant )*

Well done! It was definitely worth my time and will aid me in my current work. *(Participant, ENSCO, Inc. )*

Great course, great professor…lot of practical examples. *Participant, SeekTech, Inc. )*

(Most useful) Concepts and tricks to getting Kalman filters to work in the real world. How to build and tune the models, choose states, apply pre-filters or shape filters, determine unknowns, etc. ……*(Participant, Pinnacle Technologies )*

(Most useful) The error/noise modeling, insight in how you can know the filter is working properly………*(Participant)*

…Days 2 and 3 were worth the price of admission alone…Dr. Grewal did an excellent job of explaining/clarifying some issues that I was uncertain on……*(Participant, McMaster University )*

This was exactly what I was looking for…Thanks for gearing it towards the practical applications…*(Participant, Sierra Nevada Corporation )*

The course exceeded my expectation regarding application to real-world problems (Most useful) GPS/INS integration, tightly and loosely coupled…Excellent course and instructor. Dr. Grewal is amazingly knowledgeable on material and real-world examples. …*(Participant, MTSI )*

“Course met all my expectations. Great presentation. Instructor was extremely knowledgeable and presented information clearly, concisely at an understandable level. *(Most useful will be)* INS & GPS error modeling, KF equation implementation, GPS/INS integration techniques. Course material was logically presented with theory to implementation using MATLAB. I will recommend this course to other colleagues.” *(Participant, Holloman AFB)*

(Most useful will be)* *“data fusion/two sensors tight coupling, UDU^{T} algorithm, suggestions from the experience of Dr. Grewal. Very complete and interesting, good notes.” *(Participant)*

* *“…a positive and useful course…large amount of reference material will be useful...” *(Participant, Space Exploration Technologies)*

(Most useful will be) “…understanding how to use the covariance matrix and residues to monitor the performance.” *(Participant)*

* *“…a very good course. It covers a lot in 5 days....” *(Participant)*

* *“…I find that the GPS and INS integration with examples to the Kalman filter is most useful to me. Good and detailed course notes (are) very useful...” *(Participant)*

(Most useful will be)* *“data fusion/two sensors tight coupling, UDU^{T} algorithm, suggestions from the experience of Dr. Grewal. Very complete and interesting, good notes.” *(Participant)*

(Most useful will be)* *“the fundamental concept of Kalman filtering and …the knowledge to be able to work with others in this field of applications. Very good. Now I have a precise understanding of the different DOPs, even though I have worked with it for many years.” *(Participant, Aerospace Corporation)*

(Most useful will be)* *“introduction to terminology and concepts in order to further research and learn the subject material. Class discussion was very good…” (small class size). *(Participant)*

(Most useful will be)* *“Practical implementation of issues of Kalman filtering. MATLAB analysis files available and explained helps in post course studies.” *(Participant)*

"Most reassuring is this careful presentation of real world tricks needed to make it work and to trouble shoot it...It is certain that the real world implementation solutions I learned will let me save a lot of time. *(Participant, Bombardier Transport) *

"After years struggling with Kalman filters on various problems, I know now for the first time how every part fits together." *(Participant, Hermanus Magnetic Observatory)*

Most useful from the course-- "The usage of the discrete Kalman filter, extended Kalman filter, modeling techniques, and especially things that can go wrong and how to watch for them." *(Participant, NovAtel)*

Most useful from the course-- "Application and practical considerations, specifically with regards to INS and state augmentation." *(Participant, Hermanus Magnetic Observatory)*

"The course was quite in line with my expectations...well-organized and covered Kalman filtering extensively (both theory and applications). The examples were useful in understanding actual implementation of Kalman filtering in real-life practical applications. Dr. Grewal taught the course with tremendous energy...The interaction with other participants was...a good learning experience." *(Participant, HRL Laboratories)*

"This course was everything I expected. It gives a very detailed introduction to the Kalman filter...(Most helpful was) the textbook and software provided." *(Participant, National Imagery & Mapping Agency)*

Most helpful..."the examples; the willingness of Dr. Grewal to address all questions." *(Participant, NSWCDD Coastal Systems)*

"I liked the fact that the course started from first principles. The cross-referencing of the textbook with the notes will be very useful. I enjoyed the informal atmosphere." *(Participant, Philips Semiconductors) *

"Good course--suitable for individuals with a wide range of backgrounds and previous experience with Kalman filtering and GPS." *(Participant, NovAtel) *

"The theory and background for creating the Kalman filter were well done. The fact that you have applied filtering to many problems and discussed them with us was very helpful." *(Participant, NASA) *

"All the examples help to put things together to apply the filter in the real world and not only theoretically." *(Participant) *

"Yes, (the course was as expected). I wanted a good overview of Kalman filtering and its use in GPS and INS applications. I enjoyed the class and found it informative." *(Participant)*

"Very good course to understand both Kalman filter and GPS. Thank you!" *(Participant, Kasai Design Office Ltd.)** *

"The course was what I expected and more...Teacher very knowledgeable, Reference material very good...I would definitely recommend it to other engineers/scientists...great exposure to many applications of theory..." *(Participant, Boeing)*

"I was surprised that the non-linear problems were addressed in such a clear way, showing the applications of EKF, UDUT etc. in the real world." *(Participant, Brazilian Navy)*

"This class certainly gives a clear view of what is possible to achieve with the Kalman filter and what is not." *(Participant, Bombardier, Canada)*

"The mathematical formulas presented were very good. Slides were abundant and the book was very comprehensive." *(Participant, Bell Mobility Cellular, Inc.)** *

"Most helpful were the sequence charts, which show how to proceed. The second benefit is the people who are working using Kalman filters, though in different application areas." **(Participant, VTT Automation, Finland)**

The theoretical combined with the practical knowledge of the instructor is substantial...*(Participant, Kongsberg Aerospace & Defense, Norway**) *

"Most helpful was the level of discussion about what role each of the parts of the filter play. Q, R, P, the innovation matrix--all good discussions. It helped provide something of an intuitive feel for these items in a short (1 week) amount of time..."*(Participant, Boeing) *

"Most helpful were the practical, rather than theoretical emphasis of the material...the computer demonstration and implementation of Kalman filtering. Overall, I thought the class was extremely informative, covering a wide range of material in a short time period. Dr. Grewal shows his experience in his ability to clearly lecture and interact with this complex subject." *(Participant, Applied Physics Laboratory)*

"The applied nature was very helpful. I especially liked the tips for checking if the Kalman filter works. This course stimulated my enthusiasm for Kalman filters, GPS, and Navigation." *(Participant, Array Systems Computing)*

**Expansive coverage of the topics, issues & methods for GPS/INS navigation. Covers the ideas & methods without bogging down in the math. The INS navigation & correction methods were presented well. The complete coverage of the indivudal components of GPS/INS navigation was helpful.**

Kalman Filtering Consultant Associates

PO Box 17224

Anaheim, CA 92817

ph: 714-281-4619

fax: 714-281-4619

KFCAS