CA2051681A1 - Apparatus and method for calibrating a sensor system - Google Patents

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

20~ 6~L l~(~/Fl9(J/01)122 APPARATUS AND METHOD FOR CALI~RATING A SENSOR SYS~EM

Technical Field -This invention relates generally to sensor signal proccssing and morc particularly to the calibradon and standard;zation of sensor outputs using multiple sensor systems.

Background Art ., Electrically controlled systems often respond, at least in part, to e~cternal events. Sensors of various kinds are typically utiliz~d to allow such a system to monitor the desircd e~ternal events. Such sensors provide predictable electrical responses to specific environmental sdmuli.
Sensors are comprised of onc or more components, and such components are usually only accurate within some degree of tolerancc. As a result, sensors are calibrated prior to installadon and use.

However, such calibradon techniques are reladvely costly. Instead, a data base can be empirically prepared for each sensor to relate that sensor's output to known environmental influences. Such an apparatus and method for calibrating a sensor was recently patented (PCI/US86/00908; see WO 87/00267 of January lS, 1987). However, such a complete empirical data base may still be much too e~pensive to prepare and update in real-time for every sensor of a large sensor system.

Fonunately, it has turned out that there seldom is an absolute need for such an empiric31 data base if the sensor system only has some data-redundancy or overdetermination in it (see Antti A. Lange, 1986: ~A
High-pass Filter for Optimum Calibration of Observing Systems with Applications"; pages 311-327 of Siml~lation an~ Optimization of I~rge Systcm~, edited by Andrzej J. Osiadacz and published by Clarendon Press/O~ford University Press, O~ford, llK, 1988).

205~L6~3~ 2 It has for a much longer time been known how the calibration of relatively small sensor systems can be maintained in real-time by using various computational methods under the general title of Kalman Filtering (Kalman, 1960; and Kalman and Bucy, 1961). However, certain stability conditions must be satisfied otherwise all the estimated calibration and other desired parameters may start to diverge towards false solutions when continuously updated again and again.

Fortunately, certain observability and controllability conditions guarantee the stability of an optimal Kalman Filter. These conditions together 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 been possible in large real-time applications. Instead, much faster suboptimal Kalman Filters using only a few measurements at a time are exploited in the real-time applications of navigation technology and process control.

Unfortunately, the pAor art real-time calibration techniques either yield the severe computation loads of optimal Kalman Filtering or their stability is more or less uncertain as it is the situation with suboptimal Kalman Filtering and Lange's High-pass Filter. A fast Kalman Estimation algorithm has been reported but it only applies to a restricted problem area (Falconer and Ljung, 1978: "Application of Fast Kalman Estimation to Adaptive Equalization~, IEEE Transactions on Communications, ~ol. COM-26, No. 10, October 1978, pages 1439-1446).

There e~ists a need for a calibration apparatus and method for large sensor systems that offers broad application and equal or better computational speed, reliability, accuracy, and cost benefits.

Summary of the Invention These needs are substantially met by provision of the apparatus and method for calibrating a sensor system in real-time or in near real-time as described in this specification. Through use of this apparatus and ~vo ~)()/1379~ Cl/1 1~0/00122

2~5~681 method, unreliable trim points and most c~pensive internal calibration techniques can be eliminated from the sensors. Instead, a data base is created from more or less scratch and updated in real-time for the entire multiple sensor system. In addition, to aid convergence and accuracy of the measuring process, entirely uncalibrated but otherwise predictable sensors can be included in the sensor system.

Pursuant to the apparatus of the invention, a microcomputcr or othcr element capable of performing in real-time or near real-time the specified logic functions receives output from a system of several sensor units, accesses a data base, and determines readings of the sensor units in view of the data base information to yield standardized calibrated outputs and updates the data base information; and, pursuant to the method of invention, the logic functions are based on such a revision of Lange's High-pass Filter for Optimum Calibration of Observing Systems that transforms the filter into a Kalman Filter.

Brief Descri~tion of the Dra~ings -These and other attributes of the invention will become more clear upon making a thorough revie~ and study of the following description of the best mode for carrying out the invention, particularly when reviewed in conjunction with the drawings, wherein:

Fig. l comprises a block diagram depiction of a prior art sensor and calibration unit;

Fig. 2 comprises a block diagram depiction of a prior art apparatus and method for calibrating a large sensor system (based on so-called decentralized Kalman Filtering);

Fig. 3 comprisès 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 preferred embodiment of the apparatus of the invention.

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~, , PCr/n90/001t2 WO 9()/ 1 3794 205~68~ 4 'i Best Mode for Carr~ing out the In~ention Prior to e~plaining the invention, it will be helpful to first understand the prior art calibration technique of Fig. 1. A typical prior art sensor and calibration unit includes a logic unit (11) and a data base unit (12). The sensor signal from a sensor un~t (13) proceeds directly through an amplifier/transmission (16) unit to an output/interface unit (18). Based upon this input and upon the information contained in the data base unit (12), the logic unit (11) then provides a calibrated sensor reading for use as desired.

Referring now to Fig. 3, the apparatus of the invention has been outlined. It includes generally 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 all information on most recent control and performance aspects of the sensors including, if any, tcst point sensor output values and the corresponding empirically determined e~ctcrnal 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 updated calibration data, sensor readings and monitoring information on the desired e~ternal events. Prior to e~plaining the invented Fast Kalman Filtering (FKF) method pursuant to the way in which the logic unit (1) is used, it will be helpful to first understand some fundamentals of Kalman Filtering.

An optimal recursive filter is one for which there is no need to store all past measurements for the purpose of computing present estimates of the state parameters. This is the Markov p~operty of a stochastic process and fundamental to optimal Kalman Filtering. For the wind-tracking apparatus of Fig. 4 the position coordinates of the weather balloon - and, as we shall soon see, all more or less unknown calibration parameters of the tracking sensors as well - are referred to as the state of the system.

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s The process is described by tbe equations from ( 1 ) to (3) . The first equation tells how a measurement vector Yt depends on the state vector st at timepoint t, (t=0,1,2...). This is the linearized Measurement (or observation) equation:
Yt = Ht St + et (I) The design matrix Ht is typically composed of the partial derivatives of the actual Measurement equations. The second equation describes the time evolution of e.g. a weather balloon flight and is the System (or state) equation:
St = St_l + Ut-l + at (2) (or~ st A St-l + B ut l + at more generally) which tells how the balloon position is composed of its previous position St 1 as well as of increments ut 1 and at. These increments are typically caused by a known uniform motion and an unknown random acceleration, respectively.

The measurements, the acceleration term and the previous position usually are mutually uncorrelated and are briefly described here by the following covariance matrices:
Re = Cov(et) = E(etet ) Ra = CV(at) = E(atat~) and Pt 1=Cov(st l)=E{(St_l-St-l)(St-l St-l) }
The Kalman forward recursion formulae give us the best linear unbiased estimates of the present state St St-l +Ut-l +Kt{Yt-Ht(st-l +Ut-l)} (4) and its covariance matri~
Pt = Cov(st) = Pt-l-KtHtPt-l where the Kalman gain matrix Kt is defined by Kt (pt-l+Ra)Ht{Ht(pt-l+Ra)Ht+Re~-l (6) : , WO 90/13794 PCr/FI~0/~J1~122 20S2~ 6 .

Lct us now partition tbe estimatcd state vector st and its covariancc matri~ Pt as follows:
A ~. ~ ~. ~
st= ~btl, Pt=Cov(st)= ~ Pb Cov(bt,ct)l (7) LCt~ Lcov ( ct bt, cl ~ ?

where bt tells us the estimated balloon position; and, Ct the estirnated calibration parameters.

The respective partitioning of the other quantities will then be as follows: i [Uc ] [9c ]
and, (8) Ra =~ Ra Cov(ab ~ac LCV(ac~ab ) Ra The recursion formulae from (4) to (6) gives us now a filtered (based on updated calibration parameters) position vector bt bt-l+Ub ,+Kb{Yt-Ht(st-l+ut-~)} (9) and the updated calibration parameter vector Ct Ct-l+uc ~+KC{Yt-Ht(st-l+ut-l)} (10) The Kalman gain matrices are respectively Kb, (Pbt l+Rab )Hbt{Ht(Pt-l +Ra )Ht+Re,} +
and (1 1) C, C, ~ aC) c,{Ht(Pt-l+Ra?Ht+Re}-1+,,, ,. : ' , . ~',': :
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Equation (9) specifies a high-pass filter because it supprcsses from the position coordinates all those ~noise~ effects that stem fro~n constant or slow-varying calibration errors of the tracking sensors Its frequency responses depend on the calibration stability of eac~ sensor and optimal tuning takes place automatically. However, one must use accuratc estimatcs for the covariance matrices Pt=o, Re and Ra as well as to keep track of recalibration or adJustments UC of the sensors at all timepoints t, t= 1,2,... Equation (10) specifies a low-pass filter because it suppresses the random noise ac from the calibration parameters and it can be used for updating the calibration parameter vector. It resembles an exponential smoothing filter where the weights of the moving averaging come from (11) Because the calibration parameters are very closely related to the measurements a design matri~ Ht usually has linearly dependent cohlmn vectors. I~nis will cause numerical problems unless adequate precautions are taken. Firstly, an initializatton is needed for adequate initial guesses of the position vector bt=o and the calibration vector &=o.
Lange's High-pass Filter (Lange, 1988a) can c~tract this information from all available data sources e.g. instrument calibration, laboratory tests, intercomparisons and archived measurements. Secondly, the well-known stability conditions of Kalman Filtering should also be satisfied otherwise truncation and roundoff errors may gradually contarninate the filtering results (see e.g. Geld, 1974 nApplied Optimal Estimation", ~T
Press, page 132).

The stability of a Kalman Filter refers to the behaviour of estimated parameters when measurements are suppressed. The calibration parameters typically are unobservable during many e~ternal events. In fact, the number of measurements must always be greater than that of entirely unknown state parameters. This is a matter of great practical importance for all observing systems with many calibration parameters to be estimated. The very necessary observability condition can usually be satisfied by processing the incoming sensor signals in large data batches or, altcrnatively, employing tests for "whiteness~ on long time series of the residuals e and making the corrective actions when established.

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20S~L6~ 8 In fact, for a t3 uly optimal Kalman Filter, not only the Kalman Gain matrices (I l) but the volume of a data batcb also depend OD the state aDd model parameters in dynamic fashion. Prior art methods use the Kalman Recursions (4) to (6) for estimating these parameters.

Now, we introduce the following modified form of the State equation St l + Ut-l = I st + (st l-st l) at (12) where s represents an estimated value of a state vector s. We combine it with the Measurement equation (1) in order to obtain so-called Augmented Model:

L l = ~ 1st + ~A l (13) Lst l+ut l ~ L I ~ L(St l St~ t~
i.e. Zt Zt St + ~t ~he state parameters can now be computed by using the well-known solution of a Regression Analysis problem given below. We use it for Updating:

St (Ztvt Zt) Ztvt Zt (14) The result is algebraically equivalent to use of the Kalman Recursions but not numerically (see e.g. Harvey, 1981: r'Time Series Models~, Philip Allan Publishers Ltd, O~cford, UK, pp. 101-119). For the balloon tracking problem with a large number sensors with slipping calibration the matri~c to be inverted in equations (6) or (11) is larger than that in formula (14).

The initialization of the large optimal Kalman Filter for solving the calibration problem of the balloon tracking sensors is done by Lange's High-pass Filter. It e~ploits an analytical sparse-matrix inversion formula (Lange, 1988a) for solving regression models with the following so-called Canonical Block-angular matri~ structure:

XK~ eK~

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o 90/137 9~ pcr/ Fl(~o/oo l This is a mat~ reprcsentation of the Measurement equation of an cntirc windfinding intercomparison e~periment or one balloon flight. The vectors bl,b2,...,bK typically refer to consecutive position coordinates of a weather balloon but may also contain those calibration paramctcrs that have a sig--ificant time or space variation. The vector c refers to the other calibration parameters that are constant over the sampling period.

Updating of the state parameters including the calibration drifts in particular, is based on optimal Kalman filtering. However, the Kalman Recursions would now require the inversions of the very large matrices in cquations (6) or (11) because measurements must be processed in large data batches in order to create observability for the calibration parameters. A
data batch usually is a new balloon flight.

Fortunately, the Regression Analytical approach lcads almost to thc same block-angular matri~ structure as in equation (15). The optimal estimates (^) of bl,b2,..,bK and c are obtained by making the following logical inscrtions into formula (15) for each timepoint t, t=1,2,...:

[ , b, IJ [ ]

Gk: = [--- '--]; bk: =bt k; and, I(bt 1 k-b ~ J; for k=1,... K;

and, (16) YK~ 1 Ct-l +Uc; XK+ 1 = Lempty~ ;
GK+l:=[ I ]; c:=ct; and~ eK~1 (Ct-l Ct-l) c, These insertions conclude the specification of the Past Kalman Filter (FKF) algorithm for the embodiment of the invention for calibrating the upper-air wind tracking system of Fig. 4.

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205~ o i Another preferred mode for carrying out the invention is the &lobal Observing System of the World Weather Watch. Here, the vector Yk contains various observed inconsistencies and systematic errors of weathcr rcports (e.g. mcan day-night differenccs of prcssure values which should be sbout zero) from a radiosonde system k or from a homogcncous clustcr k of radiosonde stations of a country (Lange, 1988a/b). The calibration d~ift vector bk will thcn tell us what is wrong and to what e~ctent. Thc calibration drift vector c refers to errors of a global nature or which are more or less common to all observing systems (e.g. biases in satellite radiances and in thcir vcrtical weighting functions or some atmospheric tide effccts).

For all large multiple sensor systems their design matrices H
typically are sparse. Thus, one can usually perform P~tion; ~g St E~ K] ~t L~t~2] Ht ¦X t,2 t 2] (17) where ct typicaDy represents calibraffon parameters at time t; and, bt k all other state parameters in the time and/or space vol~me.

If the partitioning is not obvious one may try to do it automatically by using a specific algoAthm that converts every sparse linear system into the above Canonical Block-angular Form (Weil and Kettler, 1971:
"Rearranging Matrices to Block-angular Form for Decomposition (and other) Algorithms~, Management Science, Vol. 18, No. 1, Semptember 1971, pages 98-107).

Augmented model for a space volume case: see equations (15) and (16).

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WO 91~137~4 PCltFI~0/~)0122 2t;~

Aogmented Model for a moving time ~olume (length L):

~st l+ u~ ¦= ~ t ~~ at ¦St-L+1~ ( t 2 St-2) at Ct ~ Y t -L + 1 Ht L + lFt L + 1 A et - L+ 1 St-L+ U t L (St-L-St-L) at-L+I
Ct 1 +UC I I (Ct- 1 Ct 1 ) aCt i.e. Z~ = ~ S~ + e~ (18) and where vector Ct rcprescnts all those calibration parameters tbat are constants in the moving volusne. As previously, we procecd with Updatsng: St {ZtVt Zt} Ztvt Zt (19) Please observe, that the gigantic matri~ Z takes a nested block-angularform when. adding the space domain. Lange's High-pass Filter cao be rcvised to cope with all such sparsities of Augmented Models.

The Fast Kalman Filter (FKF) formulae for the recursion step at any timepoint t arc as follows:

St ~={Xt Ivtl,xt 1} x; ,v l(Yt rGt lct) for l=0,1,2,...,L-l Ct =fl_OGt-lRt-lGt-J l~ Gt ,Rt IY I (20) where, for l=0,1,2,...,L-I, R~=Vtl~ X~{Xt'~Vt-l~Xt~} Xt'~Vt-'~}

., :, ' ' ',', :-' Vt l= [ (et-l) Cov{A(st l ]-St-l-l)-at-l}~

[ASt l I + BUt I 1 X [ Ht 1]

Gt l= [__t~ I]

and, i.e. for l=L, Rt L= Vt L

Vt L= COV{A(Ct-l-Ct-l)-act}
Yt-L= ACt_l+
Gt L= I-When the state vectors are also decoupled in the space domain those subsystems are indicated by equations (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 substructures are permuted to conform with the overall block-angular form of equation (18).
For a CoDtinuous Kalman Eilter: ut = F(t) at bt (Gelb 1974, pp.l22-124).
Referring now to Fig.; 2, a specific embodiment of a prior art navigation system using a decentralized Kalman Filtering technique will be explained. As suggested by the block diagram, Federated Piltering (Neal A.
Carlson, 1988: 7Federated Filter for Fault-Tolerant Integrated Navigation Systems~, Proceedings of the IEEE 1988 PLANS, IEEE AES Society, see figure 1 on page 111) is a two-stage data processing technique in which the outputs of local, sensor-related filters are subsequently processed and combined by a larger maste~ filter. Each local fflter is dedicated to a ' , -. '' . .
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~vo 90/l3794 2(~5~L6~ r~ o/r~0l22 separate subsystem of sensors. One or more local filters may also use data from a common reference system, e.g., an inertial navigation system (~S).
The advantages over an prior art centralized Kalman filtering technique are an increased total system throughput by parallel operation of local filters and a further increase of system throughput by using the local filters for data compression. Approaches of this kind bave been absolutely necessary for large multi-sensor navigation systems because of high-speed computing requirements. From the viewpoint of a prior art centralized Kalman Filter of a large sensor system, these approaches for speeding up the computations fall into the two general categories of appro~imative methods i.e. decollpling states and prefiltering J~or data compression (see e.g. Gelb, 1974: ~Applied Optimal Estimation", MIT Press, pages 289-291).
The disadvanges are that an appro~imative Kalman Filter never is strictly optimal and, consequently, its stability becomes more or less uneertain.
In any ease, the stability is more difficult to establish in a theoretically rigorous way.

Referring now to Fig. 3, a bloek diagram of the apparatus of the invention that makes use of a theoretieally sound yet praetieal eentralized Kalman Filtering method will be deseribed.

As can be seen by comparing Figs. 1 and 3, the logie unit (1) of the invention has a two-way communieation link to the data base unit (2) whereas the prior art logic unit (11) ean only read from its data base unit (12). In order the prior art sensor and ealibration unit to operate properly, the data base unit (12) must have an appropriate eolleetion of data regarding sensor (13) performanee. Sueh information must be empirieally established, and often needs to be re-established at adequate intervals, for each individual sensor (13) by sequentially e~posing each sensor (13) to a number of known e~ternal events of known magnitudes. This is not possible in many eases of practieal importanee; eonsider e.g. a radiometrie sensor of an orbiting weather satellite. In eontrast, the logie unit (1) of the invention has a capability of stretching and updating the calibration information collected in its data base (2) assuming only that a ccrtain observability condition of K~ an Piltering is satisfied.

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WO 90/1379 ~ ~Cr/FI~1)/00122 205~6~3~
~4 As can be seen by comparing Figs. 2 and 3, the Fcdcratcd Kalman Filter solution is the same as that of a single, ccntralized Kalman Filtcr only if the information fusion and division operations arc performed aftcr every local filter measuremcnt update cycle (and when the mastcr filter should be able to cope with the large Kalman Filtering problem without any help from decol~pling statcs). Thus, the prior art solution of Fig. 2 is theorctically inferior bccause it is a full centralizcd Kalman Filter solution of Fig. 3 that yields optimal results as shown by Kalman in l9oO
or, in fact, by Gauss and Markov already in the early 1800. However, the computation load of a prior art centralized Kalman Filter is proportional to n3 where n is the number of the state pararneters i.e. the number of all unknown quantities that necd to be solved for an update of the process parameter estimates.

Pursuant to use of this apparatus and method, simple and ine~pensive sensors can be fully e~cploited without too much regard for thcir internal calibration provisions and the speed of logic units. Despite use of entirely uncalibrated but predictable sensors, accurate results can be obtaincd in real-time applications through use of the calibration and standardization method and apparatus disclosed herein.

The invented Fast Kalman Filtering (FKF) method is based on the general principle of deco~pling states. The use of Lange's analytical sparse-matn~c inversion method is pursuant to the invention (see e.g.
Lange, 1988a). Because the solution is straightfor vard and e~cact the optimality of a large centralized Kalman Filter can be achieved vith a hard-to-beat computational efficiency.

Those slcilled in the art will appreciate that many variations could be practiced vith respect to the above described invention without departing from the spirit of the invention. Therefore, it should be understood that the scope of the invention should not be considered as limited to the specific embodiment described, e~cept in so far as the claims may specifically include such limitations.

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,' wo ~)o/137~ PCI/Fl90Jo012 ~5~68 Referçnce~

(1) Kalman, R. E. (1960): 'rA new approach to linear filtering and prediction problems". Trans. ASME J. of Basic Eng. 82:35-45.

(2) Lange, A. A. (1982): nMultipath propagation of VLF Omega signals~.
ILEE PLANS '82 - Position Location and Navigation Symposium Record, December 1982, 302-309.

(3) Lange, A. A. (1984):"Integration, calibration and intercomparison of windfinding devices". WMO Instruments and Obser~ring Methods Report No. 15.

(4) Lange, A. A. (1988a): "A high-pass filter for optimum calibration of observing systems with applications". Simulation and Optimization of Large Systems, edited by A. J. Osiadacz, O~cford University Press/Clarendon Press, O~cford, 1988, 311-327.

(S) Lange. A. A. (1988b): "Determination of the radiosonde biases by using satellite radiance measurcmentsn. WMO Instruments and Observing Mct~ods l~eyon No. 33, 201-206.

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Claims (12)

WO 90/13794 PCT/Fl90/00122 AMENDED CLAIMS
[received by the International Bureau on 26 September 1990 (26.09.90);
original claims 1-4 replaced by amended claims 1-12 (5 pages)]

1. A method for calibrating readings of a multiple sensor system, the sensors providing output signals in response to external events, the method comprising the steps of:

a) providing data base means for storing information on:
- a plurality of test point sensor output signal values for some of said sensors and a plurality of values for said external events corresponding to said test point sensor output values;
- said calibrated sensor readings or, alternatively, said readings accompanied with their calibration parameters and values for said external events corresponding to a situation; and, - controls of or changes in, if any, said sensors or said external events corresponding to a new situation;

b) providing logic means for accessing said calibrated readings or, alternatively, said readings accompanied with their calibration parameters, said logic means having a two-way communications link to said data base means;

c) providing said sensor output signals from said sensors to said logic means;

d) providing information, if any, on said controls or changes to said data base means;

e) updating by using the Fast Kalman Filter (FKF) formulae, in said logic means, values of both said external events and said calibration parameters corresponding to said new situation;
and, f) providing updated values of said calibrated readings and/or said values of said external events, as desired.

2. The method of claim 1 wherein said logic means operates in a decentralized or cascaded fashion but exploits in one way or another the Fast Kalman Filter (FKF) formulae.

3. A calibration apparatus for use with a multiple sensor system that provides substantially predictable sensor outputs in response to a monitored event, the apparatus comprising:

a) data base means for storing information on a plurality of sensor output values for each sensor with which the calibration apparatus will be used and a plurality of values for said external event corresponding to a situation and to some test points, if any; and, b) logic means, based on the Fast Kalman Filter (FKF) formulae, operably connected to said multiple sensor system 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 for said external event, for providing an output that comprises calibrated readings for said multiple sensor system and/or, as desired, current values of said external event that may all be substantially standardized to preselected standards.

4. The apparatus of claim 3 wherein said logic means operates in a decentralized or cascaded fashion but exploits in one way or another the Fast Kalman Filter (FKF) formulae.

5. The method of claim 1 including the step of:

a) adapting by using the Fast Kalman Filter (FKF) formulae, in said logic means, said information on said controls of or changes in said sensors or said external events as far as their true magnitudes are unknown.

6. The method of claim 2 including the step of:

a) adapting by using the Fast Kalman Filter (FKF) formulae, in said logic means, said information on said controls of or changes in said sensors or said external events as far as their true magnitudes are unknown.

7. A data-assimilation apparatus for use with an observing system and a dynamical prediction system that provides substantially predictable outputs in response to a monitored event, the apparatus comprising:

a) data base means for storing information on a plurality of sensor output values for each sensor system with which the apparatus will be used and a plurality of values including their changes predicted by said dynamical system for said external event 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 prediction systems 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 for said external event, for providing an output that comprises calibrated readings for said observing system and/or, as desired, current values of said external event that may all be substantially standardized to preselected standards.

8. A prediction apparatus for use with an observing system and a dynamical prediction system that provides substantially predictable outputs ahead of monitored events, the apparatus comprising:
a) data base means for storing information on a plurality of sensor output values for each sensor system with which the apparatus will be used and a plurality of values including their changes predicted by said dynamical system for said external events and for some test points, if any; and, WO 90/13794 PCT/Fl90/00122 b) logic means, based on the Fast Kalman Filter (FKF) formulae, operably connected to said observing and prediction systems 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 for said external events, for providing an output that comprises predicted readings for said observing system and/or, as desired, predicted values of said external events that may all be substantially standardized to preselected standards.

9. A control apparatus for use with a sensor system and a dynamic system that provides substantially predictable state parameters of said dynamic system, the apparatus comprising:

a) data base means for storing information on a plurality of sensor output values for said sensor system with which the apparatus will be used and a plurality of values, controls and changes predicted by a model of said dynamic system for said state parameters and for some test points, if any;

b) logic means, based on the Fast Kalman Filter (FKP) formulae, operably connected to said sensor and dynamic systems for receiving said sensor outputs and said controls 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, controls and predicted changes for said state parameters, for providing an output that comprises calibrated/predicted readings for said sensor system and/or current/predicted values of said state parameters, as desired, that are substantially standardized to preselected standards.

10. Apparatus of claim 7, 8 or 9 wherein said logic means operates in a decentralized or cascaded fashion but exploits in one way or another the Fast Kalman Filter (FKF) formulae.

WO 90/13794 PCT/Fl90/00122

11. Apparatus of claim 3, 7, 8, or 9 wherein information on controls or changes in said sensors or said external events as far as their true magnitudes are unknown is adapted by using the Fast Kalman Filter (FKF) formulae.

12. Apparatus of claim 4 or 10 wherein information on controls or changes in said sensors or said external events as far as their true magnitudes are unknown is adapted by using the Fast Kalman Filter (FKF) formulae.