WO2005050138A1

WO2005050138A1 - Apparatus, system, method, and program for determining the value of a measurement that changes over time

Info

Publication number: WO2005050138A1
Application number: PCT/EP2004/013046
Authority: WO
Inventors: Alexander V. Lopatin; Sergey Ermishin
Original assignee: Madison Technologies Limited
Priority date: 2003-11-17
Filing date: 2004-11-17
Publication date: 2005-06-02
Also published as: RU2003133241A

Abstract

A method and system for processing measurements. The method comprises producing, at plural sensing stations, corresponding uncompensated output signals responsive to detected physical phenomena, and determining an error in at least one of the uncompensated output signals, based upon those uncompensated output signals. A next step includes compensating for error in at least one uncompensated output signal, based on the determined error. A compensated signal is generated, representing a value substantially equal to a quantity of a physical phenomenon subjected to detection by the sensing station that produced the signal subjected to compensation. The determined error includes at least systematic and random error components Δsyst and Δrand. Detections made by a sensing station producing signals not subjected to compensation preferably are separated by greater time intervals than are detections made by a sensing station producing signals subjected to compensation.

Description

APPARATUS, SYSTEM, METHOD, AND PROGRAM FOR DETERMINING THE VALUE OF A MEASUREMENT THAT CHANGES OVER TIME

BACKGROUND OF THE INVENTION

Cross Reference to Relation Applications

[0001] This application claims priority of Russian Patent Application No. 2003133241, filed November 17, 2003, which is hereby incorporated by reference herein in its entirety, as if fully set forth herein.

Field of the Invention

[0002] This invention relates to metrology, and, in particular, to general purpose measuring devices for measuring variable values, and more specifically, to a measuring apparatus, system, method, and program that perform digital calculation or data processing in order to reduce measurement errors. The invention can be used to make reference measurements of any measurable quantity.

Related Background Art

[0003] A known device for determining the value of a measurement that changes over time is described in certificate of authorship SU 1649460 Al, 5/15/91, G 01 R 19/00, and contains two approximate measurement modules that can give an output signal for the value of the measurement and for three previously set parameters of the same type as the measurement. The device can indicate the relationship between the true value of a measurement and the measured value for each of the approximate measurement modules, as well as between the true value of the parameter and the measured value of the parameter for each of the approximate measurement modules in the form of linear relationship with undetermined constant coefficients. At the same time, the device can detect unambiguously determined relationships between the true value of the measurement and the measured value as measured by the approximate measurement modules, by selecting the values of these coefficients. The device can also determine the true value of a measurement based on this unambiguously determined relationship. [0004] The principal disadvantages of the foregoing device are the inadequate precision of the measurements, such that the representation of the relationship between the true and measured values is limited by the linear function, as well as the inadequate universality and undesired complexity of the use of the device, since data on the true values of the parameter (a sample measure), measured with reference-level precision, are required in order to take measurements. A need exists, therefore, to provide a device for reducing measurement errors that does not suffer from the foregoing disadvantages.

SUMMARY OF THE INVENTION

[0005] It is an object of this invention to provide an apparatus, system, method, and program for reducing measurement errors, and which overcome to foregoing problems. [0006] It is another object of this invention to provide an apparatus, system, method, and program for processing measurement data.

[0007] It is a further object of this invention to provide an apparatus, system, method, and program for increasing the precision of measurements. [0008] It is still a further object of the present invention to provide an apparatus, system, method, and program for making reference measurements of a variable measurable quantity.

[0009] According to an aspect of the present invention, a method, and an apparatus, system, and program that operate in accordance with the method, are provided, which achieve the foregoing objects. The method enables there to be an increase in the precision of processing measurement data by taking into account both incidental and systematic constituent errors and correcting for them in a measurement output signal. [0010] According to a preferred embodiment of the present invention, the system comprises plural sensing stations. At least a first sensing station comprises a sensor and an indirect measurement module, and detects a measurable physical quantity or phenomenon, such as, e.g., voltage, current, a quantity of liquid flow, or some other measurable physical quantity. The station produces a corresponding uncompensated measurement signal representing the detection, varied at least somewhat by an error introduced by the indirect measurement module. Preferably, the system also includes at least a second sensing station that includes an approximate measurement module and another sensor, for preferably measuring either the same type of physical quantity (or parameter) as that measured by the first sensing station or another type of physical quantity that is related to the physical quantity measured by the first sensing station through a predetermined relationship. The second sensing station outputs a corresponding uncompensated measurement signal that includes an error resulting from the approximate measurement module. A relative error rate of the indirect measurement module preferably is less than a relative error rate of the approximate measurement module.

[0011] The system also comprises a measurement error correction module, having a first input coupled to an output of the approximate measurement module, and a second input coupled to an output of the indirect measurement module. The measurement error correction module performs calculations employing one or more mathematical formulas based on a relationship between a variable representing a substantial approximation of the "true" or actual value of the physical quantity being measured and physical measurements made over a predetermined time period. The module determines a substantial approximation of the actual, or true, value of a measurement (for at least two instances in time) in accordance with signals received through its first and second inputs. An output of that module is provided to a measurement value module, which then determines an error in at least one uncompensated measurement signal, such as at least one signal outputted from the second sensing station. The error determination is based on an unambiguous relationship between the substantial approximation and at least one corresponding measurement (preferably by the second sensing station). [0012] According to an aspect of this invention, the error includes at least a systematic error component A_syst and a random error component A_ra„_d, each of which is determined according to this invention.

[0013] The measurement value module then compensates for error in at least one uncompensated measurement signal outputted by the second sensing station, based on the error determined in the determining. As a result, the measurement value module generates a compensated signal representative of a value that is substantially equal to the value of the actual physical phenomenon that is subjected to detection by the second sensing station. [0014] Detections made by the first sensing station preferably are separated by greater time intervals than are detections made by the second sensing station. Both sensing stations preferably make detections over a same predetermined time period. [0015] The output of the measurement error correction module preferably remains unchanged for use by the measurement value module, until a next uncompensated measurement signal is received from the indirect measurement module. [0016] The sensing stations may be spaced apart from each other, and may even be physically distant from each other, depending on predetermined design criteria, and their measurements can be obtained for use by the method of the invention regardless of the distance between the sensors.

[0017] The system is capable of more universal application than are known measurement correction devices, is less complex than such devices, and is easier to use, especially because, according to one embodiment, at least one of the measurement value module and the measurement error correction module is a modular component.

BRIEF DESCRIPTION OF THE DRAWINGS [0018] FIG. 1 is a block diagram of a system (1) according to a preferred embodiment of this invention, for determining the value of a measurement that changes over time. [0019] FIG. 2 represents two heterogeneous sets of measurement results employed in a method of the present invention.

[0020] FIG. 3, consisting of FIGS. 3A and 3B, depicts a flow diagram of a method performed according to the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT [0021] A preferred embodiment of the present invention will be described in detail below with reference to the accompanying drawings.

[0022] FIG. 1 depicts a block diagram of a system (1) according to the present invention, for determining the value of a measurement that changes over time and increasing the measurement's accuracy so that it approximates substantially the actual or "true" value being measured. In the illustrated embodiment, the system (1) comprises a plurality of sensing stations, such as stations (4') and (5') (only two are shown for convenience), and at least one worknode or user station (6'). In that illustrated embodiment, sensing station (4') includes a sensor (4) and an approximate measurement module (2), and sensing station (5') includes a sensor (5) and an indirect measurement module (3). [0023] The sensor (5) may be spaced apart from the sensor (4), and may even be physically distant therefrom, depending on predetermined design criteria, and their measurements can be obtained for use by the method of the invention regardless of the distance between the sensor (4) and (5). The sensors (4) and (5) each provide an output signal in response to detecting a predetermined physical parameter or phenomenon, such as a predetermined type of energy, temperature, liquid, pressure or mass flow, or any other measurable physical quantity. In an exemplary embodiment, the sensors (4) and (5) measure an electrical energy quantity, such as voltage and/or current, at different parts of a same electrical circuit (not shown). As an example, sensor (5) may be a voltmeter measuring the voltage output of a power generator located in one loop of the electrical circuit, and sensor (4) may be a voltmeter for measuring a voltage in another loop of the circuit powered by the same generator, or vice versa. As a further example, in a case where a quantity of fluid flow in a pipeline is being measured, fluid meters with operational precision may be employed to measure the quantity of fluid flow. [0024] In other embodiments, the sensors (4) and (5) can measure different types of parameters that are related through a predetermined relationship, depending on applicable operating criteria. For example, the sensor (5) may measure a parameter (e.g., current) that is related to the parameter (e.g., voltage) measured by the sensor (4) through a predetermined functional relationship. However, for convenience, the present description is made in the context of the sensors (4) and (5) both measuring the same type of electrical energy parameter (e.g., voltage). [0025] According to a preferred embodiment of the invention, the sensors (4) and (5) make detections and provide corresponding output signals over a same predetermined time period, but at distinct points in time, so that the signals from the sensors (4) and (5) are not eventually received at the user station (6') simultaneously. Those signals may be outputted from the sensors (4) and (5) at a same or different frequency, as long as they are outputted at different points in time. By virtue of the sensors (4) and (5) outputting signals over a same time period, the user station (6') is able to recognize that the signals originated from those sensors (4) and (5) as opposed to from other sensors (not shown) that may transmit signals over a different time period. Preferably, the interval between measurements taken by the sensor (5) is greater than the interval between measurements taken by the sensor (4).

[0026] The approximate measurement module (2) and the indirect measurement module (3) each represent a separate physical component that undesirably introduces some error quantity into the measurements made by the sensors (4) and (5), respectively. By example only, in an embodiment where the sensors (4) and (5) are analog devices, the modules (2) and (3) may be A/D converters that introduce an error quantity into the measurements, wherein the error quantity depends on a characteristic error inherent in the respective 5 modules (2) and (3). In another embodiment, the modules (2) and (3) may be voltage- frequency converters with a counter, although it should be noted that the modules (2) and (3) are not limited only to A D or voltage frequency converting devices. Preferably, the relative error rate (i.e., characteristic error) inherent in the indirect measurement module (3) is less than that of the approximate measurement module (2). Also, although in the 0 illustrated embodiment the modules (2) and (3) are depicted as being physically separate from the sensors (4) and (5), respectively, in other embodiments the modules (2) and (3) and sensors (4) and (5), respectively, may be integrally formed. [0027] By virtue of the characteristic error inherent in the modules (2) and (3), their output signals represent the original measurements made by the sensors (4) and (5), 5 respectively, but varied by (plus or minus) an error value corresponding to the characteristic error inherent in the respective modules (2) and (3). For convenience, these output signals are hereinafter referred to as uncompensated parameter measurement signals, and may include random and systematic errors (described below). The measurements may vary over time owing to, for example, error fluctuations.O [0028] The user station (6') may be, e.g., a PC, laptop or other remote personal computer, a personal digital assistant, or the like. The user station (6') is communicatively coupled with the modules (2) and (3) through any suitable type of communication link, using, for example, telephone, cable, or other, wireless technologies, and at least part of the cornmunication link may be part of a communication network, such as the Internet (not5 shown) and/or some other network. The number and variety of user stations (6') that may be linked with the sensing stations (4') and (5') can vary widely, as can the number of sensing stations (4') and (5') that are employed, depending upon applicable operating criteria. In general, the teaching of this invention may be employed in conjunction with any suitable type of user station device that is capable of communicating with other, O sensing components, and which preferably includes one or more user interfaces for enabling a user to input and/or perceive presented (e.g., displayed) information. [0029] The user station (6') preferably comprises a controller (11 ') and an associated data storage device (9), an output-user interface, such as a display (13), and a user-input interface (6"), all of which are communicatively coupled to the controller (11 '). The controller (11 ') controls the overall operation of the user station (6'), and includes, for example, one or more microprocessors and/or logic arrays for performing arithmetic and/or logical operations required for program execution.

[0030] A measurement value module (11) and a measurement error correction module (6) may be included in the controller (11 '), although in other embodiments one or more of the modules (6) and (11) may be separate from the controller (11 '). According to a preferred embodiment of this invention, one or both of the modules (6) and (11) are distinct modular components (e.g., microchips) that are adapted for universal application with various types of devices, such as the user station (6'), and those modules (6) and (11) may be included in or be separate from the user station (6'). The modularity of the components (6) and/or (11) makes them less complex, more universally applicable, and easier to use relative to prior art error correction devices.

[0031] The measurement error correction module (6) has a first input (7) coupled to an output of the approximate measurement module (2), and a second input (8) coupled to an output of the indirect measurement module (3). An output of the measurement error correction module (6) is coupled to a first input (10) of the measurement value module (11). A second input (12) of the module (11) is coupled to the output of the approximate measurement module (2). The module (11) generates output information that is provided to the display (13), which responds to receiving the information by presenting it to a user. Such information, as will be described below, represents a reference measurement value. [0032] Referring now to the user-input interface (6"), that interface may include, for example, a keyboard, a mouse, a trackball, touch screen, and/or any other suitable type of user-operable input device(s), and the output-user interface may include, for example, a video display, a liquid crystal or other flat panel display, a speaker, a printer, and/or any other suitable type of output device for enabling a user to perceive outputted information, although for convenience, only the display (13) is shown in Fig. 1. [0033] The data storage device (9) represents one or more associated memories (e.g., disk drives, read-only memories, and/or random access memories), and stores temporary data and instructions, as well as various routines and operating programs that are used by the controller (11 ') for controlling the overall operation of the user station (6'). Preferably, at least one of the programs stored in the device (9) includes instructions for performing a method in accordance with this invention, to be described below, although in other embodiments at least some of the instructions may be included within the module (6) and/or (11). The data storage device (9) preferably also stores data representing uncompensated parameter measurement signal values outputted by the indirect measurement module (3), data representing uncompensated parameter measurement signal values outputted by the approximate measurement module (2), and various other information obtained during performance of the method of the invention to be described below.

[0034] One or more components of the system (1) may conform to various types of technology standards, such as, for example, PXI, VXI, IEEE 1451.4 (TEDS), FIELDBUS technologies, or any other suitable types of technologies. [0035] The method according to a preferred embodiment of this invention will now be described, with reference to FIGS. 3A and 3B.

[0036] At block 20 detections are made by the sensors (4) and (5) in the above-described manner and then, in the illustrated embodiment, their outputs are processed by the respective modules (2) and (3) at block 22. For example, in a case where the modules (2) and (3) are analog-to-digital converters, the sensor outputs are A/D-converted by the modules (2) and (3), which, in the present example, introduce an undesired error into those outputs, depending on the characteristic error inherent in the respective modules (2) and (3). Uncompensated parameter measurement signals outputted by the modules (2) and (3) are then provided to the user station (6')- The controller (I T) responds to receiving the initial signals from the respective modules (2) and (3) by, for example, identifying the sensors from which the received signals originated (by recognizing, for example, a predetermined unique identification code included in the signals), and also recognizing the types and number of the sensors and the type of parameter(s) detected thereby. These identification and recognition functions may be performed in accordance with any suitable, known identification and recognition technique(s), and will not be described in further detail herein.

[0037] A high-precision error compensation procedure according to the present invention then is performed. During the procedure, which, for example, may be initiated by a user entering a predetermined command into the user station (6'), first values Yi representative ofthe uncompensated parameter measurement signals outputted by the indirect measurement module (3) (over the predetermined time period) and provided to the user station (6'), are stored in data storage device (9) in a first array of such values (block 24). 5 Second values Y₂ representative ofthe uncompensated parameter measurement signals outputted by the approximate measurement module (2) (over the predetermined time period) also are provided to the user station (6') and stored in the device (9), but in a second array that includes such values, at the block 24. [0038] Next, at block 26 the module (6) performs a number of procedures. First, anO arithmetic mean ofthe measurement results is determined. As an example, the array of first values Yi and the array of second values Y₂ are each subdivided into a first subset and a second subset thereof, wherein, the each subset includes a predetermined number (e.g., five) ofthe respective first or second values. The first values ofthe first subset of first values are summed in the equation (F11) and the first values ofthe second subset of 5 first values are summed in equation (Fl₂), and each sum is divided by n/2

O where: « represents the number of first values; yi represents a first value (originally outputted by module (3)); Y_\ ^l represents an average ofthe first subset of first values; and Y_^l represents an average ofthe second subset of first values. [0039] The second values ofthe first subset of second values are summed in the equation5 (F2τ) and the second values ofthe second subset of second values are summed in equation (F2₂), and each sum is divided by n/2:

Σ^² Y² = ^j- (F2₂) n / 2 where: n represents the number of second values; yi represents a second value (originally outputted by module (2)); Yi represents an average the first subset of second values; and Y2 represents an average ofthe second subset of second values.

[0040] A transpose of Y and 7 can be represented by (F3) below, and a transpose of Yj² and Y_² can be represented by (F4) below:

[0041] A ratio fo represents a first general approximation of a multiply-systematic effect in the error in the indirect measurement module as a proportion (fo -1), and essentially is a difference between the averages ofthe second and first subsets of second values to a difference between the averages ofthe second and first subsets of first values. The ratio k is determined using the following equation (F5) (preferably the middle portion is employed in the calculation), based on the averages determined above.

[0042] A linear operator 7 representing the sensing station (4') can be represented in matrix form (F6) below, and, based thereon, another form ofthe above formula (F5) can be obtained, as represented by formula (F7) below.

γ² _ v² (T - Y Ϋ - E" Y_ - Y_x ^l Y₂ ^l -Y_x ^l where E" is a unit vector as follows: E' =

[0043] In the process of real technical measurements, the approximate measurement module (2) can introduce a multiply-systematic error effect (factor), and thus disturbances in the linear operator T occur, where the influence of disturbance can be represented by the following expression: T{χ) = T + χ - T where: χ represents a disturbance value caused by external influencing factors. E.g., at least part, if not all, ofthe disturbance χ may be caused by the multiply-systematic effect of the module (2).

[0044] It is known that linear operators ofthe type T(χ) are characterized by their own ambiguous functions with two branches. For example, in a publication by Kato T., entitled "Theory of Disturbance of Linear Operators", pp. 62-67, M: Mir (1972) (hereinafter "the Kato publication"), a description is given of an example analysis resulting from research, ofthe disturbance (perturbation) of individual characteristic values (eigenvalues) of a disturbed operator ofthe following type:

where: x) = ^ + X² (F9) ^ω =-^+?

[0045] Thus, a "perturbed" form of formula (F7) can be represented as shown in the following expression (10). Y₂ -Y² (T' - Ϋ₂)^τ - E" γl _ γl γl _ γl (F10) ^J 2 l ¹2 ¹ l [0046] Based on the definition of eigenvectors, two eigenvalues of linear operator are λ_1>2( ), and thus eigenvectors ujj of 2" can be obtained through the following equations (Fill) and (Fl l₂), which generally relate to a matrix of eigenvectors: T' -U _(x) = ₂(x) - u_{x X}) (FHi) (T' - ₂ (χ) - E) - u ₂ (χ) = 0 (Fl l₂) where: E is a unit vector X) = ^ + X² (F12) X) = -^ + X² (_F13) and u is a vector representing a single matrix (with one diagonal). [0047] According to the definition of eigenvectors, and based on the form of formulas (F5) and (F10), values k_\ and &₂ are obtained by the module (6) based on formula (F14): _{k =} Y² - Y² ₌ (T - Ϋ₂)^τ - E" _ ( ₂ (χ) - _h2 (χ))^τ -E" ^!>² γl _ γ γ γl γl γl ^l2 ^Xl ¹2 ^ll ¹2 ¹ι (F14) where: k_\ represents one possible value ofthe approximation ofthe multiply-systematic effect in the error in the indirect measurement module (3) as a proportion (k_\ -1); and kχ represents another possible value ofthe approximation of the multiply-systematic effect in the error in the indirect measurement module (3) as a proportion (k -l). [0048] Based on the above expression (F14), a multi- valued function (F15), defining the equation of a straight line (disposed at an angle), can be represented by:

[0049] After block 26, control passes to block 28 where data obtained based on at least some ofthe foregoing formulas is stored in the data storage device (9). Thereafter, control passes through connector A to block 30 of FIG. 3B. At block 30, a determination is made as to whether k_\ or k_∑ should be selected as being closest to k₀, using a target function formed using min-max criteria. For example, according to a preferred embodiment ofthe invention, this procedure first includes assignment ofthe required type of function, using expression (F18):

where: x_t represents ideally the "true" value ofthe measurement (i.e., a substantial approximation thereof); ψ- is a transformation function representing the sensing station (5'); i¹ represents measurement values taken by sensing station (5') and stored in device (9); and Co is a value representing a common (systematic) effect expressed as an additive correction. Generally, value α₀ is near zero, and is less than the multiplicative systematic error.

[0050] Also, a constraint zone is formed based on the following formula (F19):

where: y_t ^l represents a first value, influenced by kj and k_∑ (through formulas (F14) and (F15)) (i.e., a signal from the indirect measurement module (3) and stored in device (9); yf represents the second value (i.e., a signal from the approximate measurement module (2) and stored in device (9)); and σ_t represents a predetermined error constraint value defining the limit of acceptable yf values. The predetermined error constraint value preferably is substantially equal to a predetermined characteristic error inherent in the approximate measurement module (2), although in other embodiments other values may be employed instead, such as, for example, a characteristic error inherent in the module (3).

[0051] Thereafter, the criterion function His formed as represented in formula (F20) (block 30). H = Min Max(k₀ - k ₂ (χ)) ■ y) ^1,2 ' (F20) [0052] The formula (F20) employs only those values that are determined to satisfy the formula (19), and determines essentially a difference between (ko - kϊ) and (ko - ). The lesser difference is then selected, as is the corresponding value kj or &₂. [0053] Thereafter, control passes to block 32, where the module (6) calculates a value for X, based on formula (18) above, using values determined to satisfy formula (19) as well as the result of formula (20). The resulting calculated value x_t is stored in the device (9) and provided to (or accessed from device (9) by) the measurement value module (11) (block 34). Thereafter, at block 36 the measurement value module (11) uses the result from formula (18) and a second value yf (originating from module (2)) in performing formula (F21) below, to calculate a corresponding error Af, that includes both random and systematic components:

[0054] It should be noted that in formula (F21) second value(s) y (originating from the approximate measurement module (2)) preferably are employed rather than first value(s) (originating from the indirect measurement module (3)). Those second values may be ones received in real time from sensing station (4'), or, in another embodiment, they may be previously received and/or stored second values, depending on predetermined operating criteria. In other embodiments ofthe invention, values from the module (3) may be used in formula (F21) instead, depending on the application of interest. [0055] The random component (ofthe above error), which also is referred to as a random effect, is then calculated by module (11) using equation (F22) (block 36): rand (F22) where: A_rand represents the random component; and D_AX represents a known mathematical dispersion. [0056] Moreover, according to an aspect of this invention, the systematic component (also referred to as a systematic effect) is calculated by the module (11) using equation (F23): st = ^rend( χ) (F23) where: ^_t represents the systematic component (also referred to as the systematic effect) of sensing station (4') (e.g., particularly module (2)), in the exemplary embodiment described herein; and 5 trend(A_x) represents a trend function.

[0057] The error coefficients determined in the foregoing manner in formulas (F21) to (F23) are then stored in the data storage device (9) at block 40. [0058] Thus, when uncompensated parameter measurement signals are received by theO module (11) from the approximate measurement module (2) (after the value x,has been obtained by module (11)), random and systematic errors that may be included in the signals are substantially compensated for by the module (11), based on a random error value A_ra,_ιd and systematic error value A_syst calculated using formulas (F22) and (F23), respectively. As a result, the module (11) generates corresponding compensated signals 5 that are substantially close in value (or at least closer than the corresponding value outputted from module (2)) to the actual or "true" value ofthe corresponding parameter (phenomenon) subjected to measurement by the sensor (4) (block 42). Information outputted from the module (11) represents the compensated signal(s) (as well as a reference magnitude ofthe measured parameter) and is forwarded to the display (13),O which responds to receiving the information by presenting it to the user (block 44). In the foregoing manner, the measurements originating from the sensor (4) and provided to the module (2) are corrected to improve their accuracy. [0059] It should be noted that, although not described herein for convenience, additional procedures/calculations also may be performed in the module (11) and/or module (6) to5 standardize the value(s) from the stations (4') and/or (5') to ensure that they are processed in a same workable format that depends on the application of interest. For example, in a case where it is expected that a voltage detected by sensing station (4') differs by a predetermined factor from a voltage detected by sensing station (5') because ofthe stations' given locations within an electrical circuit, voltage values obtained from one orO both stations can be weighted as deemed necessary to account for the factor, and the output value from the module (11) can be modified to account for any such weighting. Also, in embodiments where the sensors (4) and (5) measure different types of parameters (e.g., current and voltage), the calculations preferably also account for this difference as well by converting values derived from a predetermined one ofthe sensors from one format (i.e., current) to another selected format (e.g., voltage), based on the predetermined relationship through which the parameter types are related, so that values ofthe same type are obtained for each sensor (4) and (5) for use in the formulas. These calculations may me performed in accordance with any suitable known techniques.

[0060] Also, in accordance with a preferred embodiment of this invention, the output from the module (6) to the module (11) is generated only after a signal is applied to the module (6) from the module (3), and the output from module (6) is maintained the same until a next signal received from module (3) is applied to and processed by the module (6) (or the module (6) processes a next subset of values received from module (3), depending on the embodiment employed).

[0061] Also, it should be noted that, according to one embodiment ofthe invention, the signals that are subjected to compensation are the same signals for which the error is determined. However, in other embodiments the signals that are subjected to compensation may be ones that are received at module (11) after the error is determined based on earlier received signals.

[0062] Also, according to another embodiment ofthe invention, formulas (F21) to (F23) are performed by the module (6) instead ofthe module (11), and the error values determined in those formulas are provided from module (6) to module (11), which then employs them to compensate uncompensated parameter measurement signals.

[0063] Having described the method of this invention is detail, mathematical theory upon which this invention is based will now be described. A basis ofthe principal on which the error correction module (6) operates is the effect of ambiguousness. The effect of ambiguousness, which is the basis ofthe technical result produced by this invention, is illustrated in diagram 2.

[0064] In particular, the principal problem in increasing the accuracy of processing technical measurements on the basis of mathematical methods of processing the results of measurements is eliminating systematic constituent errors in the measurements, which generally account for more than 90% of total errors in measurement. Traditional mathematical methods of processing data examine a set of measurement results as a homogenous aggregation Ω, and therefore they do not allow for the reduction of systematic constituent errors without conducting additional highly precise measurements. The invention, on the other hand, provides a method for obtaining virtual reference measurements based on the use of two (or more) heterogeneous sets of measurement results (Ωl Ω2 in Fig. 2), and on that basis, reduces systematic constituent errors in measurements as well as incidental errors. [0065] If measurements are represented as a function of unknown incidental and systematic constituent errors in measurement, then an equation that is a function of only a single set of measurement results will be unsolvable. However, by examining the results ofthe measurements as two heterogeneous sets, a system can be obtained that is made up of two equations that are a function of two unknowns, namely, incidental and systematic constituent errors of measurement. Such a system is solvable, and can take into account known measurement results and computational errors to evaluate the true value of a measured parameter. For example, the coefficients of a functional dependency that is a function of unknown incidental and systematic constituent errors of measurement are determined on the basis of multiple measurements with a consistently changing (decreasing or increasing) determining parameter.

[0066] By example, as the two heterogeneous sets of measurement results (Ωl Ω2 in Fig. 2) the following can be used, respectively: a set of results of multiple measurements, obtained as the measured parameter changes (decreases or increases) consistently, and a set of a priori information representing the measured parameter at each moment of time of the measurement.

[0067] The method of processing measurements depends on the use of reliable a priori information representing the measured parameter at each moment of time of measurement. Generally, such a priori information is very frequently present in the process of measurement, and if the necessary a priori information about the measured parameter is absent, it can be obtained on the basis of additional measurements that need not be extremely precise. The fact that the accuracy of measurement is elevated to the reference level as a result ensures that a very significant effect is achieved in this case as well. [0068] It follows that the discovery of ambiguity in the relationship between the true value of a measured parameter and the results of measurements allows the formulation and solution ofthe system indicated above from two mutually independent equations, and on that basis ensures reference-level precision in the measurements, taking into account the incidental as well as the systematic errors.

[0069] The physical origin of this effect of ambiguity in whether the true value of a parameter is consistent with the results ofthe measurements will now be examined. The interaction ofthe measured parameter and the means of measurement (MM) occurs on the potential field ofthe measured parameter, which generally is accompanied by a transformation ofthe potential energy between two points with different potentials into different forms of energy in the method of measurement. During measuring, the measuring instrument or gauge can disturb the object of measurement and introduce an error in the result of measurement.

[007O] A principal idea of a measurement procedure is the transformation of a closed mutually exclusive (isomorphic, as known in abstract algebra) system, "object of measurement — MM", into a unidirectional (homomorphous) system. This ideal condition with unidirectional (homomorphous) connections, "object of measurement — MM", corresponds to the true value ofthe measured parameter. The actual value of the measured parameter differs from the true value by the size ofthe measurement error. [0071] Assume that on the object of measurement during the time of measurement tj, a set of values ofthe measured parameter S is observed, and the output ofthe measuring device records the set of measurement results J. Let

where sπ and s₂₁ are the values ofthe measured parameter on the first point ofthe first object of measurement at the moment in time ti and t₂, respectively, and s₁₂ ands₂₂ are the values ofthe measured parameter on the second point ofthe second object of measurement at the moment in time ti and t₂. [0072] Then

where jπ andj₁₂ are, for example, direct current voltage values at the moments in time ti and t₂ .

[0073] In this example the measuring instrument can be represented by a linear operator T, where

J = T-D -S, (4") wherein D is the linear operator representing the nature ofthe conversion. It should be noted that technical measurements virtually always involve converting potential energy (two different potentials) from the object of measurement in the measuring instrument.

Therefore, the linear operator ofthe type represented by expression (3") is a general form of recording conversions of a signal of measuring information in measuring instruments. [0074] Formula (4") represents a mathematical conversion of coordinates, most frequently used in the process of technical measurements. [0075] As described above, in the process of real technical measurements, disturbances of the linear operator T exist due to external influencing factors, where the influence of disturbance can be represented by the following expression: T(χ) = T + χ -T (5") where χ is some small disturbance due to external influencing factors. [0076] As also described above, it is known that linear operators ofthe type T(χ) are characterized by their own ambiguous functions with two branches (see, e.g., Kato T., Theory of Disturbance of Linear Operators, M: Mir, 1972). The Kato publication describes an example analysis resulting from research, ofthe disturbance (perturbation) of individual characteristic values of a disturbed operator ofthe following type:

[0077] Characteristic values represented by *fe⁾= +* en ofthe operator T(χ) ofthe type (6') in essence are the branches of one double valued 110 analytical function, ±(l+χ ) , i.e., its area of determination (definitional domain) has so- called exclusive (exceptional) points χ=±i, in which incrementation of characteristic values during splitting represents an infinitely large quantity in comparison with the change in the operator itself T(χ). In the aforementioned publication by Kato, an evaluation is made for the radius of convergence of a perturbation theory series. The radius of convergence is represented by the expression r₀=l . [0078] The ambiguity ofthe characteristic values (7") ofthe disturbed operator (6") is manifested in the process of restoring the functional dependence (relationship) according to the results ofthe measurements. Therefore, consider multiple measurements, when the value ofthe physical amount on the object changes (increases or decreases) consistently, or evenly. The errors of multiple measurements represents the sum of two components, namely, the incidental component that is symmetrical relative to the true value ofthe measured amount, and the asymmetrical systematic component. The incidental component that is symmetrical relative to the true value ofthe measured amount is reduced rather easily by using traditional mathematical methods of processing measurement results, which examine a homogenous set of measurement results, corresponding to a closed mutually exclusive (isomorphic, as known in abstract algebra) system "object of measurement — MM."

[0079] In order to reduce the asymmetric component, which is a systematic constituent that is asymmetrical relative to the true value ofthe measured amount, it is necessary to examine the set of measurement results as a varying heterogeneous (non-homogeneous) aggregation, corresponding to unidirectional (homomorphous, according to abstract algebra) system "object of measurement — MM." One part ofthe heterogeneous aggregation of measurement results may conditionally correspond to the information (indicators) ofthe object of measurement, and another part to the respective indicators of the means of measurement. Applying mathematical methods of restoring the functional dependency (relationship) according to the measurement results relative to these calculations, it is possible to reduce not only the incidental, but also the systematic component of error. Such algorithms for processing measurement results transform the system "object of measurement — MM" from a closed mutually-exclusive (isomorphic, in the language of abstract algebra) system into a unidirectional (homomorphous in the language of abstract algebra) system. To the extent that, as noted above, the true value of the measured parameter corresponds to this ideal condition with unidirectional (homomorphous) connections "object of measurement — MM", the described information conversion can be considered to be standard, or referential. Certainly, despite its informational nature, this method of increasing the precision of measurements has the primary features (properties) of a referential standard. These features include invariability, repeatability, comparability, and constancy. All of these features are attained by moving measured values closer to true magnitudes of measured values, due to the unidirectional (homomorphous) nature ofthe connections "object of measurement —

MM."

[0080] A principal advantage ofthe method described is that it does not require the use of references to make reference measurements.

[0081] While the invention has been particularly shown and described with respect to a preferred embodiment thereof, it will be understood by those skilled in the art that changes in form and details may be made therein without departing from the scope and spirit ofthe invention.

Claims

CLAIMS:

1. A method for processing measurements, the method comprising the steps of: producing, at plural sensing stations, corresponding uncompensated output signals responsive to detected physical phenomena; and determining an error in at least one ofthe uncompensated output signals, based upon those uncompensated output signals, wherein the error includes at least a systematic error component Δ^.

2. A method as set forth in Claim 1, wherein the error also includes a random error component A_rand-

3. A method as set forth in Claim 1 , further comprising the step of compensating for error in at least one uncompensated output signal, based on the error determined in the determining.

4. A method as set forth in Claim 3, wherein the error also includes a random error component A_rand-

5. A method as set forth in Claim 1 , wherein the physical phenomena detected by one ofthe sensing stations relates to physical phenomena detected by another one ofthe sensing stations, through a predetermined functional relationship.

6. A method as set forth in Claim 3, wherein detections are made by the sensing stations over a predetermined time period.

7. A method as set forth in Claim 6, wherein an interval between detections made by a first one ofthe sensing stations that outputs uncompensated output signals that are not subjected to compensating, is greater than an interval between detections made by a second one ofthe sensing stations that outputs the at least one uncompensated output signal for which the error is compensated in the compensating.

8. A method as set forth in Claim 7, wherein the error is determined in the determining as a function ofthe at least one uncompensated output signal and a calculated value representing a substantial approximation of a quantity ofthe physical phenomena subjected to detection, and the calculated value remains unchanged until a next uncompensated output signal is outputted by the first sensing station.

9. A method as set forth in Claim 1, wherein the sensing stations are separated physically in space.

10. A method as set forth in Claim 1 , wherein the error is determined by performing a calculation that defines the error as a function ofthe at least one uncompensated output signal and at least an approximation of a true value of corresponding physical phenomenon subjected to detection.

11. A measurement system, comprising: plural sensing stations, each producing corresponding uncompensated output signals in response to detecting respective physical phenomena; and a processor arranged to receive the uncompensated output signals, and to determine an error in at least one ofthe uncompensated output signals, based upon those uncompensated output signals, wherein the error includes at least a systematic error component A_syst.

12. A measurement system as set forth in Claim 11, wherein the error also includes a random error component A_rand-

13. A measurement system as set forth in Claim 11, wherein the processor further compensates for error in at least one received uncompensated output signal, based on the error determined by the processor.

14. A measurement system as set forth in Claim 13, wherein the error also includes a random error component A_ra„_d.

15. A measurement system as set forth in Claim 13, wherein an interval between detections made by a first one ofthe sensing stations that outputs uncompensated output signals that are not subjected to compensating by the processor, is greater than an interval between detections made by a second one ofthe sensing stations that outputs the at least one uncompensated output signal for which the error is compensated.

16. A measurement system as set forth in Claim 15, wherein the processor determines the error as a function ofthe at least one uncompensated output signal and a calculated value representing a substantial approximation of a quantity ofthe physical phenomena subjected to detection, and the calculated value remains unchanged until a next uncompensated output signal is outputted by the first sensing station.

17. A measurement system as set forth in Claim 11 , wherein the sensing stations are separated physically in space.

18. A measurement system as set forth in Claim 11, wherein the physical phenomena detected by one ofthe sensing stations relates to physical phenomena detected by another one ofthe sensing stations, through a predetermined functional relationship, and are different from each other.

19. A measurement module comprising at least a measurement error correction module arranged to receive applied uncompensated measurement signals representative of externally detected physical phenomenon subjected to a measurement error that includes at least a systematic error component ^_t, the measurement error correction module determining a substantial approximation of a quantity ofthe physical phenomenon subjected to detection, based on a predetermined mathematical relationship defining the substantial approximation as a function of at least one applied uncompensated measurement signal converted though a conversion function representative of a measuring station.

20. A measurement module as set forth in Claim 19, wherein the measurement module further comprises a measurement value module having first and second inputs, the first input coupled to an output ofthe measurement error correction module, the second input for receiving further uncompensated measurement signals representative of externally detected physical phenomena subjected to a measurement error that includes at least a systematic error component A_sysh wherein the measurement value module is adapted to determine error in at least one ofthe uncompensated measurement signals, based upon the substantial approximation ofthe physical phenomenon determined by the measurement error correction module, and wherein the measurement value module also compensates for error in at least one uncompensated measurement signal received at the second input, based on the error that was determined.

21. A memory medium storing a program having instructions for performing a method of processing measurements, the program comprising: code for determining an error in at least one of plural uncompensated signals representative of detections made by plural sensing stations, based upon those uncompensated signals, wherein the error includes at least a systematic error component A_syst; and code for compensating for error in at least one uncompensated signal, based on the error determined by the code for determining.

22. A memory medium as set forth in Claim 21 , wherein the error also includes a random error component A_rand.