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Kalman filter structure in the task of inertial navigation
INS price for integrating system
Market for inertial product
What the wander angle is?
Consulting request
Lost GPS position recovery
DGPS doesn't work in all environments
Assistance with a new product
4 question on the book contents
Strapdown or platform ?
Problems with some formulas...
How to use the external sensor to correct the inertial ?

?Let us take a moving body whose no assumptions on its motion can be made. The trajectory in cartesian coordinates has to be estimated. Accelerometers and gyros are used to measure the 3 accelerations and 3 angular rates. Because of sensors errors, the trajectory will exhibit an error growthing with time and distance. Thus, a Kalman filter is used to blend inertial data with absolute position fixes (no matter what aiding system is used) regarding the complementary approach.
My question is on the structure on the Kalman filter. It is quite obvious that the measurement vector is the aiding x, y-positions. But what does the state vector really contain? 3 positions, 3 velocities, and pitch, roll, yaw angles? Provided we use the extended Kalman filter equations, are these state variables error variables or total dynamical quantities? Besides, should the state vector include necessarily additional state variable to describe the sensor error? Finally, how is formed the state transition matrix? I am clear with the strapdown equations, but I would like to check how they are linearised in a Kalman filter suited for an integrated strapdown inertial system.
Catherine Marselli
Research assistant at the Institute of Microtechnology (University of Neuchatel, Switzerland),

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?I am very happy to hear you have experence on the development of mobile mapping system with GPS/INS integrated CCD camera. I have been studied the mobile mapping system for 1 year. I prepared dual frequency GPS receivers and two digital cameras. Now I am going to purchase Inertial system. Also I have studied Pipeline inspection system using INS and caliper (ultra sonic). Therefore, I want to find INS with several size. Anyhow I want to receive the formal price list of INS, integrated GPS/INS system and processing software and so on. When I have received price list of INS series, I will order INS to you depending on price list.
Dr. Hong-Sic Yun
Department of Civil Engineering, Sungkyunkwan University, Korea

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?we do obtain <1m positions XYZ for more than 4h in real time, and more than 8h after post-processing, with our strapdown 32cm RLG Inertial Navigation Systems, in pure inertial solution. Would you foresee a market for our product in your range of activities An answer would be appreciated. Congratulations on your Web site.
Joel Gillet / Brad Benedict. Benco S.c. (281) 398-8585 [also at]

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?I am a french student and I study the inertial navigation system's structure. I cannot afford a book like the one you have written, nevertheless I need  somebody to  explain me what the "wander angle" is and why it is better to use such a frame for
navigation in the northern territories. Thank you.
Cyril Heliot, France

!Dear young collegue! For the determination of navigation parameters (velosity, pozition, attitude) is certain navigation frame the acceleration projections on   that frame have to be provided. In order to realize that, the gyroplatform (physical or calculated) has to be controled by the same angular velosity as a navigation frame. Above angular velocity is calculated in the on board computer using the accelerometer mesasurements and introduced into gyro torques. As a result, physical (local-level INS) or calculated  (strapdown INS) gyroplatform is precessed with the same angular velocity as a navigation frame. Assume, that the navigation frame is a local level frame. In this case  the local-level frame absolute angular in projection on "Up" axis is: OMEGAup = (Ve/R)tg(fi) + U sin(fi) and if (fi) tends to 90 degree than (OMEGAup) tends to infinity. It  means, that at very high latitude a large rotation about "Up" axis is  necessary to maintain the orientation of the local-level frame wherenever it is moved towards the East even by a small movement. It means that very powerful torque for the vertical channel has to be needed. This problem may be avoided by performing all computations in a coordinate frame, that does  not point North. Such a frame is called a "wander frame". In case a wander frame a control signal would not include the large  first component of local-level angular velosity, but only the second  component. The first component will be calculated only as a derivative of the wander angle. Using the wander angle one can easily to recalculate all  navigation parameters from the wander frame to the local-level frame.

I thank you very much for your reply. I had asked many american people, but they did not reply.
Cyril Heliot, France
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?I forward this email to you after reviewing the LIGS web site. I represent a manufacturer of acoustic positioning systems and we are interested in combining acoustic observations with an INS. Does LIGS, yourself or Dr Salychev offer consulting on such subjects? We would need help with INS component selection, integration and adjustment (I understand that this may not be a Kalman adjustment) development. Any help you can offer will be greatly apreciated.
Keith Vickery, Sonardyne International Ltd., Houston, Texas


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? I am a fourth year student at the Naval College in Amsterdam, field of study  Hydrographics. Me and a fellow-student are working on a paper about an  assignment provided by a Hydrographic Company based in The Hague, The  Netherlands. The assignment can be described as follows: During Hydrographic surveying a problem arises when there's a lose of  postion (provided by GPS) when the vessel sails under a bridge. Therefore an  online calculated position is needed to replace the lost GPS position. We  think this can be done by the use of a simple Kalman filter which can  calculate a predicted position based on know position from GPS. During a  simple Kalman filter calculation the heading and speed of the vessel is  needed. The heading can be obtained from the vessels gyro and the speed will  be an average speed calculated from earlier GPS postion readings.
Allthough we have some understanding of the working principle of the Kalman  filter we need to find more detailed information on how to use it for our purpose. We do hope you could help us on our quest for more knowledge.
Tigger , Naval College in Amsterdam, The Netherland


Thank you for your reply on my e-mail. For the moment I am trying to configure the Kalman filter for my purpose. Then the next step will be writing a programm in C++. Therefore I have been searching the internet for some programming structures for Kalman filters. When I encounter any problems which I am not able to solve, I do hope I can call on you again.
Tigger , Naval College in Amsterdam, The Netherland
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?Our application is positioning of geophysical equipment for unexploded ordnance and landmine detection. Precision required is 10cm over 50m. Size and weight are critical. I would appreciate any information on emerging technologies that might be of interest to us. DGPS doesn't work in all environements!
Peter J. Clark, Manager Environmental Services, Geophysical Technology Limited

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?I am writing to you to ask for your assistance with a new product . My US based company, Benchtie, has developed a new surveying marker that is currently being used by professional surveyors in the United States. The marker is a nail that can be inserted into a vertical surface such as a tree or telephone pole and still accept a prism pole or stadia rod. To learn more about this product, please visit our web site at   We are currently looking to take this product world wide and thought that you might be able to provide some assistance. If you could let us know some of the suppliers that you buy surveying products from it would be a tremendous help for us.  Also if you have any questions about the product or would like a free sample of it, please feel free to contact me via email or fax 201-242-0205. 
Ari Lehman Benchtie International Sales

!Dear collegues, unfortunatelly we have not very close connection with survey products end-users. Our field of activity is inertial technology and related applications, including geodetical and geophysycal survey. However, we can place your message on our web page for our Russian visitors .
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Mr. Min Xi, Agsystems Pty Ltd, Brisbane, Australia

1?I start to simulate the strapdown inertial navigation algorithm based on the book "Inertial Systems in Navigation and Geophysics" by Pref. Oleg Salychev at Matlab.By following the procedures that listed on page 72-73, 1. I found that I don't understand the Sculling compensation. The recurrent solution in equation 4.4 shows the integration of 8 samples data. I cannot see how the 8 samples are involved in this equation. It seems have 2 groups of updating routines, and I don't know which one I should apply. Would you explain it a little further?
!Sculling procedure realizes the cycle with 8 steps (equation 4.4) The output of three first equations play role of the input for the last three equations
2? When applying the quaternion calculation 2 (a correction of quaternionaccording to the change of the navigation frame), how can I initialize the ""?the projections of the absolute angular velocity of the navigation frame x, y, z on their axes?
! In order to initialize navigation algorithm you need to fulfill the following procedure:
a) Alignment (within this procedure  the initial parameters of quaterninon have to be determined)
b) You introduce the initial parameters such as initial longitude and lattitude of starting point.

3? How can I initialize the B matrix which can be used to determine the vehicles position of latitude and longitude, and used to calculate the velocity (equations 4.16, 4.17, 4.18)? I have been suggested to use the GPS reading (latitude, and longitude data) to initialize B matrix (equation 4.15). I wondering how people use only inertial sensor for navigation?
! For the initialization of B matrix you can use the eq. 4.15 where azimuth angle equals to zero, lattitude and longitude are the coordinates of the initial position. All teh INS use the apriori information on the initial position.  
4? This algorithm has included some error corrections and compensations. Can you explain what difference with psi-angle error model? Do I need to apply psi-angle error model after this algorithm procedure?
! Pure navigation algorithm for the verticat channel of INS is not used because the errors of channel has a very unstable behaviour. If you do not use the external information, such as barometric altimeter or GPS data you can assume that Vz=0. There is no contradiction in formulas (4.16) and (3.23) in sense og signs. Eq. (4.16) contains the compensation of Coriolis acceleration. This is a reason why above compensation has a reverse sign.

Dear Mr. Min Xi, we highly appreciate your attention to my book. But unfortunatelly, I am not able to keep answering to all of your questions because it takes more to a lectures courses in distance education program. We can offer it to you on a mutually beneficial basis. However the text of the book contains alredy the most of answers on your questions. Please read it carefully,
With best regards,
Prof . Oleg Salychev

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?While we know that a stable platform with conventional gyros suffers from schuler errors, we have had numerous discussions on whether laser ring gyros used in the strap down system of inertial navigation systems suffer from schuler errors or not.  I have a note that the strapdown platform is still subject to schuler loop usually at the first integrator level. Please can you clear this one up for me? Thank you.
! Note, that in principle, the local-level(platform) system and the strapdown system have the identical scheme. But, in the strapdown system instead the gyroplatform the calculation of the direction cosine matrix between body frame and navigational frame is used. Above matrix is actually the analitical image of the gyroplatform. It is a reason why the error behaviour of strapdown system has the similar Schuler oscillation as in platform system.  This problem is investigated in all the details in my book "Inertial Systems in Navigation and Geophysics". See our web page for more information about this book and how to get it. [go top]

1?Dear Mr. Salychev.
Thank you for your book on INS. However I am myself not so good in mathematics so I have problems with the formulation of some formulas. Do you want to be so kind to give me more information on that?
The formula on page 68 :
D_l_0 = 1 - D_j^2 / 8 + D_j^4/348
Do you mean: D_j^2 =
D_j * (D_j)T and D_l_0 = the norm (square root of the sum of the square terms)
Thanks in advance. Hugo Marien, Software Engineer
Belgian Road Research Center

!The series expansion of sin(x), cos(x) are

  Substituting in above formula 

And using equation (4.11) the expression (4.12) can be determinated. [go top]
2?Dear Professor Salychev,
Sorry to bother you again but I am trying to develop an INS system using a DMU-AHRS from Crossbow/USA ( ). I have difficulties with the alignment formulas 4.27 and 4.28 in your book. What is the meaning of k? In formula 4.30, k is defined as 2 * c *
W . What is W_0 and c ? Further how fits the stored azimuth alignment in the alignment procedure, given that the initial quaternion q0 = [1 0 0 0]T
!The selection of K, Kb coefficients makes the influence on the error damping process. The Kb is responsible for the frequency of process damping.  Kb= W_0^2/g. If you select the large magnitude of Kb, the error transiction process would be short but noisy if small then long, but smooth. It is a reason why the reasonable solution is to select the large magnitude for coarse alignment and small one fir the fine alignment.
Crossbow is very rough IMU and can't realize pure inertial mode. In this case the INS/GPS integration in close-loop Shuler mode can be used.

?Dear sir, I am student working in the field of aiding inertial navigation from other sources such as camera for mobile robot. Can you  explain to me how I can use the external sensor to correct the inertial. I mean the structure of kalman filter and is it there any programs in matlab to implement extended kalman filter.
Thank you very much JLETA@EUnet.yu
!In order to develop Kalman filter for INS and external device integration you need to create the INS error model as a model for Kalman filter and the difference between INS and extrenal device indications as a measurement. I really doubt that you can reach something usefull in Mathlab.


This page was last updated   20.12.00