BS EN 16603-60-10:2014 BSI Standards Publication Space engineering — Control performances BS EN 16603-60-10:2014 BRITISH STANDARD National foreword This British Standard is the UK implementation of EN 16603-60-10:2014 The UK participation in its preparation was entrusted to Technical Committee ACE/68, Space systems and operations A list of organizations represented on this committee can be obtained on request to its secretary This publication does not purport to include all the necessary provisions of a contract Users are responsible for its correct application © The British Standards Institution 2014 Published by BSI Standards Limited 2014 ISBN 978 580 84090 ICS 49.140 Compliance with a British Standard cannot confer immunity from legal obligations This British Standard was published under the authority of the Standards Policy and Strategy Committee on 30 September 2014 Amendments issued since publication Date Text affected BS EN 16603-60-10:2014 EN 16603-60-10 EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM September 2014 ICS 49.140 English version Space engineering - Control performances Ingénierie spatiale - Performance de systèmes de contrôle Raumfahrttechnik - Steuerungsleistung This European Standard was approved by CEN on March 2014 CEN and CENELEC members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN and CENELEC member This European Standard exists in three official versions (English, French, German) A version in any other language made by translation under the responsibility of a CEN and CENELEC member into its own language and notified to the CEN-CENELEC Management Centre has the same status as the official versions CEN and CENELEC members are the national standards bodies and national electrotechnical committees of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels © 2014 CEN/CENELEC All rights of exploitation in any form and by any means reserved worldwide for CEN national Members and for CENELEC Members Ref No EN 16603-60-10:2014 E BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) Table of contents Foreword Introduction Scope Normative references Terms, definitions and abbreviated terms 3.1 Terms from other standards 3.2 Terms specific to the present standard .9 3.3 Abbreviated terms 14 Performance requirements and budgeting 15 4.1 4.2 Specifying a performance requirement 15 4.1.1 Overview 15 4.1.2 Elements of a performance requirement 16 4.1.3 Elements of a knowledge requirement 16 4.1.4 Probabilities and statistical interpretations 17 Use of error budgeting to assess compliance 17 4.2.1 Scope and limitations 17 4.2.2 Identification and characterisation of contributors 18 4.2.3 Combination of contributors 19 4.2.4 Comparison with requirement 21 Stability and robustness specification and verification for linear systems 23 5.1 Overview 23 5.2 Stability and robustness specification 24 5.2.1 Uncertainty domains 24 5.2.2 Stability requirement 26 5.2.3 Identification of checkpoints 26 5.2.4 Selection and justification of stability margin indicators 27 5.2.5 Stability margins requirements 27 5.2.6 Verification of stability margins with a single uncertainty domain 28 BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) 5.2.7 Verification of stability margins with reduced and extended uncertainty domains 28 Annex A (informative) Use of performance error indices 29 A.1 A.2 Formulating error requirements .29 A.1.1 More about error indices 29 A.1.2 Statistical interpretation of requirements 30 A.1.3 Knowledge requirements 32 A.1.4 Specifying the timescales for requirements 32 More about performance error budgets 34 A.2.1 When to use an error budget 34 A.2.2 Identifying and quantifying the contributing errors 35 A.2.3 Combining the errors .36 A.2.4 Comparison with requirements 38 Annex B (informative) Inputs to an error budget 40 B.1 Overview 40 B.2 Bias errors 41 B.3 Random errors 42 B.4 Periodic errors (short period) 44 B.5 Periodic errors (long period) 44 B.6 Distributions of ensemble parameters 45 B.7 Using the mixed statistical distribution 48 Annex C (informative) Worked example 49 C.1 Scenario and requirements .49 C.2 Assessing the contributing errors 50 C.3 Compiling the pointing budgets .52 Annex D (informative) Correspondence with the pointing error handbook 54 References 55 Bibliography 56 Figures Figure A-1 : Example showing the APE, MPE and RPE error indices 30 Figure A-2 : Example showing the PDE and PRE error indices 30 Figure A-3 : Example of a statistical ensemble of errors 31 Figure A-4 : The different ways in which a requirement for P(|ε| 0,9 can be met 32 Figure A-5 : Illustration of how the statistics of the pointing errors differ depending on which statistical interpretation is used 32 BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) Figure C-1 : Scenario example .50 Tables Table B-1 : Parameters whose distributions are assessed for the different pointing error indices (knowledge error indices are similar) 41 Table B-2 : Budget contributions from bias errors, where B represents the bias 42 Table B-3 : Budget contributions from zero mean Gaussian random errors 43 Table B-4 : Uniform Random Errors (range 0-C) 43 Table B-5 : Budget contributions for periodic errors (low period sinusoidal) 44 Table B-6 : Budget contributions for periodic errors (long period sinusoidal) 45 Table B-7 : Some common distributions of ensemble parameters and their properties 47 Table C-1 : Example of contributing errors, and their relevant properties 51 Table C-2 : Example of distribution of the ensemble parameters 52 Table C-3 : Example of pointing budget for the APE index 53 Table C-4 : Example of pointing budget for the RPE index 53 Table D-1 : Correspondence between Pointing error handbook and ECSS-E-ST-60-10 indicators 54 BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) Foreword This document (EN 16603-60-10:2014) has been prepared by Technical Committee CEN/CLC/TC “Space”, the secretariat of which is held by DIN This standard (EN 16603-60-10:2014) originates from ECSS-E-ST-60-10C This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by March 2015, and conflicting national standards shall be withdrawn at the latest by March 2015 Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights This document has been prepared under a mandate given to CEN by the European Commission and the European Free Trade Association This document has been developed to cover specifically space systems and has therefore precedence over any EN covering the same scope but with a wider domain of applicability (e.g : aerospace) According to the CEN-CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) Introduction This standard focuses on the specific issues raised by managing performance aspects of control systems in the frame of space projects It provides a set of normative definitions, budget rules, and specification templates applicable when developing general control systems The standard is split up in two main clauses, respectively dealing with: • Performance error indices and analysis methods • Stability and robustness specification and verification for linear systems This document constitutes the normative substance of the more general and informative handbook on control performance, issued in the frame of the E-6010 ECSS working group If clarifications are necessary (on the concepts, the technical background, the rationales for the rules for example) the readers should refer to the handbook NOTE It is not intended to substitute to textbook material on automatic control theory, neither in this standard nor in the associated handbook The readers and the users are assumed to possess general knowledge of control system engineering and its applications to space missions BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) Scope This standard deals with control systems developed as part of a space project It is applicable to all the elements of a space system, including the space segment, the ground segment and the launch service segment It addresses the issue of control performance, in terms of definition, specification, verification and validation methods and processes The standard defines a general framework for handling performance indicators, which applies to all disciplines involving control engineering, and which can be applied as well at different levels ranging from equipment to system level It also focuses on the specific performance indicators applicable to the case of closed-loop control systems – mainly stability and robustness Rules are provided for combining different error sources in order to build up a performance error budget and use this to assess the compliance with a requirement NOTE Although designed to be general, one of the major application field for this Standard is spacecraft pointing This justifies why most of the examples and illustrations are related to AOCS problems NOTE Indeed the definitions and the normative clauses of this Standard apply to pointing performance; nevertheless fully specific pointing issues are not addressed here in detail (spinning spacecraft cases for example) Complementary material for pointing error budgets can be found in ECSS-EHB-60-10 NOTE For their own specific purpose, each entity (ESA, national agencies, primes) can further elaborate internal documents, deriving appropriate guidelines and summation rules based on the top level clauses gathered in this ECSS-E-ST-60-10 standard This standard may be tailored for the specific characteristic and constrains of a space project in conformance with ECSS-S-ST-00 BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) Normative references The following normative documents contain provisions which, through reference in this text, constitute provisions of this ECSS Standard For dated references, subsequent amendments to, or revision of any of these publications not apply, However, parties to agreements based on this ECSS Standard are encouraged to investigate the possibility of applying the more recent editions of the normative documents indicated below For undated references, the latest edition of the publication referred to applies EN reference Reference in text Title EN 16601-00-01 ECSS-S-ST-00-01 ECSS System – Glossary of terms BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) B.4 Periodic errors (short period) By short period, it is meant that the timescale of variation is much shorter than the averaging time used in the indices, so that the average of the error is zero (any non-zero average can be treated as a separate bias-type error) The distribution of the error can be found assuming that it has sinusoidal form Table B-5 shows the appropriate means and distributions to be used See B.6 for discussion of how to find distributions of the ensemble parameter A (amplitude of the periodic error) It is worth mentioning that there is a lot of literature dealing with the relationship between time and frequency domains requirements using the RPE, some of the relevant techniques being already in use in the industry Refer for example to [1] Table B-5: Budget contributions for periodic errors (low period sinusoidal) Index APE S.I E T Distribution Notes P(e) µ(e) σ(e) P(A) µA σA For P(A), µA and σA see B.6 A WC AWC = worst case A π -1 (A WC - e )(A WC + e ) M ∫ (e | A )P(A )dA MPE All 0 RPE All PDE All PRE All 2 A For P(A), µA and see B.6 For derivation see B.7 No MPE for low period errors As for APE No mean so RPE, APE same No contribution No change over time so no contribution to PDE, PRE NOTE: Zero mean is assumed; if a non-zero mean is present it can be treated as a separate bias-type error B.5 Periodic errors (long period) By long period, it is meant that the timescale of variation is much longer than the averaging time used in the indices, so that to a good approximation the index does not change during an observation The distribution of the error can be found assuming that it has sinusoidal form Table B-6 shows the appropriate means and distributions to be used See B.6 for discussion of how to find distributions of the ensemble parameter A 44 BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) Table B-6: Budget contributions for periodic errors (long period sinusoidal) Inde x APE Distribution S.I E P(e) P(A) T π -1 σ(e) µA σA For P(A), µA and σA see B.6 A WC AWC = worst case A (A WC - e )(A WC + e ) M ∫ P(ε | A )P(A )dA MPE All As for APE RPE All E P(2A ) = 12 P(A ) PDE PRE π −1 Notes µ(e) A For P(A), µA and see B.6; For derivation see B.7 0 2µA 2σA Actual values depend on the definitions of PDE, PRE These values are computed assuming a worst case where the intervals are taken ½ period (time T/2) apart, so that δe= 2e T (2A WC - e )(2A WC + e ) A WC M ∫ P(δe | A )P(A )dA σA All As for PDE NOTE: Zero mean is assumed; if a non-zero mean is present it can be treated as a separate bias-type error B.6 Distributions of ensemble parameters In Clauses B.2 to B.5 the error statistics (in ensemble or mixed interpretations) depend on the statistics of the ensemble parameters A (periodic), B (bias), C (uniform random) and s (Gaussian random) For a general ensemble parameter, x, we need to be able to determine the probability distribution of x given the data available, in particular the mean and standard deviation Case 1: measured data If a measurement is made of the parameter x, this gives a measured value plus some error range, xest ± δx, where δx corresponds to the n-σ level of a Gaussian In this case the appropriate distribution is a Gaussian with: µx = xest, σx = δx /n This is appropriate for example for the measured bias of a sensor Case 2: bounds known, distribution not known If it is known that X is in the range xmin to xmax, and that intermediate values are possible, but no other information is available, then the appropriate distribution is a uniform distribution between these bounds This is appropriate for example for alignment using shimming Case 3: PDF of ensemble parameter known In such case the relevant properties can be extracted directly from the probability distribution: µ x = ∫ xP( x)dx σ= x ∫ (x − µ ) x , P( x)dx , 45 BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) x = ∫ x P( x)dx This can occur if the physical process underlying the ensemble is known well enough to predict its behaviour An example is a pointing error caused by position uncertainty, in which the distribution of the ensemble parameter can be obtained knowing the uncertainties in the process of determining the orbit Table B-7 gives some common distributions used to describe ensemble parameters, and their important properties 46 EN 16603-60-10:2014 (E) Table B-7: Some common distributions of ensemble parameters and their properties Distribution P(x) Name Delta Gaussian Uniform P( x) = δ ( x − µ ) x − µ 2 = P( x) exp − σ 2π 2 σ P( x) = xmax − xmin for xmin < x < xmax P ( x) = otherwise Bimodal (PDF for sinusoid) P( x) = π −1 ( xmax − x )( x − xmin ) P ( x) = otherwise for xmin < x < xmax Mean µx Variance σx2 RMS µ µ σ2 xmax + xmin ( xmax − xmin ) 3 xmax − xmin 12 3( xmax − xmin ) xmax + xmin ( xmax − xmin ) 2 µ µ2 + σ x = 2 x max + x + x max x 47 BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) B.7 Using the mixed statistical distribution When using the mixed statistical interpretation, there is a different temporal distribution (i.e behaviour over time) for each value of the ensemble parameter When taking the mean or variance, the appropriate PDF to quantify is the distribution over both time and ensemble: P( x ) = ∫ P( x | A) P( A) dA Where normalisation constants are omitted However, rather than computing this distribution and then finding µ and σ, there is a simpler way Starting from the definition of the mean µ x = ∫ xP( x)dx Substituting the above expression for P(x) and doing some manipulation gives (∫ P(x | A) P( A) dA)dx = ∫ ( ∫ x P( x | A) dx )P( A) dA µx = ∫ x = ∫ µ x ( x | A)P( A) dA That is, the overall mean can be found using the distribution of A providing that the mean is known for a given value of A Similarly for the variance σ2: σ x2 = ∫ σ x2 ( x A) P( A)dA This avoids computing the full distribution P(s) For example, suppose that we have a noise error with a zero mean Gaussian distribution over time: = P( x S ) 2π S x2 2S exp − In this case the ensemble parameter is the temporal standard deviation, S, and for a given value of S µ=0 and σ=S If we know that S lies between and Smax, but nothing else, then assuming a uniform distribution gives = µx µ ( S ) P ( S ) dS ∫= = σ x S max σ ( S ) P ( S ) dS ∫= S (1/ S ) ds ∫= 2 max Which is much easier than finding the full distribution Smax = P( x) ∫ 48 1 S max 2π S x2 dS 2S exp − S max BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) Annex C (informative) Worked example C.1 Scenario and requirements Consider a simple scientific spacecraft, whose objective is to take images of various star fields, as shown in Figure C-1 Attitude measurement is done using a star sensor, attitude control using reaction wheels The requirements (formulated according to the recommendations of Clause 4.1) on the spacecraft are: • “The APE on the payload boresight shall be less than 20 arcsec about the y and z axes (the axes perpendicular to the boresight) and less than arcmin about the xaxis (i.e about the boresight)” • “The RPE on the payload boresight shall be less than 10 arcsec about the y and z axes (the axes perpendicular to the boresight) and less than 30 arcsec about the xaxis (i.e about the boresight), i.e no more than half the error can be due sources which vary on short timescales The timescale RPE is taken to be 30 seconds (the payload integration time)” • “These requirements should be met for 95 % of the time using the ‘mixed’ statistical interpretation” These requirements are derived from the payload parameters, such as field of view, pixel size, integration time and so on, as shown in Figure C-1 This derivation is beyond the scope of this note and so is not done here NOTE The example presented in this Annex is intended to illustrate the specification and budgeting procedure described in the standard, and does not intend to represent a real or even realistic spacecraft NOTE The performance budgets worked out in this Annex (clauses C.2 and C.3) are strictly based on the method described by Clause 4.2 (in particular the summation rules) 49 BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) y Attitude determination using star tracker z x Target star Payload Target imaged on payload detector grid Figure C-1 : Scenario example C.2 Assessing the contributing errors For this example, the contributing errors can be classified into groups: • Measurement errors The attitude measurement error of the star sensor is separated into two parts: an attitude dependent bias, and a timedependent term It is assumed that the distribution of the time varying errors (after filtering) is known exactly, but that of the attitude errors is not • Control errors The error in reaching the (measured) target frame For the purpose of this example this also includes actuator errors (e.g reaction wheel noise) as well as errors due to the controller itself The resulting error distribution is assumed to be Gaussian, with a standard deviation (ensemble parameter) which is itself described by a Gaussian distribution • Targeting errors The dominant contribution here comes from the error in knowing the exact spacecraft position along its orbit, and hence the error varies sinusoidally at the orbital period • Structural errors The payload and the star sensor both have some misalignment with respect to the nominal body reference frame, so even after calibration there remains some misalignment between the two In addition there is a thermoelastic distortion of the spacecraft, assumed to vary at the orbit period Table C-1 summarises these errors, together with their important properties In order to provide some numerical inputs to the budget, the numerical values of the ensemble distribution are assumed to be those given in Table C-2 Note that these values are for illustration only, and are not necessarily representative of any given mission 50 BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) Note also that correlations between errors are not considered for this simple example Table C-1 : Example of contributing errors, and their relevant properties Temporal behaviour Error Period Ensemble distribution STR time-dependent errors (after filtering) Random Less than observation period Delta function (value known) STR attitude dependent bias Bias observation period Gaussian (variance known) Controller and actuator errors Random Less than observation period Gaussian (variance known) Thermoelastic distortion STR & payload Sinusoidal (assumed) Orbit period Uniform (range known) Payload –STR misalignment after calibration Bias Does not vary Uniform (range known) Targeting error due to position knowledge Sinusoidal Orbit period Gaussian (variance known) Flexible modes & fuel slosh Sinusoidal (assumed, not generally so simple) Less than observation period Gaussian (variance known) The choice of the ensemble parameter distribution is different for each error: • The time dependent star sensor errors are assigned a delta-function distribution This means that the value of the ensemble parameter (i.e the noise level) are essentially known exactly • The thermoelastic distortion and payload/star sensor misalignment are assigned uniform distributions This means that their bounds can be identified, but not the behaviour between them (see B.6) • The other errors are assigned Gaussian distributions, meaning that a distribution of their possible values is known For example, the targeting error is related to the initial position error, and even though this is not known a-priori we can predict the probability of it having a particular value More details are given in Annex B 51 BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) Table C-2 : Example of distribution of the ensemble parameters Error Ensemble parameter E dim Distribution of ensemble parameter P(E) µE σE STR timedependent errors Standard deviation over time x δ(10”) 10,0” 10,0” y δ(5”) 5,0” 5,0” z δ(5”) 5,0” 5,0” STR attitude dependent bias Value of bias x G(0, 6.67”) 6,67” 6,67” y G(0, 3.33”) 3,33” 3,33” z G(0, 3.33”) 3,33” 3,33” x G(1”,3”) 1,00” 3,00” 3,16” y G(1”,3”) 1,00” 3,00” 3,16” z G(1”,3”) 1,00” 3,00” 3,16” Controller and actuator errors Standard deviation over time Thermoelastic distortion STR & payload Amplitude of sinusoidal variation x U(0, 4”) 2,00” 1,15” 2,31” y U(0, 4”) 2,00” 1,15” 2,31” z U(0, 4”) 2,00” 1,15” 2,31” Payload –STR misalignment Value of bias x U(-5”,5”) 2,89” 2,89” y U(-5”, 5”) 2,89” 2,89” z U(-5”,5”) 2,89” 2,89” x G(0, 5”) 5,00” 5,00” y G(0, 1”) 1,00” 1,00” z G(0, 5”) 5,00” 5,00” x G(0, 3”) 3,00” 3,00” y G(0, 5”) 5,00” 5,00” z G(0, 3”) 3,00” 3,00” Targeting error due to position knowledge Amplitude of sinusoidal variation Flexible modes & fuel slosh Amplitude of sinusoidal variation ΝΟΤΕ C.3 δ(A) = delta function, G(µ,σ) = Gaussian distribution with specified mean and standard deviation, U(A,B) = uniform distribution with bounds A and B Compiling the pointing budgets Using the values in Table C-2, the contributions to the pointing budgets for the APE and RPE indices can be worked out using the formulae given in annex B Since the mixed statistical interpretation is being used here, all of the errors in the budget have zero mean, even if the ensemble parameter has non-zero mean This is not the general case Combining the contributing standard deviations using the formula from Clause 4.2.3, it can be shown that the APE is compliant with the requirement (20 arcsec about y and arcmin about x) However the RPE budget is not compliant with the requirement, as the short term variations are too large 52 BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) Table C-3 : Example of pointing budget for the APE index σ (arcsec) Error Formula from: x y z STR time-dependent errors 10,0 5,0 5,0 Table B-3 STR attitude dependent bias 6,67 3,33 3,33 Table B-2 Controller and actuator errors 3,16 3,16 3,16 Table B-3 Thermoelastic: STR & payload 1,63 1,63 1,63 Table B-6 Payload –STR misalignment 2,89 2,89 2,89 Table B-2 Targeting error (position knowledge) 3,54 0,71 3,54 Table B-6 Flexible modes & fuel slosh 2,12 3,54 2,12 Table B-5 Total (RSS): 13,51 8,37 8,61 Total x (for 95 % confidence): 27,01 16,75 17,21 60 20 20 Original requirement: APE budget compliant Table C-4 : Example of pointing budget for the RPE index σ (arcsec) Error Formula from: x Y z STR time-dependent errors 10,0 5,0 5,0 Table B-3 STR attitude dependent bias 0,0 0,0 0,0 Table B-2 Controller and actuator errors 3,16 3,16 3,16 Table B-3 Thermoelastic: STR & payload 0,0 0,0 0,0 Table B-6 Payload –STR misalignment 0,0 0,0 0,0 Table B-2 Targeting error (position knowledge) 0,0 0,0 0,0 Table B-6 Flexible modes & fuel slosh 2,12 3,54 2,12 Table B-5 Total (RSS): 10,70 6,89 6,28 Total x (for 95 % confidence): 21,40 13,78 12,57 30 10 10 Original requirement: RPE budget not compliant 53 BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) Annex D (informative) Correspondence with the pointing error handbook For the specific domain of AOCS and spacecraft pointing, the terminology introduced in this Standard brings in some innovation in regard to the ESA Pointing Error Handbook This was made mandatory by the care for covering a more general field of application, not restricted to AOCS, and to deal with error signals of any physical type – not only angles and angular rates In order to help the user to switch to the new reference terms, Table D-1 explains how to translate the Pointing Error Handbook indicators into the ECSS- E-ST-60-10 ones: Table D-1: Correspondence between Pointing error handbook and ECSS-E-ST-60-10 indicators PEH indicators ECSS- E-ST-60-10 equivalence APE (absolute pointing error) APE (absolute performance error), applied to the pointing error RPE (relative pointing error) RPE (relative performance error), applied to the pointing error PDE (pointing drift error) PDE (performance drift error), applied to the pointing error PRE (pointing reproducibility error) PRE (performance reproducibility error), applied to the pointing error MPE (median pointing error) MPE (mean performance error), applied to the pointing error AME (absolute measurement error) AKE (absolute knowledge error), applied to the angular knowledge ARE (absolute rate error) APE (absolute performance error), applied to the angular rate ARME (absolute rate measurement error) AKE (absolute knowledge error), applied to the angular rate knowledge 54 BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) References [1] “New definition of pointing stability: AC and DC effects” Lucke, Sirlin, San Martin The Journal of the Astronautical Sciences Vol.40 No.4 Oct Dec 1992 pp 557-576 55 BS EN 16603-60-10:2014 EN 16603-60-10:2014 (E) Bibliography EN reference Reference in text Title EN 16601-00 ECSS-S-ST-00 ECSS system – Description, implementation and general requirements ECSS-E-HB-60 Space engineering – Control engineering guidelines ECSS-E-HB-60-10 Space engineering – Control performance guidelines 56 This page deliberately left blank NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAW British Standards Institution (BSI) BSI is the national body responsible for preparing British Standards and other standards-related publications, information and services BSI is incorporated by Royal Charter British Standards and other standardization products are published by BSI Standards Limited About us Revisions We bring together business, industry, government, 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