OA9793A - Apparatus and method for calibrating a sensor system - Google Patents

Apparatus and method for calibrating a sensor system Download PDF

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OA9793A
OA9793A OA60091D OA60091D OA9793A OA 9793 A OA9793 A OA 9793A OA 60091 D OA60091 D OA 60091D OA 60091 D OA60091 D OA 60091D OA 9793 A OA9793 A OA 9793A
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Antti Aarne Ilmari Lange
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Antti Aarne Ilmari Lange
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Priority to FI892071A priority Critical patent/FI892071A/en
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Priority to SG151694A priority patent/SG151694G/en

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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01DMEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D3/00Indicating or recording apparatus with provision for the special purposes referred to in the subgroups
    • G01D3/02Indicating or recording apparatus with provision for the special purposes referred to in the subgroups with provision for altering or correcting the law of variation
    • G01D3/022Indicating or recording apparatus with provision for the special purposes referred to in the subgroups with provision for altering or correcting the law of variation having an ideal characteristic, map or correction data stored in a digital memory
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01DMEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D18/00Testing or calibrating of apparatus or arrangements provided for in groups G01D1/00 - G01D15/00
    • G01D18/008Testing or calibrating of apparatus or arrangements provided for in groups G01D1/00 - G01D15/00 with calibration coefficients stored in memory

Abstract

A method and apparatus for calibrating a sensor system output that includes a logic unit (1) for receiving uncalibrated sensor signals from a centralized sensor system (3) and for reading/writing data from/to a data base unit (2) that contains updated information on all control (4) and performance aspects of the sensors. Based upon these inputs, the logic unit (1) can provide real-time or near real-time optimum calibration (5) of the sensors by using the Fast Kalman Filtering (FKF) method when the stability conditions of standard Kalman Filtering are met by the sensor system.

Description

•4 WO 90/13794 PCT/FI90/00122 €9 793

APPARATUS AND METHOD FOR CALIBRATING A SENSOR SYSTEM

Technicaï Field

This invention relates generally to sensor signal processing and moreparticularly to the calibration and standardisation of sensor outputsusing multiple sensor Systems.

Background Art

Electrically controlled Systems often respond, at least in part, toexternal events. Sensors of various kinds arc typically utilized to allowsuch a System to monitor the desired external events. Such sensors providepredictable electrical responses to spécifie environmental stimuli.Sensors are comprised of one or more components, and such components areusually only accurate within some degree of tolérance. As a resuit,sensors are calibrated prior to installation and use.

However, such calibration techniques are relatively costly. Instead,a data base can be empirically prepared for each sensor to relate thatsensor’s output to known environmental influences. Such an apparatus andmethod for calibrating a sensor was recently patented (PCT/US86/00908; seeWO 87/00267 of January 15, 1987). However, such a complété empirical database may still be much too expensive to préparé and update in real-timefor every sensor of a large sensor System.

Fortunately, it has tumed out that there seldom is an absolute needfor such an empirical data base if the sensor System only has somedata-redundancy or overdetermination in it (see Antti A. Lange, 1986: "AHigh-pass Filter for Optimum Calibration of Observing Systems withApplications"; pages 311-327 of Simulation and Optimisation of LargeSystems, edited by Andrzej J. Osiadacz and published by ClarendonPress/Oxford University Press, Oxford, UK, 1988). f 9793 2

It has for a much longer time been known how the calibration ofrelatively small sensor Systems can be maintained in real-time by usingvarious computational methods under the general title of Kalman Filtering(Kalman, 1960; and Kalman and Bucy, 1961). However, certain stabilityconditions must be satisfied otherwise ail the estimated calibration andother desired parameters may rstart to diverge towards false solutions whencontinuously updated again and again.

Fortunately, certain observability and controllability conditions guarantee the stability of an optimal Kalman Filter. These conditionstogether with a strict optimality usually require that a full measurement cycle or even several cycles of an entire multiple sensor System should be able to be processed and analysed at one time. However, this has not beenpossible in large real-time applications. Instead, much faster suboptimal

Kalman Filters using only a few measurements at a time are exploited inthe real-time applications of navigation technology and process control.

Unfortunately, the prior art real-time calibration techniques eitheryield the severe computation loads of optimal Kalman Filtering or theirstability is more or less uncertain as it is the situation with suboptimalKalman Filtering and Lange’s High-pass Filter. A fast Kalman Estimationalgorithm has been reported but it only applies to a restricted problemarea (Falconer and Ljung, 1978: "Application of Fast Kalman Estimation toAdaptive Equalization", IEEE Transactions on Communications, Vol. COM-26,No. 10, October 1978, pages 1439-1446).

There exists a need for a calibration apparatus and method for largesensor Systems that offers broad application and equal or bettercomputational speed, reliability, accuracy, and cost benefits.

Summary of the Invention

These needs are substantially met by provision of the apparatus andmethod for calibrating a sensor System in real-time or in near real-timeas described in this spécification. Through use of this apparatus and PCT/FI90/00122 WO 90/13794 „ G9793 3 method, unreliable trim points and most expensive internai calibrationtechniques can be eliminated from the sensors. Instead, a data base iscreated from more or less scratch and updated in real-time for the entiremultiple sensor System. In addition, to aid convergence and accuracy ofthe measuring process, entirely uncalibrated but otherwise predictablesensors can be included in the sensor System.

Pursuant to the apparatus of the invention, a microcomputer or otherelement capable of performing in real-time or near real-time the specifiedlogic functions receives output from a System of several sensor units,accesses a data base, and détermines readings of the sensor units in viewof the data base information to yield standardized calibrated outputs andupdates the data base information; and, pursuant to the method ofinvention, the logic functions are based on such a révision of Lange’sHigh-pass Filter for Optimum Calibration of Observing Systems thattransforms the filter into a Kalman Filter.

Brief Description of the Drawings

These and other attributes of the invention will become more clearupon making a thorough review and study of the following description ofthe best mode for carrying out the invention, particularly when reviewedin conjunction with the drawings, wherein:

Fig. 1 comprises a block diagram depiction of a prior art sensor andcalibration unit;

Fig. 2 comprises a block diagram depiction of a prior art apparatusand method for calibrating a large sensor System (based on so-calleddeccntralized Kalman Filtering);

Fig. 3 comprises a block diagram of the apparatus of the invention (based on so-called centralized Kalman Filtering); and

Fig. 4 comprises a schematic diagram of an example of a preferredembodiment of the apparatus of the invention. PCT/F190/00122 WO 90/13794 ! €9793 ί

Best Mode for Carrying out the Invention

Prior to explaining the invention, it will be helpful to first understand the prior art calibration technique of Fig. 1. A typical priorart sensor and calibration unit includes a logic unit (11) and a data baseunit (12). The sensor signal from a sensor unit (13) proceeds directlythrough an amplifier/transmission (16) unit to an output/interface unit(18). Based upon this input and upon the information contained in the data j base unit (12), the logic unit (11) then provides a calibrated sensor j reading for use as desired. } i !

Referring now to Fig. 3, the apparatus of the invention bas beenoutlined. It includes gencrally a logic unit (1) and a data base unit (2) that operate in conjunction with a centralized multiple sensor System (3).

The data base unit (2) provides storage for ail information on most recentcontrol and performance aspects of the sensors including, if any, test ! point sensor output values and the corresponding empirically determined ί extemal event values. The logic unit (1) receives sensor outputs from the sensor System (3), and accesses the data base unit (2). Based on these inputs, the logic unit (1) provides the outputs (5) that comprise updatedcalibration data, sensor readings and monitoring information on the ( desired extemal events. Prior to explaining the invented Fast Kalman !

Filtering (FKF) method pursuant to the way in which the logic unit (1) isused, it will be helpful to first understand some fundamentals of KalmanFiltering.

An optimal recursive filter is one for which there is no need tostore ail past measurements for the purpose of computing présent estimâtesof the State parameters. This is the Markov property of a stochasticprocess and fondamental to optimal Kalman Filtering. For the wind-trackingapparatus of Fig. 4 the position coordinates of the weather balloon - and,as we shall soon see, ail more or less unknown calibration parameters of s the tracking sensors as well - are referred to as the State of the System. 5 69793

The process is described by the équations from (1) to (3). The firstéquation tells how a measurement vector y* dépends on the State vqcùqtat timepoint t, (t=0,1,2... ). This is the linearized Measurement (orobservation) équation: », = H, s, + et (1)

The design matrix H{ is typically composed of the partial dérivatives ofthe actual Measurement équations. The second équation describes the timeévolution of e.g. a weather balloon flight and is the System (or State)équation: st = st-l + "t-l + “t(or, st = A st_j + B ut_i + at more generally) which tells how the balloon position is composed of its previous positionst_j as well as of incréments ut_j and at. These incréments are typicallycaused by a known uniform motion and an unknown random accélération,respectively.

The measurements, the accélération term and the previous positionusually are mutually uncorrelated and are briefly described here by thefollowing covariance matrices:

Re = Cov(et) = E(etet’)

Ra = Cov(ftt) = E(atat’) t and (3) pt.I=cov(st.I)=E^(;t.I-St.1)(;t_I-St

The Kalman fonvard recursion formulae give us the best linearunbiased estimâtes of the présent State ’t=®t-i+"t-i +Kt{vHÂ-i +u,-i>} <4> and its covariance matrix P, = Cov(st) = Pt.rKtH;ptl (5) where the Kalman gain matrix Kt is defined by K,=<P,-,+Κ.^ίΗ,ίΡ,.,+Κ. t t (6) PCT/F190/00122 WO 90/1J794 CS 793

Lct us now partition tbc estimated State vector st and its covariance matrix P{ as follows: > II 1- , Pt = Cov(st) = Pb Cov(bt,ct)' A ct Cov(ct,bt) Pc (7) where b. tells us the estimated balloon position; and,

A V ct the estimated calibration parameters.

The respective partitioning of the other quantities will then be asfollows: H =1

‘t-fHfc, θ«]’ V

[ubl ’ at= [%! t t u a c c t t and,

Rat Cov<ab )Cov(ac',ab ) Ra (8)

The recursion formulae from (4) to (6) gives us now a filtered (basedon updated calibration parameters) position vector it=it-i+ub +Kb{*rHÂ-i+ut-i>}

t-l J and the updated calibration parameter vector S“S-i+uc ,+Kc{yt-Ht(“t-i+ut-p}

t-l t*- J

The Kalman gain matrices are respectively

Kb=<Pb +Ra >HbiH/Pt-l+Ra’H;+Re}"I + -

t t-l b 11 t tJ (9) (10) and (H)

Kc=(pc +Ra )Hâ{Ht(Pt-l+Ra)H;+Re}‘1 + ·t t-l c t L t tJ PCT/FI90/00122 WO 90/13794 €9793

Equation (9) spécifiés a high-pass filter because it suppresses fromthe position coordinates ail those 'noise- effects that stem from constantor slow-varying calibration errors of the tracking sensors. Its frequencyresponses dépend on the calibration stability of each sensor and optimaltuning takes place automatically. However, one must use accurate estimâtesfor the covariance matrices Ρι=θ, Re and as well as to kecp track of t t recalibration or adjustments uc of the sensors at ail timepoints t,t-i t=l,2,... Equation (10) spécifiés a low-pass filter because it suppresses the random noise a from the calibration parameters and it can bc usedç t for updating the calibration parameter vector. It resembles an exponentialsmoothing filter where the weights of the moving averaging corne from (11).

Because the calibration parameters are very closely related to themeasurements a design matrix Ht usually has linearly dépendent columnvectors. This will cause numerical problème unless adéquate précautionsare taken. Firstly, an initialization is needed for adéquate initialguesses of the position vector bt==Q and the calibration vector ct—θ-Lange’s High-pass Filter (Lange, 1988a) can extract this information fromail available data sources e.g. instrument calibration, laboratory tests,intercomparisons and archived measurements. Secondly, the well-knownstability conditions of Kalman Filtering should also be satisfiedotherwise tnmcation and roundoff errors may gradually contaminate thefiltering results (see e.g. Geld, 1974: "Applied Optimal Estimation", MITPress, page 132).

The stability of a Kalman Filter refers to the behaviour of estimatedparameters when measurements are suppressed. The calibration parameterstypically are unobservable during many external events. In fact, thenumber of measurements must always be greater than that of entirelyunknown State parameters. This is a matter of great practical importancefor ail observing Systems with many calibration parameters to beestimated. The very necessary observability condition can usually besatisfied by processing the incoming sensor signais in large data batchesor, altematively, employing tests for "whiteness" on long time sériés ofthe residuals e and making the corrective actions when established. 8 C 9 79 3

In fact, for a truly optimal Kalman Filter, not only the Kalman Gainmatrices (11) but the volume of a data batch also dépend on the State andmodel parameters in dynamic fashion. Prior art methods use the KalmanRecursions (4) to (6) for estimating these parameters.

Now, we introduce the following modified form of the State équation "t-ι + ut-i = ’. + Λ (,2)

A where s represents an estimated value of a State vector s. We combine itwith the Measurement équation (1) in order to obtain so-called AugmentedModel: yt A. Η,' st + et X st-l+ot-l I l

The State parameters can now be computed by using the well-known solutionof a Régression Analysis problem given below. We use it for Updating:

St = (z;v'1zt)’1z;v-1zt 04)

The resuit is algebraically équivalent to use of the Kalman Recursions butnot numerically (see e.g. Harvey, 1981: "Time Sériés Models", Philip AllanPublishers Ltd, Oxford, UK, pp. 101-119). For the balloon tracking problemwith a large number sensors with slipping calibration the matrix to beinverted in équations (6) or (11) is larger than that in formula (14).

The initialization of the large optimal Kalman Filter for solving thecalibration problem of the balloon tracking sensors is done by Lange’sHigh-pass Filter. It exploits an analytical sparse-matrix inversionformula (Lange, 1988a) for solving régression models with the followingso-called Canonical Block-angular matrix structure:

fPl Fi *2 Gll θ2 y + e1 2 (15) ?K xkgkJ [cKJ eK WO 90/13794 PCT/FI90/00122 £9793 9

This is a matrix représentation of the Measurement équation of an entirewindfînding intercomparison experiment or one balloon flight. The vectorsbpb2»...,bjr typically refer to consecutive position coordinates of aweather balloon but may also contain those calibration parameters thathâve a significant time or space variation. The vector c refers to theother calibration parameters that are constant over the sampling period.

Updating of the State parameters including the calibration drifts inparticular, is based on optimal Kalman filtering. However, the KalmanRecursions would now require the inversions of the very large matrices inéquations (6) or (11) because measurements must be processed in large databatches in order to create observability for the calibration parameters. Adata batch usually is a new balloon flight.

Fortunately, the Régression Analytical approach leads almost to thesame block-angular matrix structure as in équation (15). The optimalestimâtes (*) of bj,b2>..,bj^ and c are obtained by making the followinglogical insertions into formula (15) for each timepoint t, t=l,2,...: t,k bt-l,k+ub

Gk: = 3.A_ X, ; xk:= bk:_bt,k; t,k et,k

A ^Ι-Ι,Λ-Ι,Ρ"^ tjr1 for k=l,...,K; and, (16) *K+1:= ct-l+nc · ΧΚ+1:=[βηΉ;

t-1 L J θΚ+ί=[ 1 l· c:=ct'· “0· «κ+ι:“<'ι-ι-*ι-ι>-% t

These insertions conclude the spécification of the Fast Kalman Filter (FKF) algorithm for the embodiment of the invention for calibrating the upper-air wind tracking System of Fig. 4.

’USGTtTUTE SHEET WO 90/13794 fk,i/riw/uuui 1 £9793 10

Another preferred mode for carrying oui the invention is thc GlobalObserving System of the World Weather Watch. Here, the vector y^ containsvarious observed inconsistencies and systematic errors of weather reports(e.g. mean day-night différences of pressure values which should be aboutzéro) from a radiosonde System k or from a homogeneous cluster k ofradiosonde stations of a country (Lange, 1988a/b). The calibration driftvector will then tell us what is wrong and to what extent. Thecalibration drift vector c refers to errors of a global nature or whichare more or less common to ail observing Systems (e.g. biases in satelliteradiances and in their vertical weighting functions or some atmospherictide effects).

For ail large multiple sensor Systems their design matrices Htypically are sparse. Thus, one can usually perform

Partitioning: st= \i bt,K yt= ?t,2 Ht= Îct J -yt,K- &amp;,1

°t,2Λ.Κ ®t,KJ (17) where ct typically représente calibration parameters at time t; and, bt ail other State parameters in the time and/or space volume.

If the partitioning is not obvious one may try to do it automatically byusing a spécifie algorithm that couverts every sparse linear System intothe above Canonical Block-angular Form (Weil and Kettler, 1971:"Rearranging Matrices to Block-angular Form for Décomposition (and other)Algorithme", Management Science, Vol. 18, No. 1, Semptember 1971, pages98-107).

Augmented model for a space volume case: see équations (15) and (16). î, PCT/FI90/00122 WO 90/13794 11 C9793

Augmented Model for a moving timc volume (length L): y t *t-l + ut-l = [Ht I Ft st st-l + X et <st-l st-l> - at . yt-i St-2 + u t -2 Ht-1 I Ft-1 St-L+1 . et-l (st-2"st-2^ at-l ; C, ; . J t -L+lSt-L+ ’t-L Ht-L+lFt-L+l I x et-L4-l (st-L‘st-I? ‘ at-L + l Ct-1 +uc L 1 1 c t -1-1 I Arc.-l>-»ct (18) and where vector représente ail those calibration parameters that areconstants in the moving volume. As previously, we proceed with

Updating: S, = {Z^Z,}'’ Z^Z, (19)

Please observe, that the gigantic matrix Z takes a nested block-angularform when· adding the space domain. Lange’s High-pass Filter can be revisedto cope with ail such sparsities of Augmented Models.

The Fast Kalman Filter (FKF) formulae for the recursion step at anytimepoint t are as follows: for /=0,1,2,...,1.1 ' L Ι-l L _ ,Ξοθ.Α-/θ.-ζ) (î0Gt-zRt-zyt.z where, for /=0,l,2,...,L-l,

Rt-Z= v4i - X^V^/x^'· (20) C.9793 12 II Cov(et./) Co v{A<st-z-rst-z- yt.r yt-z A xt-,= H,-/ I G.-z= Ft-zl and, i.e. for /=L,

-1

t-L

Vt-L= CovP^t-l-Ct-l>acJ yt.L= G,-l= AC. , +2?ut-1 ct_i I.

When the State vectors are also decoupled in the space domain thosesubsystems are indicated by équations (17), (16) and (15). In fact,Lange’s revised High-pass Filter algorithm as specified by the formulae(20) will do the whole job in one go if only the detailed substructuresare permuted to conform with the overall block-angular form of équation(18).

For a Continuous Kalman Filter: ut = F(t) Jt bt (Gelb 1974, pp. 122-124).

Referring now to Fig. .2, a spécifie embodiment of a prior artnavigation System using a decentralized Kalman Filtering technique will beexplained. As suggested by the block diagram, Federated Filtering (Neal A.Carlson, 1988: "Federated Filter for Fault-Tolerant Integrated NavigationSystems", Proceedings of the IEEE 1988 PLANS, IEEE AES Society, see figure1 on page 111) is a two-stage data processing technique in which theoutputs of local, sensor-related filters are subsequently processed andcombined by a larger mastef filter. Each local filter is dedicated to a PCT/FI90/00122 WO 90/13794 C3 793 13 scparate subsystem of sensors. One or more local filters may also use datafrom a common référencé System, e.g., an inertial navigation System (INS).The advantages over an prior art centralized Kalman fîltering techniqueare an increased total System throughput by parallel operation of localfilters and a further increase of System throughput by using the localfilters for data compression. Approaches of this kind hâve bcen absolutelynecessary for large multi-sensor navigation Systems because of high-specdcomputing requirements. From the viewpoint of a prior art centralizedKalman Filter of a large sensor System, these approaches for speeding upthe computations fall into the two general categories of approximativemethods i.e. decoupling States and prefiltering for data compression (seee.g. Gelb, 1974: "Applied Optimal Estimation", MIT Press, pages 289-291).The disadvanges are that an approximative Kalman Filter never is strictlyoptimal and, consequently, its stability becomes more or less uncertain.In any case, the stability is more difficult to establish in atheoretically rigorous way.

Referring now to Fig. 3, a block diagram of the apparatus of theinvention that makes use of a theoretically sound yet practicalcentralized Kalman Filtering method will be described.

As can be seen by comparing Figs. 1 and 3, the logic unit (1) of theinvention has a two-way communication link to the data base unit (2)whereas the prior art logic unit (11) can only read from its data baseunit (12). In order the prior art sensor and calibration unit to operateproperly, the data base unit (12) must bave an appropriate collection ofdata regarding sensor (13) performance. Such information must beempirically established, and often needs to be re-established at adéquateintervals, for each individual sensor (13) by sequentially exposing eachsensor (13) to a number of known external events of known magnitudes. Thisis not possible in many cases of practical importance; consider e.g. aradiomctric sensor of an orbiting weather satellite. In contrast, thelogic unit (1) of the invention has a capability of stretching andupdating the calibration information collected in its data base (2)assuming only that a certain observability condition of Kalman Filteringis satisfied.

Ο’ ίΓΣ?Π—·|~Ι ITC WO 90/13794 PCT/FI90/00122 €9793 14

As can be sccn by comparing Figs. 2 and 3, the Federated KalmanFilter solution is the same as that of a single, centralized Kalman Filteronly if the information fusion and division operations are perfonned afterevery local filter measurement update cycle (and when the master filtershould be able to cope with the large Kalman Filtering problem without anyhelp from decoupling States). Thus, the prior art solution of Fig. 2 istheoretically inferior because it is a full centralized Kalman Filtersolution of Fig. 3 that yields optimal résulte as shown by Kalman in 1960or, in fact, by Gauss and Markov already in the early 1800. However, thecomputation load of a prior art centralized Kalman Filter is proportionalto n where n is the number of the State parameters i.e. the number of ailunknown quantifies that need to be solved for an update of the processparameter estimâtes.

Pursuant to use of this apparatus and method, simple and inexpensivesensors can be fully exploited without too much regard for their internaicalibration provisions and the speed of logic unit s. Despite use ofentirely uncalibrated but predictable sensors, accurate results can beobtained in real-time applications through use of the calibration andstandardixation method and apparatus disclosed herein.

The invented Fast Kalman Filtering (FKF) method is based on thegeneral principle of decoupling States. The use of Lange’s analyticalsparse-matrix inversion method is pursuant to the invention (see e.g.Lange, 1988a). Because the solution is straightforward and exact theoptimality of a large centralized Kalman Filter can be achieved with ahard-to-bcat computafional effîciency.

Those skilled in the art will appreciate that many variations couldbe practiced with respect to the above described invention withoutdeparting from the spirit of the invention. Therefore, it should beunderstood that the scope of the invention should not be considered aslimited to the spécifie embodiment described, except in so far as thedaims may specifically include such limitations.

SUBSTÏTUTE SMEET WO 90/13794 PCT/FI90/00122 15 ί 9 793 Références (1) Kalman, R. E. (1960): "A new approach to îinear filtering andprédiction problems". Trans. ASME J. of Basic Eng. 82:35-45. (2) Lange, A. A. (1982): "Multipath propagation of VLF Oméga signais".IEEE PLANS *82 - Position Location and Navigation Symposium Record,December 1982, 302-309. (3) Lange, A. A. (1984): "Intégration, calibration and intercomparison ofwindfinding devices". WM O Instruments and Observing Methods Report No. 15. (4) Lange, A. A. (1988a): "A high-pass filter for optimum calibration ofobserving Systems with applications". Simulation and Optimization of LargeSystems, edited by A. J. Osiadacz, Oxford University Press/ClarendonPress, Oxford, 1988, 311-327. (5) Lange. A. A. (1988b): "Détermination of the radiosonde biases byusing satellite radiance measurements". WMO Instruments and ObservingMethods Report No. 33, 201-206.

SUEST'TUTE SHEET

Claims (9)

WO 90/13794 PCT7FI90/00122 1979 3 Claims
1. A method for calibrating readings of a multiple sensor System,the sensors providing output signais in response to external events, themethod comprising the steps of: a) providing data base means for storing information on: - a plurality of test point seùsor output signalvalues for some of said sensors and a plurality ofvalues for said external events corresponding to saidtest point sensor output values wherein theimprovement comprises minimal requirements for theamount and quality of said test point data and thatuncalibrated sensors can be added; - said calibrated sensor readings or, altematively,said readings accompanied with their calibrationparameters and values for said external eventscorresponding to a situation; and, - Controls of or changes in, if any, said sensors orsaid external events corresponding to a new situation; b) providing logic means for accessing said calibratedreadings or, altematively, said readings accompanied with theircalibration parameters, wherein the improvement comprises bothread and write so that said logic means has a two-waycommunications link to said data base means; c) providing said sensor output signais from said sensors tosaid logic means; d) providing information, if any, on said Controls or changesto said data base means; e) updating by a Kalman recursion wherein the improvementcomprises the use of an algorithm obtained from the Fast KalmanFilter (FKF) formulae (20) of the description, in said logicmeans (1), values of both said external events and saidcalibration parameters corresponding to said new situation; and, f) providing updated values of said calibrated readings and/orsaid values of said external events, as desired. 25 (9 793
1. A method for calibrating readings of a multiple sensor System,the sensors providing output signais in response to extemal events, themethod comprising the steps of: a) providing data base means for storing information on: - a plurality of test point sensor output signalvalues for some of said sensors and a plurality ofvalues for said extemal events corresponding to saidtest point sensor output values; - said calibrated sensor readings or, alternatively,said readings accompanied with their calibrationparameters and values for said external eventscorresponding to a situation; and, - Controls of or changes in, if any, said sensors orsaid extemal events corresponding to a new situation; b) providing logic means for accessing said calibratedreadings or, alternatively, said readings accompanied with theircalibration parameters, said logic means having a two-waycommunications link to said data base means; c) providing said sensor output signais from said sensors tosaid logic means; d) providing information, if any, on said Controls or changesto said data base means; e) updating by using the Fast Kalman Filter (FKF) formulae, insaid logic means, values of both said extemal events andsaid calibration parameters corresponding to said new situation;and, f) providing updated values of said calibrated readings and/orsaid values of said extemal events, as desired. WO 90/13794 PCI/FI90/00122 I 9 ί 9 793
1. A method of providing calibrated readings for a multiple sensorSystem, the sensors providing output signais in response to externalevents, the method comprising the steps of: a) providing data base means for storing information on: - a plurality of test point sensor output signalvalues for some of said sensors and a plurality ofvalues for said external events corresponding to saidtest point sensor output values; - said calibrated sensor readings and values for saidexternal events corresponding to a current situation;and, - Controls or adjustments of said sensors and of saidexternal events corresponding to said currentsituation, if any; b) providing logic means for providing said calibratedreadings, said logic means having a two-way communications linkto said data base means; c) providing said sensor said logic means; output signais from said sensors to d) providing information, if any, on said Controls or adjustments to said data base means; e) updating by the optimal Fast Kalman Filtering (FKF) method,in said logic means, said calibrated sensor readings and saidvalues of said external events corresponding to a new situation;and, f) providing said updated values of calibrated sensor readingsand/or said external events, as desired. SU3STÏTUTE SHEET WO 90/13794 PCT/FI90/00122 17 €9 79 3
2. The method of claim 1 wherein said logic means (1) opérâtes in adecentralized or cascaded fashion but exploits in one way or anotherKalman filtering wherein the improvement comprises the use of an algorithmobtained from the Fast Kalman Filter (FKF) formulae (20) of thedescription.
2. The method of claim 1 wherein said logic means opérâtes in adecentralized or cascaded fashion but exploits in one way or another theFast Kalman Filter (FKF) formulae.
2. The method of claim 2 wherein said logic means opérâtes in adecentralized or cascaded fashion but exploits in one way or another saidFast Kalman Filtering (FKF) method.
3. A calibration apparatus for use with a multiple sensor Systemthat provides substantially predictable sensor outputs in response to amonitored event, the apparatus comprising: a) data base means for storing information on a plurality ofsensor output values for each sensor with which the calibrationapparatus will be used and a plurality of values for saidextemal event corresponding to a situation and to some testpoints wherein the improvement comprises minimal requirementsfor the amount and quality of said test point data and thatuncalibrated sensors can be added; and, b) logic means (1), based on Kalman filtering wherein theimprovement comprises the use of an algorithm obtained from theFast Kalman Filter (FKF) formulae (20) of the description,operably connected to said multiple sensor System for receivingsaid sensor outputs and further being operably connected to saiddata base means for accessing and updating said information onsaid plurality of sensor output values and said plurality ofvalues for said extemal event, for providing an output thatcomprises calibrated readings for said multiple sensor Systemand/or, as desired, current values of said extemal event thatmay ail be substantially standardized to preselected standards.
3. A calibration apparatus for use with a multiple sensor Systemthat provides substantially predictable sensor outputs in response to amonitored event, the apparatus comprising: a) data base means for storing information on a plurality ofsensor output values for each sensor with which the calibrationapparatus will be used and a plurality of values for saidextemal event corresponding to a situation and to some testpoints, if any; and, b) logic means, based on the Fast Kalman Filter (FKF) formulae, operably connected to said multiple sensor System forrcceiving said sensor outputs and further being operablyconnected to said data base means for accessing and updatingsaid information on said plurality of sensor output values andsaid plurality of values for said external event, for providingan output that comprises calibrated readings for said multiplesensor System and/or, as desired, current values of saidexternal event that may ail be substantially standardized to preselected standards.
3. A calibration device for use with a multiple sensor System thatprovides substantially predictable sensor outputs in response to amonitored event, the device comprising: a) data base means for storing information on a plurality ofsensor output values for each sensor with which the calibrationdevice will be used and a plurality of values for said externalevents corresponding to some test points and a currentsituation; and, b) logic means, based on the optimal Fast Kalman Filtering(FKF) method, operably connected to said multiple sensor Systemfor receiving said sensor outputs and further being operablyconnected to said data base means for reading and updating saidinformation on said plurality of sensor output values and saidplurality of values for said external events, for providing anoutput that comprises calibrated readings for said multiplesensor System or, if also desired, current values of saidexternal events that may ail be substantially standardized topreselected standards.
4. The apparatus of claim 3 wherein said logic means (1) opérâtes in a decentralized or cascaded fashion but exploits in one way or another Kalman filtering wherein the improvement comprises the use of an algorithm obtained from the Fast Kalman Filter (FKF) formulae (20) of the description. f 9793 26
4. The apparatus of claim 3 wherein said logic means opérâtes in adecentralized or cascaded fashion but exploits in one way or another theFast Kalman Filter (FKF) formulae.
4. The device of claim 3 wherein said logic means opérâtes indecentralized or cascaded fashion but exploits in one way or another saidFast Kalman Filtering (FKF) method. SU23TÎTUTE SHEET WO 9U/I37y4 PC17H90/Ü0122 ,θ (.3793 AMENDED CLAIMS [received by the International Bureau on 26 September 1990 (26.09.90);original daims 1-4 replaced by amended daims 1-12 (5 pages)]
5. The method of claim 1 including the step of: a) adapting by using Kalman filtering wherein the improvementcomprises the use of an algorithm obtained from the Fast KalmanFilter (FKF) formulae (20) of the description, in said logicmeans (1), said information on said Controls of or changes insaid sensors or said extemal events as far as their truemagnitudes are unknown.
5. The method of claim 1 including the step of: a) adapting by using the Fast Kalman Filter (FKF) formulae, insaid logic means, said information on said Controls of orchanges in said sensors or said external events as far as theirtrue magnitudes are unknown. WU 90/13794 rvi/rnu/um/z 20 C 9 79 3
6. The method of claim 2 including the step of: a) adapting by using Kalman filtering wherein the improvementcomprises the use of an algorithm obtained from the Fast KalmanFilter (FKF) formulae (20) of the description, in said logicmeans (1), said information on said Controls of or changes insaid sensors or said extemal events as far as their truemagnitudes are unknown.
6. The method of claim 2 including the step of: a) adapting by using the Fast Kalman Filter (FKF) formulae, insaid logic means, said information on said Controls of orchanges in said sensors or said extemal events as far as theirtrue magnitudes are unknown.
7. A data-assimilation apparatus for use with an observing Systemand a dynamical prédiction System that provides substantially predictableoutputs in response to a monitored event, the apparatus comprising: a) data base means for storing information on a plurality ofsensor output values for each sensor System with which theapparatus will be used and a plurality of values including theirchanges predicted by said dynamical System for said extemalevent and for some test points wherein the improvement comprisesminimal requirements for the amount and quality of said testpoint data and that uncalibrated sensors can be added; and, b) logic means (1), based on Kalman filtering wherein theimprovement comprises the use of an algorithm obtained from theFast Kalman Filter (FKF) formulae (20) of the description,operably connected to said observing and prédiction Systems forreceiving said sensor outputs and further being operablyconnected to said data base means for accessing and updatingsaid information on said plurality of sensor output values andsaid plurality of values and predicted changes for said extemalevent, for providing an output that comprises calibratedreadings for said observing System and/or, as desired, currentvalues of said extemal event. 28 €9 79 3 b) logic means (1), based on Kalman filtering wherein theimprovement comprises the use of an algorithm obtained from theFast Kalman Filter (FKF) formulae (20) of the description,operably connected to said sensor and dynamic Systems forreceiving said sensor outputs and said Controls and furtherbeing operably connected to said data base means for accessingand updating said information on said plurality of sensor outputvalues and said plurality of values, Controls and predictedchanges for said State parameters, for providing an output thatcomprises calibrated/predicted readings for said sensor Systemand/or current/predicted values of said State parameters, asdesired.
10. Apparatus of claim 7, 8 or 9 wherein said logic means (1)opérâtes in a decentralized or cascaded fashion but exploits in one way oranother Kalman filtering wherein the improvement comprises the use of analgorithm obtained from the Fast Kalman Filter (FKF) formulae (20) of thedescription.
11. Apparatus of claim 3, 7, 8, or 9 wherein information on Controlsor changes in said sensors or said extemal events as far as their tniemagnitudes are unknown is adapted by using Kalman filtering wherein theimprovement comprises the use of an algorithm obtained from the FastKalman Filter (FKF) formulae (20) of the description.
12. Apparatus of claim 4 or 10 wherein information on Controls orchanges in said sensors or said extemal events as far as their truemagnitudes are unknown is adapted by using Kalman filtering wherein theimprovement comprises the use of an algorithm obtained from the FastKalman Filter (FKF) formulae (20) of the description. (.9793 27
7. A data-assimilation apparatus for use with an observing Systemand a dynamical prédiction System that provides substantially predictableoutputs in response to a monitored event, the apparatus comprising: a) data base means for storing information on a plurality ofsensor output values for each sensor System with which theapparatus will be used and a plurality of values including theirchanges predicted by said dynamical System for said extemalevent and for some test points, if any; and, b) logic means, based on the Fast Kalman Filter (FKF) formulae, operably connected to said observing and prédictionSystems for receiving said sensor outputs and further being operably connected to said data base means for accessing and updating said information on said plurality of sensor output values and said plurality of values and predicted changes forsaid extemal event, for providing an output that comprisescalibrated readings for said observing System and/or, asdesired, current values of said extemal event that may ail besubstantially standardized to preselected standards.
8. A prédiction apparatus for use with an observing System and adynamical prédiction System that provides substantially predictableoutputs ahead of monitored events, the apparatus comprising: a) data base means for storing information on a plurality ofsensor output values for each sensor System with which theapparatus will be used and a plurality of values including theirchanges predicted by said dynamical System for said externalevents and for some test points wherein the improvementcomprises minimal requirements for the amount and quality ofsaid test point data and that uncalibrated sensors can be added;and, b) logic means (1), based on Kalman filtering wherein theimprovement comprises the use of an algorithm obtained from theFast Kalman Filter (FKF) formulae (20) of the description,operably connected to said observing and prédiction Systems forreceiving said sensor outputs and further being operablyconnected to said data base means for accessing and updatingsaid information on said plurality of sensor output values andsaid plurality of values and predicted changes for said externalevents, for providing an output that comprises predictedreadings for said observing System and/or, as desired, predictedvalues of said external events.
8. A prédiction apparatus for use with an observing System and adynamical prédiction System that provides substantially predictableoutputs ahead of monitored events, the apparatus comprising: a) data base means for storing information on a plurality ofsensor output values for each sensor System with which theapparatus will be used and a plurality of values including theirchanges predicted by said dynamical System for said extemalevents and for some test points, if any; and, WO 90/13794 PCT/FI90/U0122 21 C9793 b) logic means, based on the Fast Kalman Filter (FKF)formulae, operably coimected to said observing and prédictionSystems for receiving said sensor outputs and further beingoperably connected to said data base means for accessing andupdating said information on said plurality of sensor outputvalues and said plurality of values and predicted changes forsaid extemal events, for providing an output that comprisespredicted readings for said observing System and/or, as desired,predicted values of said extemal events that may ail besubstantially standardized to preselected standards.
9. A control apparatus for use with a sensor System and a dynamicSystem that provides substantially predictable State parameters of saiddynamic System, the apparatus comprising: a) data base means for storing information on a plurality ofsensor output values for said sensor System with which theapparatus will be used and a plurality of values, Controls andchanges predicted by a model of said dynamic System for saidState parameters and for some test points, if any; b) logic means, based on the Fast Kalman Filter (FKF)formulae, operably connected to said sensor and dynamic Systemsfor receiving said sensor outputs and said Controls and furtherbeing operably connected to said data base means for accessingand updating said information on said plurality of sensor outputvalues and said plurality of values, Controls and predictedchanges for said State parameters, for providing an output thatcomprises calibrated/predicted readings for said sensor Systemand/or current/predicted values of said State parameters, asdesired, that are substantially standardized to preselectedstandards.
10. Apparatus of claim 7, 8 or 9 wherein said logic means opérâtes in a decentralized or cascaded fashion but exploits in one way or another the Fast Kalman Filter (FKF) formulae. WO 90/13794 PC1/M9O/UI>IZ2 22 €9793
11. Apparatus of claim 3, 7, 8, or 9 wherein information on Controlsor changes in said sensors or said extemal events as far as their truemagnitudes are unknown is adapted by using the Fast Kalman Filter (FKF)formulae.
12. Apparatus of claim 4 or 10 wherein information on Controls orchanges in said sensors or said extemal events as far as their truemagnitudes are unknown is adapted by using the Fast Kalman Filter (FKF)formulae. WO 90/13794 PCT/F190/00122 €9 79 323 STATEMENT UNDER ARTICLE 19 New expression "the Fast Kalman Filter (FKF) formulae" instead of"the Fast Kalman Filtering (FKF) method" is now being used throughout ailthe daims. This will hâve an impact on the description because the newexpression is used there in the narrow sense of the preferred embodiments.It is therefore understood that the formulae (20) of the description willbe replaced by a general form of the équations, reflecting broadapplication of the FKF method. C9793 24 AMENDED CLAIMS [receivcd by the International Preliminary Eaaminïng Anthority onIl March 1991 (11.03.90); original clairns 1-4 replaced byamended daims 1-12 (5 pages)]
9. A control apparatus for use with a sensor System and a dynamicSystem that provides substantially predictable State parameters of saiddynamic System, the apparatus comprising: a) data base means for storing information on a plurality ofsensor output values for said sensor System with which theapparatus will be used and a plurality of values, Controls andchanges predicted by a model of said dynamic System for saidState parameters and for some test points wherein theimprovement comprises minimal requirements for the amount andquality of said test point data and that uncalibrated sensorscan be added; and,
OA60091D 1989-04-28 1991-11-01 Apparatus and method for calibrating a sensor system OA9793A (en)

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