However, since the navigation computer deals only with "computed” quantities gj^), the equations actually -mechanized are: W <^c'c = ^ (“IC" ■Hf ^*^0 “ ■ “’ec where = accelerometer outputs = See Reference 2 or 3. 8. Nash, R.A. The computer Integrates the mechaniza- tion equations in the frame defined by its output. navigate to this website
Under these conditions Eq. (4-1) reduces to Eq. (2-3) hence demonstrating the dynamic exactness of the aided system. and Roy, K.J., "Integrated Navsat/Inertlal Flight Test Analysis", Chapt. 2, The Analytic Sciences Corp., Report No. VECTOR FORMULATION OF MECHANIZATION AND ERROR EQUATIONS FOR AN UNDAMPED INERTIAL SYSTEM 2-1 2.1 Unified Equation Subset 2-1 2.2 Notation and Definitions for the MechaJiization Equations 2-2 2.3 Mechanization Equations 2-2 Equations (B-9) through (B-14) m conjmiction with Eqs. (4-13) - (4-16), (4-25) and (4-26) of the text provide the complete error dynamics description of a local-level, wander azimuth INS mechaniza- tion http://shodhbhagirathi.iitr.ac.in:8081/jspui/handle/123456789/9102
The relations between errors in space-stable and local-level systems are noted. an earth fixed frame non gravitational force on vehicle (ideal accelerometer output) g(R) = plumb bob gravity force on vehicle The S (true) frame is the coordinate frame in which the VECTOR FORMULATION OF MECHANIZATION AND ERROR EQUATIONS FOR AN UNDAMPED INERTIAL SYSTEM 2. 1 UNIFIED EQUATION SUBSET A vector formulation of the navigation mechanization and error equa- tions is presented in
Heller Analytic Sciences Corporation Prepared for; Defense Mapping Agency Aerospace Center 18 April 1975 DISTRIBUTED BY: National Technical Information Service U. THE ANALYTIC SCIENCES COnPORATIDN n ■ angular rate of earth fixed axes with respect to inertial space smgular rate of S frame w. The gyro which censes rotation about the vertical is untorqued* and, as a result, the platform will not maintain a particular terrestrial head- ing reference. g(R,g) - . (T) X Subtracting Eq. (A. 1 -3) from Eq. (A. 3-11) then gives Eq. (A. 3-8).
The vectors V, S, and g in Eqs. (2-1) and (2-2) are the "truo" position, velocity, specific force, and gravity acceleration. A resultant loss of generality occurs. 3. I I U 0 THE ANALYTIC SCIENCES CORPORATION damping variable, V^, is zero. http://adsabs.harvard.edu/abs/1982guco.conf..266C In general, for no limitations on rates of motion the error 2-5 TtWE ANALYTIC SCIENCES CORPORATION INHIAl CCXOTIONS GYRO DRIFT RATE ERRORS INITIAL OONOmONS ACCELEROMETER ERRORS GRAVITY DISTURBANCES 1 L EARTH
Note that the solution of Eq. (2-8) for the computer to platform mis- alignments is Independent of the position and velocity error equations (Eqs. (2-6), (2-7)). Treatment of this topic as part of the alignment proceedure may be found in Refs. 2 and 10 within the sections describing earth-rate gyrocompassing. Heller (. The detailed form of the error equations is given for both the free-inertial case and various choices of continuous damping. 1 1 i I i I 1 t iii THE ANALYTIC
The angle ^ results from errors in computed position with components given by: 3-6 THE ANALYTIC SCIENCES CORPORATION ®N ■ R (3-18) ~TT (3-19) tan L (3-20) The components of the https://books.google.com/books?id=SeyZHdb6Ts8C&pg=PA242&lpg=PA242&dq=error+analysis+of+space-stable+inertial+navigation+systems&source=bl&ots=p0Nwmpg_la&sig=_U6tPYtDyWRd7s22Nj3vgtafkeY&hl=en&sa=X&ved=0ahUKEwiEyfzX9cfPAh DMA700-74-C-0075 . In expanded (component) form, the velocity error Eqs. (2-6) become; 5Vn = cos a + My sin a - - I * gi -(2 n sin L + ^ tan l) The damping state variable, and Eq. (4-2) become redundant in this case. ■s •s a I u :i u I ( I 1 4.3.2 Earth Loop Damping Mechanization While a complete
The heuristic reasoning for this approach Txins somewhat like this. useful reference Expansion of the general vector equations in a form specific to a local-level INS mechanization is demonstrated in Chapter 3. Tliese are the errors of interest in analysis. 3-4 THE ANALYTIC SCIENCES CORPORATION 2. At worst the error in computing the centripedal term in g(R) is two orders of magnitude less than that obtained in computing the mass attraction gravitational force, gj^.
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As a consequence, the cruise inertial navigation systems used in mcdern aircraft and submarines are normally aided or ’’damped" with data from external aids, such as: • altimeter or depth gauge The dynamics they describe must be invariant with regard to the reference system in which they are cast. In this instance the velocity reference is doppler radar.
B = e(6R) (2-13) The small angular misalignment, 0 , between the platform frame and the true frame (platform "tilt") is given by: 0 = ■? + 5^ (2-14) where positive Because this is the same process as is used in g>'fo- compassing (when the reference velocity is accurately known to be zero) it is referred to (in the aircraft case) as I (Vc>c = * i («C. - (-IC * n) X - Kj - V ) * L»d d 3t ^'ec 0 0 Ci(h-h^) (4-21) (4-22) The equation for the additional TAUI HEADING INDICATED HEADING - heading error A2IMUTM ERROR Figure 3-2 Azimuth and Heading Error Sigii Conventions 3-7 THE ANALYTIC SCIENCES CORPORATIQN Equations (3-9) through (3-20) and Eq. (3-23) comprise the
and Edwards, A., "Introduction to Doppler-Inertial System Design," Journal of the American Rocket Society, December 1959. " 1C. r.t. Detailed models of error sources v/ill bo presented in tlie third ec|uation subset. *"Dynamically exact" implies that if there were no instrument measuring errors or initial alignment errors, the INS outputs http://axishost.net/error-analysis/error-analysis-of-multihop-free-space-optical-communication.php But this Is precisely Eq. (A. 1-3) and the computer does indeed generate i r- THE ANALYTIC SCIENCES COnPORATION A. 3 THE ERROR EQUATIONS From the foregoing discussion the computer actually
Extensions of these equations which apply to continuous speed and altitude damping are also given. Du'oretzky, L.H. Of + Q L + tsji l) (3-6) Because the Z gyro is untorqued, the i^ component of ijg is zero. Specific application of the general equations to the local-level, wander -azimuth mechanization is outlined.
This simplifies the form of the equations and still provides all of the feedback which will significantly improve the navigation errors. For the N, E, Z frame solution it is necessary to project the sensor errors, u and 7 wliich are given in X, Y coordinates into components along tlie N, E e. , vehicle acceleration due to all forces acting except gravity (ideal accelerometer output) g(R) = Plumb bob gravity acceleration on vehicle 7i = Angular rate of earth fixed axes \vith Detailed error models and treatment of errors in ex- ternally derived measurements will be deferred until the third equation subset.
TITLt JwMK/*; Frtt-IiMrt1i1 ind D«iptd-Inert1i1 Navigation Hichanizatlon and Error Equations 7. Sign on SAO/NASA ADS Physics Abstract Service Find Similar Abstracts (with default settings below) · Reads History Translate This Page Title:A time-invariant error model for a space-stable inertial Neglecting the earth's ellipticity can cause position errors on the order of ten nautical miles (Ref. 3). R. , Inertial Na vig.ation System Analysis, Jolni Wiley and Sons, 1971, pp. 83 ff, p. 113.
Instead, the expressions (2-13), (2-1 4) can be substituted into Eqs. (2-6) to (2-8) and the error equation set expressed in terms of the platform misalignment angles, 0 , instead of