Signal Linearization in Measuring Devices

Abstract

A method for pre-processing electrical sensing signals to compensate for common-mode to differential-mode conversion caused by nonlinearities in the signal transfer function, applying a linearization function to the input signals to cancel the nonlinearities. The method includes a calibration process in which a plurality of sets of standardized test signals are applied to the input channels of a measurement operation, and corresponding test outputs are measured for each set of test signals. Parameters of the linearization function are set based on a data set of acquired test outputs.

Description

[Technical field]

[0001] The present invention relates to a method for linearizing an input signal to a measuring device for calculating a measurement value of a biosignal. [Background technology]

[0002] A differential measurement is a type of measurement of a physical property (e.g. pressure, temperature, voltage) where the relevant output from this measurement is the difference y of the property measured at two points x1, x2, where the absolute value at each point is not relevant. The value of the physical property at each point is modeled as including a common mode component c and a differential mode component d. The differential mode component d occurs with opposite sign at each point x. For example, the values ​​of the property at two points x, and the ideal output measurement y from these points may be, e.g., x1=0.5d+c x2=-0.5d+c y ideal =x1-x2=0.5d+c-(-0.5d+c)=d It is.

[0003] In the ideal case, taking the difference between x1 and x2 removes the common mode component c, leaving only the differential mode component d.

[0004] However, in any real system, the signal x n Before calculating the measurement values, the transfer function f n Transfer functions arise due to the operation of electrical components in the circuit, e.g. semiconductor components such as diodes, thyristors, transistors, and more complex circuits, e.g. operational amplifiers and analog-to-digital converters. y real =f1(x1)-f2(x2)=g(d,c)

[0005] The transfer function f(x) gives the actual output value y as a function g of d and c. This is called common-mode to differential-mode conversion (CM2DM), and because c is usually large compared to d, even a small amount of c appearing at the output will affect the signal and mask some or all of d, significantly reducing the accuracy and reliability of the measurement.

[0006] If we assume that the transfer function f is linear, then CM2DM can be expressed as (x n This can be reduced by making these transfer functions more equal (regardless of the value of ). However, if the transfer functions are nonlinear, making the transfer functions more equal is not sufficient because the input signals will have different offsets and will be in different positions due to the nonlinearity, which may result in slightly different small signal gains for the input signals.

[0007] FIG. 1 shows a schematic representation of an exemplary linear transfer function 14 and a nonlinear transfer function 12a, 12b. As can be seen, in a nonlinear transfer function, the resulting gain for a signal is a nonlinear function of the input signal value (x-axis). The y-axis of the depicted graph shows the output value corresponding to a given input signal value (x-axis). The gain for small signals with at least a certain offset corresponds to the slope of the curve. Thus, the gain applied by the transfer function depends on the input signal offset, as this offset changes the position of the baseline of this input signal along the nonlinear transfer function.

[0008] This offset is understood as part of the differential component d. The main cause of the offset is the movement of the skin-electrode interface, which acts as an unintended battery creating potentials of up to several hundred millivolts. Users of measurement devices are usually not interested in this offset, but in the component of d that is due to physiological causes. Physiological electrical activity is most typically in the form of an AC signal component. The offset may in some cases be a "true" differential component, but this is not relevant if the user is only interested in the physiological (AC) component of the signal.

[0009] The nonlinearity of the transfer function of the input channel is caused by components in the input path, ranging from passive semiconductors (e.g., diodes or thyristors used for overvoltage protection) to operational amplifiers and analog-to-digital converters (ADCs), which exhibit significant nonlinear behavior.

[0010] The nonlinear behavior of the input channel can result in significant CM2DM even if the linear components of the transfer function are kept the same.

[0011] As an example, Figure 2 illustrates how a nonlinear transfer function affects the differential signal calculated in a measurement system. Figure 2(a) shows a (simulated) true differential signal d. Figure 2(b) shows two sensor signals x1 and x2, each containing a common mode c, a differential mode d and a respective offset.

[0012] Figure 2(c) shows the resulting recovered differential signal 16 calculated by the measurement device, where each input signal is constrained by a transfer function (f1 and f2 respectively) and the differential signal is calculated simply as the difference of the two input signals. Figure 2(c) also shows the true differential signal 18 on the same axis for ease of comparison. As can be seen from Figure 2(c), the calculated differential signal has a lot of noise with an amplitude nearly exceeding the magnitude of the differential signal itself, resulting in a poor signal-to-noise ratio.

[0013] Differential measurements are widely used in electrical medical applications. As an example, well-known measurement modalities such as electrocardiography and electroencephalography (electrical activity of the heart and brain, respectively) are differential measurements. Other less well-known measurement modalities include electroneurography and electromyography, which are also differential measurements. Emerging electroanatomical imaging applications are also based in part on differential voltage measurements.

[0014] The signals of interest in electrical medical applications are generally time-varying (AC) signals generated by physiological activity of muscle or nerve tissue.

[0015] The source signals have a common mode component c, a differential mode component d and an offset k, and the sampled signal is further constrained by a transfer function. The offset k is different for each source signal. The offset is caused, for example, by the electrochemical properties of the interface between the patient and the measurement system. For example, in the case of an ECG measurement device, this typically consists of adhesive electrodes that are applied to the patient's skin. The most common source of common mode components is power line interference, which can be coupled into the measurement by various possible paths / routes. In particular, interference can be coupled into the measurement by the patient (capacitive, if the patient is close to the interference source, or direct, by conduction, if the patient is in contact with an electrical ground), through the cabling (even more so if the cable is not fully shielded) or through the measurement electronics (the patient module is usually galvanically isolated, but still has a capacitive connection to ground).

[0016] Other sources of common-mode interference include, for example, electrical devices operating near or in contact with the patient, the measurement device, or simply on the same power circuit, whose characteristics (frequency, amplitude, time-varying, etc.) are significantly different from typical power line interference patterns.

[0017] Common-mode interference is addressed in state-of-the-art devices by processing operations in which a portion of the common-mode component is removed (removed) to compensate for the estimated interference contribution. The fraction of the common-mode component that is removed is known as the common-mode rejection ratio.

[0018] For example, known devices can address common-mode interference using measures such as driven-right-leg loops, shielding of recorders and cabling, the use of precision components, and linear equalization of input channels.

[0019] In cases where interference occurs in a clinical environment, sometimes the device may include functionality to instruct the operator to prepare the skin before attaching the electrodes, to verify that the electrodes are properly attached to the patient, to periodically replace the electrodes, and to check and remove electrical devices in the patient's vicinity that are possible sources of interference. If this functionality does not reduce the interference, further suggestions are made, such as rotating the patient or the equipment 90 degrees.

[0020] The nonlinearity is simply assumed to affect the output gain, and manufacturing test limits are set to keep this output gain within acceptable limits, ensuring that the device complies with applicable standards and regulations, but still allowing significant CM2DM to occur due to the nonlinearity of the transfer function. Summary of the Invention [Problem to be solved by the invention]

[0021] State-of-the-art electrophysiological recorders do not consider the effect of a possible nonlinear input channel transfer function on the common-mode rejection ratio of the device. Methods to address this nonlinearity would be valuable. [Means for solving the problem]

[0022] The invention is defined by the claims.

[0023] According to one aspect of the invention there is provided a computer implemented method for performance on a measurement device, said method comprising a differential measurement operation, said differential measurement operation comprising: reading signals from at least two input channels of the measuring device, the signals from each input channel being received from a respective sensor element; applying a linearization function to each of the input channels, the linearization function having adjustable parameters; applying a computational algorithm to the input channels after applying the linearization function to derive at least one output measurement; and outputting a data signal indicative of said output measurement; has.

[0024] The method further includes a calibration operation occurring at a different time than the differential measurement operation, the calibration operation comprising: applying a plurality of sets of constant value calibration input signals to input channels of the measurement device; applying the computational algorithm to each set of the calibration input signals without applying the linearization function and recording each output measurement to form a calibration data set; and fitting adjustable parameters of the linearization function based on the calibration data set. has.

[0025] The method is thus based on applying a linearization to input signal channels, where parameters of a linearization function are configured based on a calibration operation in which standardized test signals are applied to input channels of the measurement device and corresponding output measurement signals are recorded. Based on the relationship between the test inputs and the measured test outputs, a suitable set of parameters of the linearization function can be determined.

[0026] The signal may be an electrophysiological signal.

[0027] In some embodiments, the linearization function may be a polynomial function.

[0028] In some embodiments, the signals received at each input channel are assumed to represent the true sensed signals processed by a non-linear transfer function, where the fitting of the adjustable parameters of the linearization function comprises an optimization process in which the error between the true output measurements for a set of calibration input signals, as would be obtained if the non-linear transfer function was not applied to the input signals, and the actual output measurements recorded in the calibration data set is minimized.

[0029] It should be noted that the nonlinearity of the transfer function is typically caused mainly by the influence of electrical components in the measurement device itself, and not in sensing equipment external to the measurement device. Since the cable is modeled as a network of linear components, e.g. resistors and capacitors, the asymmetry introduced by external parts of the measurement setup is mainly a linear effect. Therefore, for this reason, the calibration process can be achieved by applying a constant-value calibration reference signal directly to the input port. The nonlinearity is induced in the electronics of the measurement device itself (e.g. from protection diodes / thyristors, operational amplifiers, A / D converters, power supplies).

[0030] In some embodiments, the computational algorithm comprises applying one or more vectors to input channels, each vector defining a mapping from a set of input channels to an output measurement. The output measurement is a linear combination of the input channels, the weights of the linear combination being defined by the elements of the vector. The calibration of the parameters of the linearization function is based in part on the one or more vectors. In other words, the calibration of the linearization function is based in part on the computational algorithm used in computing the output measurement. For example, in simple terms, the calibration of the parameters of the linearization function can comprise a process of minimizing a difference or error between an expected output from applying the vectors to a calibration input signal and an actual output from applying the vectors to a calibration input signal.

[0031] In some embodiments, the measurement operation may comprise the application of multiple of the power vectors to derive multiple different output measurements.

[0032] In some embodiments, the measurement device may have three or more input channels, hi some embodiments, each of the plurality of output vectors defines a mapping from only a subset of the input channels to a respective output measurement.

[0033] In some embodiments, the measurement operation comprises referencing a data set of a plurality of different linearization functions, where each linearization function is associated with only a subset of the plurality of output vectors, and where only the linearization function associated with a given output vector is applied to a given input channel prior to applying the respective output vector. In other words, different input channels may be subject to different linearization functions, and each input channel may be processed (separately, operating in parallel) with two or more linearization functions depending on the particular output vector to be applied.

[0034] For example, a simple illustrative case is a system with four input channels, where the computational algorithm involves the application of two vectors, the first vector calculating the difference between the first and second input channels, and the second vector calculating the difference between the third and fourth vectors.

[0035] In this case, the optimal linearization of the first and second input channels to which the first vector is applied is performed separately from the linearization of the third and fourth input channels to which the second vector is applied, since the calibration procedure does not need to take into account how well the linearities of the first and fourth input channels match, for example, since the pair of first and fourth input channels is not used together in calculating one of said two vectors.

[0036] In some embodiments, the input channels are assumed to each have a differential mode component, a common mode component and an offset, where the calibration procedure involves referencing a predefined probability distribution for the offsets of the input channels, which is used either explicitly (actively) or implicitly (implicitly) in the calibration algorithm to guide the selection or determination of an appropriate estimated offset to use in the linearization function.

[0037] For example, the calibration procedure first records a calibration data set obtained by applying a calculation algorithm to each set of calibration input signals without applying a linearization function, the calibration data set having a respective calibration output value for each applied calibration input signal and for each of the various possible offset values. The calibration procedure then, by way of example, comprises generating a cost function, which is calculated as the sum of the absolute differences in the slopes of these calibration output values ​​as a function of the calibration input values ​​for all possible combinations of offsets. In other words, for each possible combination of offsets of the input channels, a respective set of calibration output values ​​is obtained as a function of the applied calibration input signal. Each of these sets of calibration output values ​​defines a slope (as a function of the calibration input value) for the applied calibration input value. A cost function is calculated based on the differences in these slopes for the different combinations of offsets, and the optimization (fitting procedure) is based on minimizing this cost function (thereby linearizing the input channels).

[0038] If all possible offset combinations are equally likely when the device is in normal operation, no further improvement of the cost function is possible. The optimal fitting of the linearization function results in the slope of the transfer function of the input channels (i.e. the calibrated output value as a function of the applied calibrated input signal) being the same for all combinations of offsets of the input channels. This corresponds to linearizing each of the individual input channels.

[0039] For example, if there is prior knowledge that some combinations of offsets are more likely (or less likely) than others, due to the presence of additional circuitry such as a driving right leg (DRL) circuit, this knowledge can be applied to give more weight to the more likely offset combinations and less weight to the less likely combinations. Depending on the type of nonlinearity and the linearization function, this can reduce CM2DM for predicted operating conditions, at the expense of worsening CM2DM in unlikely or abnormal operating conditions.

[0040] In some embodiments, the linearization function and calibration operation are configured such that the calibrated linearization function provides a more optimal linearization for the set of offsets that have the highest probabilities in the probability distribution and a less optimal linearization for the set of offsets that have the lowest probabilities in the probability distribution.

[0041] For example, the signals received at each input channel can be assumed to represent true sensed signals processed by a non-linear transfer function, where fitting adjustable parameters of the linearization function comprises an optimization process in which the error between true output measurements for a set of calibration input signals, as would be obtained if said non-linear transfer function was not applied to the input signals, and the actual output measurements recorded in the calibration data set is minimized. In this case, a more optimal linearization for the set of possible offsets means a smaller average error in the calibrated output measurements for input signals with said set of possible offsets, and a less optimal linearization for the set of possible offsets means a larger average error in the calibrated output measurements for input signals with said set of possible offsets.

[0042] This allows all possible scenarios to be considered, but provides a smooth degradation in the quality of the linearization as the offset changes from a more common set to a less common set.

[0043] A further aspect of the invention provides a computer program product having code means configured to, when executed on a processor, cause the processor to perform a method according to any example or embodiment set forth above or further described below, or according to any claim of the present application. The code can cause the processor to perform a measurement operation of the method when the processor is operatively coupled to two or more sensor elements serving as sources of input signal channels. The code can cause the processor to perform a calibration operation of the method when the processor is successively implanted / supplied with a succession of sets of calibration input signals.

[0044] A further aspect of the invention provides a processing device having an input / output section and one or more processors operable in at least a first mode and a second mode, in the first mode the one or more processors adapted to perform a differential measurement operation comprising at least reading signals from at least two input channels of the measuring device, the signals from each input channel being received from a respective sensor element; applying a linearization function to each of the input channels, the linearization function having adjustable parameters; applying a computational algorithm to the input channels after applying the linearization function to derive at least one output measurement; and outputting a data signal indicative of said output measurement. has.

[0045] In a second mode, the one or more processors are configured to perform a calibration operation, the calibration operation comprising: applying a plurality of sets of constant value calibration input signals to input channels of the measurement device; applying the computational algorithm to each set of the calibration input signals without applying the linearization function and recording each output measurement to form a calibration data set; and fitting adjustable parameters of the linearization function based on the calibration data set. has.

[0046] A further aspect of the present invention provides a measurement device having at least two signal input ports for simultaneously reading at least two input signal channels from respective sensor elements, and a processing unit according to any embodiment or example outlined in this disclosure or according to any claim of this application, as described above.

[0047] A further aspect of the present invention provides a system comprising a measurement device according to any embodiment or example outlined in the present disclosure or according to any claim of the present application as described above, the system further comprising a signal measurement apparatus having at least two sensor elements for connection to said signal input port.

[0048] These and other aspects of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter. [Brief description of the drawings]

[0049] For a better understanding of the present invention, and to show more clearly how the same may be carried into effect, reference will now be made, by way of example only, to the accompanying drawings in which: [Figure 1] FIG. 1 shows example linear and non-linear transfer functions. [Diagram 2] FIG. 2 illustrates differential and common mode interference. [Diagram 3] FIG. 3 illustrates an example system and processing device in accordance with one or more embodiments of the invention. [Figure 4] FIG. 4 illustrates generally an exemplary processing workflow of a measurement operation performed by the processing device according to one or more embodiments of the present invention. [Diagram 5] FIG. 5 illustrates generally an exemplary processing workflow of a calibration operation performed by the processing device in accordance with one or more embodiments of the present invention. [Figure 6] FIG. 6 shows an exemplary probability distribution for the offset of a pair of two input signal channels. [Figure 7] FIG. 7 shows in more detail examples of output signals obtained in low, medium and high probability offset conditions when the offset probability density is not taken into account in the linearization. [Figure 8] FIG. 8 shows in more detail examples of output signals obtained in low, medium and high probability offset conditions when the probability density of the offset is taken into account in the linearization. [Figure 9] FIG. 9 shows an exemplary process flow according to one example in which a single linearization function is applied to each input signal channel and a single output vector is applied to both input channels. [Figure 10] FIG. 10 shows a further exemplary process flow according to a further example in which two output vectors are applied to different selected combinations of a set of three input channels. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0050] The present invention will now be described with reference to the drawings.

[0051] It should be understood that while the detailed description and specific examples set forth exemplary embodiments of the devices, systems and methods, they are for illustrative purposes only and are not intended to limit the scope of the invention. These and other features, aspects and advantages of the devices, systems and methods of the present invention will become better understood from the following description, appended claims and accompanying drawings. It should be understood that the drawings are merely schematic and are not drawn to scale. It should also be understood that the same reference numerals are used throughout the drawings to denote the same or similar parts.

[0052] The present invention provides a method for pre-processing electrical sensing signals to compensate for common-mode to differential-mode conversion caused by nonlinearities in the signal transfer function. A linearization function is applied to the input signals to nullify the nonlinearities. The method includes a calibration process in which a plurality of sets of standardized test signals are applied to the input channels of a measurement operation, and for each set of test signals, a corresponding test output is measured. The parameters of the linearization function are set based on a data set of the acquired test outputs.

[0053] As a further example of this concept, according to one exemplary set of preferred (but not exhaustive) embodiments, the details of which are further detailed in subsequent sections, one or more linearization functions h may be applied prior to calculating the difference or vector that defines the output measurement. n An approach is provided that seeks to solve the problem of common mode to differential mode conversion due to nonlinearities in the transfer functions of the input channels by providing a measurement device that applies (x) to the input signals. The linearization function uses parameters that are determined in a calibration procedure by applying a sequence of constant input signals to the inputs of the device and recording the (raw / non-linearized) outputs. A data set of calibration input and output values ​​is used together with information about the vectors used by the device in calculating the measurements, and preferably a predefined statistical distribution of expected signal offset values ​​(or combinations of offset values) assumed to be included as components in each input signal, to calculate linearization parameters that provide optimal linearization for likely combinations of channel offset values, and suboptimal linearization for rare combinations.

[0054] FIG. 3 illustrates an exemplary processing device 22 and system in accordance with one or more embodiments of the present invention.

[0055] The processing unit 22 includes an input / output (I / O) section 26 and one or more processors 24. In this example, the I / O has two input channels 32a, 32b and one output channel 36. However, in other examples, the I / O can have more than two input channels and more than two output channels.

[0056] Each sensor element 52a, 52b is connected to a respective input channel 32a, 32b. Each sensor element is adapted to acquire a biosignal at a location on the subject's body. As an example, each of the sensor elements may be an ECG electrode. The signal from each sensor element 52a, 52b provides a respective input signal 54a, 54b to the input channel 32a, 32b.

[0057] One or more processors 24 (only one is shown in FIG. 3, although in practice an assembly of multiple processors may be used) receive input signals from input channels 32a, 32b, process these signals, and derive one or more output measurements 38 which are then exported via output channels 36 as measurement data signals 42.

[0058] The one or more processors 24 are specifically adapted to perform a computer-implemented method involving differential measurement and calibration operations, which are performed at different respective times.

[0059] Figure 4 shows a schematic process workflow for a differential measurement operation. Figure 5 shows a schematic process workflow for a calibration operation.

[0060] The differential measurement operation comprises the following steps performed by one or more processors 24:

[0061] The measurement operation comprises the step of reading signals from at least two input channels (Channel A 32a and Channel B 32b) of the measurement device. A signal from each channel is received from a respective sensor element 52a, 52b. The measurement device may include analog-to-digital conversion means applied to the received input signals and for digitizing these input signals.

[0062] The measurement operation further comprises applying a linearization function 62 having adjustable parameters to each of the input channels.

[0063] The measurement operation further comprises applying a calculation algorithm 64 to the input channels after applying a linearization function 62 to derive at least one output measurement 38. The input channels provided to the calculation algorithm are preferably single-ended input channels and the output from the measurement algorithm is preferably a single-ended output signal.

[0064] A data signal 42 indicative of the output measurement 38 is output via an output channel or port 36 of the input / output section 26.

[0065] The measurement operations can be performed completely or partly using hardware (ASIC, FPGA) and / or software running on a microprocessor (microcontroller, digital signal processor).

[0066] The one or more processors are further operable to perform a calibration operation having the following steps illustrated in FIG.

[0067] The calibration operation comprises applying a plurality of n sets 72 of constant value calibration input signals 74a, 74b to the input channels 32a, 32b of the measurement device 22. The n sets are applied one at a time in sequence. The calibration input signals of each set are applied simultaneously to the input channels. The constant signal values ​​of the calibration input signals are sometimes referred to elsewhere as "calibration points".

[0068] The calibration operation further includes applying a calculation algorithm 64 to each set 72 of calibration input signals 74a, 74b, without applying a linearization function, to form a calibration data set 44, and recording each output measurement 38. Each output measurement 38 may be output in the form of a data signal 42 via an output channel 36 of the I / O 26. The calibration data set can be stored in a data store local to the device 22 or in a remote data store.

[0069] The calibration operation further includes fitting adjustable parameters of a linearization function 62 based on the calibration data set 44 .

[0070] With respect to measurement and calibration operations, the processing device 22 is operable in at least a first and a second mode, in the first mode the processing device is adapted to perform measurement operations and in the second mode the processing device is adapted to perform calibration operations.

[0071] The calibration operation is performed at a different time than the measurement operation. The calibration operation only needs to be performed once before use for measurements, e.g. at the factory or during initialization before use. Alternatively, the calibration operation may be performed in the field with the measurement device. It may also be performed repeatedly.

[0072] The measurement device 22 may include a user interface that allows a user to provide user input to control the selection of the first or second mode. These mode selection options may only be available in a particular initial configuration or mode of the device, such as, for example, when the device first enters a configuration or setup mode. In some examples, the measurement device may be adapted to enter a calibration mode in response to receiving a predefined control signal from a separate secondary device via a data connection. The data connection may be facilitated by a dedicated control or configuration port included in the measurement device. The data connection may be removable from a port of the measurement device. For example, a user may be provided with a separate device that can be connected to the measurement device and that automatically prompts the execution of the calibration step. In some examples, the calibration operation may be an algorithm or computer program stored in the secondary device, in which case the provided invention may have the measurement device in combination with this secondary device.

[0073] The ability to perform calibration operations in the field after manufacture allows for periodic recalibration to be performed to account for component aging and changes in the non-linearity of the transfer function over time.

[0074] In a further example, the two modes may not be freely selectable by the end user: for example, the device may be shipped in a measurement mode of operation, where the calibration mode is only accessible via a dedicated data entry port and / or with a key available at the factory.

[0075] In some examples, the measurement device is an ECG measurement device. In some examples, the measurement device may have a user interface for use in displaying measurements 38 and / or for receiving user control commands.

[0076] With regard to the computational algorithm 64 applied in the measurement operation, this comprises applying one or more vectors to the input channels, each vector defining a mapping from a set of input channels to an output measurement value, where the output measurement value is a linear combination of the input channels and weights defined by the elements of the vector. The one or more vectors applied in the measurement operation may be stored in a local data store, for example pre-stored during manufacture or set-up, and retrieved during the execution of the measurement operation.

[0077] The vector may define a linear combination of the input channels, where the weighting coefficients sum to zero. For example, in the simplest case, the output measurement may simply be the difference between the two input signals. In this case, the coefficients are -1 and 1, and sum to zero.

[0078] In some embodiments, the measurement operation may include the application of multiple of the power vectors to derive multiple different power measurements 38 .

[0079] In some embodiments, the measurement device has three or more input channels, and wherein each of the plurality of output vectors defines a mapping from only a subset of these input channels.

[0080] The minimal list of features described above, when combined, results in a measurement device that is more resistant to interference and provides a clean, undisturbed output signal in environments where devices not using the method of the present invention exhibit output signals corrupted by significant interference, which results in more accurate measurements and therefore more accurate diagnosis and subsequent treatment.

[0081] Further details regarding linearization are provided below.

[0082] According to one simple example, the one or more linearization functions h n (x) may be a polynomial function, where the adjustable parameters of the linearization function are, for example, h(x)=ax 3 +bx 2 +cx+d The coefficients of the polynomial are such that: This is computationally efficient since only a few multiplication operations are required to compute the polynomial value. Lower or higher order polynomials can be used, with the choice based on a desired balance between computational efficiency (lower order) and accuracy (higher order).

[0083] The one or more linearization functions are preferably monolithic functions, but may alternatively be piecewise functions, such as, for example, cubic or higher order splines, as long as the functions are sufficiently smooth to operate efficiently.

[0084] In a further embodiment, the one or more linearization functions are n As a basis for (x), other functions, e.g., trigonometric functions, e.g., h(x)=a*tanh(b*x+c)+d We can use the hyperbolic tangent tanh(x) such that

[0085] The calculation of the coefficients based on the compiled calibration data set 44 is posed as a convex optimization problem, which can be easily solved using an automated function fitting algorithm and solver, such as a regression algorithm.

[0086] One implementation according to at least one of these sets of embodiments will now be outlined in more detail. In this set of embodiments, the calculation of the linearization parameters utilizes one or more vectors used in calculating the measurements in the measurement operation.

[0087] In brief, during the calibration process, the following information is collected: the values ​​of each pair of calibration input signals, calculations performed on these signals; and Measurement results provided as output is known. Based on knowledge of the calculations performed on these signals (i.e. applying a vector to the input signal), it is theoretically possible to identify what would be the "expected" output measurement in the absence of CM2DM interference. The difference between the expected and measured output can then be used to guide the fitting of a linearization function. In other words, the fitting of this linearization function is done with the goal of minimizing the error between the "true" expected measured output based on known inputs and a known calculation function 64, and the actual measured output during calibration. As multiple sets of calibration signals are applied, ideally defining a regularly increasing or decreasing difference, the non-linearity of said error is exhibited in the calibration data set and is appropriately taken into account in the fitting of the linearization function.

[0088] Thus, in summary, the signal received at each input channel is assumed to represent the true sensed signal processed by a non-linear transfer function, where fitting the adjustable parameters of the linearization function comprises minimizing the error between the theoretical true output measurement for each calibration input signal, as would be obtained if the non-linear transfer function had not been applied to the input signal, and the actual output measurement recorded in the calibration data set.

[0089] As a further example, with respect to a calibration input signal, for linearization of a single input channel, the set of calibration points (i.e., signal values ​​of the calibration input signal) is simply the set of calibration input signals for this single channel. For example, if the input range is 0V to 1.0V, the calibration signal values ​​can be selected as 0V, 0.25V, 0.5V, 0.75V, 1.0V. This list of voltages corresponds to the set of calibration points. This also applies to the multi-channel case where each input channel is linearized independently of the other channels.

[0090] For multi-channel linearization, which considers combinations of input channels, the set of calibration points consists of combinations of calibration input signal values. In the case of two channels and the list of voltages above, the complete set of calibration points is {0V, 0.25V, 0.5V, 0.75V, 1.0V} × {0V, 0.25V, 0.5V, 0.75V, 1.0V}, all combinations 5 2 = 25 (also called the Cartesian product), i.e. (0V, 0V), (0V, 0.25V), ..., (0.25V, 0V), (0.25V, 0.25V), ..., (1.0V, 1.0V). The size of this set grows exponentially with the number of input channels; in a system with 10 input channels (e.g., a 12-lead ECG recorder) and 5 test voltages, the complete set of calibration points contains approximately 10 million elements.

[0091] In the simplest case, all of these combinations are considered in the process of fitting a linearization function. However, while state-of-the-art processors can handle such data volumes, the calibration operation can be accelerated if only a subset of the possible calibration points is used for fitting the linearization function. Based on knowledge of the vectors used in the measurement operation (e.g., knowledge that an ECG measurement operation does not form a vector that includes more than one input chest lead), elements are excluded from the set of data points.

[0092] Elements may also be excluded based on the knowledge that they do not present a condition that would predict the device would produce a valid output, or that they do not actually occur due to, for example, the presence of a driving right leg (DRL) circuit that causes the input channels to average 0.5V, which means that input signal combinations such as (1.0V, 1.0V) and (0V, 0V) can be ignored in the calculations. For example, during normal operation, the combinations (0V, 1.0V), (0.25V, 0.75V), (0.5V, 0.5V), (0.75V, 0.25V) and (1.0V, 0V) are most likely, and any other combinations would present a temporary condition or an abnormal / fault condition.

[0093] As mentioned above, one difficulty is that in practical use, the sensor measurement input signals 54a, 54b are expected to each have certain offsets in addition to the standard differential and common mode components. These offsets depend on the physical characteristics of the device setup, as mentioned above. These offsets cause significant difficulties in processing operations involving the application of a nonlinear function (i.e., the linearization function h(x)), since they will cause corresponding nonlinear distortions in the output measurement signal if the offsets are not taken into account in the linearization function itself. However, these offsets cannot be known in advance. Therefore, the most appropriate solution is to use an estimated probability distribution of the offsets of the input channels to set or adjust the parameters of the linearization function such that offsets that are at least within the highest probability range of this probability distribution do not cause too large distortions in the output measurement signal. Ideally, the linearization function is also adjusted so that the resulting offset-related distortion changes relatively smoothly as a function of the offset of the input signal. In other words, rather than there being a large jump or discontinuity in the output measurement signal as the (potential) offset of the signal moves from a more likely range to a less likely range, it is preferable that the resulting signal distortion increase smoothly and therefore the signal accuracy deteriorate smoothly.

[0094] Thus, in accordance with the set of embodiments described above, the input channels are assumed to each have a differential mode component, a common mode component and an offset, where the calibration procedure involves referencing predefined probability distributions for the offsets of these input channels.

[0095] In other words, the calibration data set 44 of calibration input values ​​and calibration output values ​​is used together with information about the vectors used by the device in calculating the measurements, and predefined statistical distributions of input signal offset values ​​(or combinations of offset values) assumed to be included as components in each input signal, to calculate linearization parameters that provide optimal linearization for likely combinations of channel offset values ​​and non-optimal linearization for rare combinations.

[0096] In particular, in some embodiments, the linearization function and calibration operation are configured such that the calibrated linearization function provides a more optimal linearization for a set of offsets that have the highest probabilities in the probability distribution, and a less optimal linearization for a set of offsets that have lower probabilities in the probability distribution.

[0097] In this situation, a more optimal linearization for the set of possible offsets means that after calibration, for input signals with said set of possible offsets, the average error in the output measurements is smaller, and a less optimal linearization for the set of possible offsets means that after calibration, for input signals with said set of possible offsets, the average error in the output measurements is larger.

[0098] In applications using only a single channel, the quality of the linearization is measured by the deviation of the transfer function (ie, the function of the calibrated output value as a function of the applied calibrated input signal) from an ideal linear function.

[0099] However, in the types of applications described in this disclosure, simply linearizing each input channel in this manner, while it may provide a significant improvement over the uncalibrated state, may not produce optimal results in terms of reducing common-mode to differential mode conversion, given the degrees of freedom of the linearization function.

[0100] In particular, optimal linearization is achieved when CM2DM is absent during the predicted operating conditions. The predicted operating conditions may be constrained by factors such as the presence of a Driven Right Leg (DRL) feedback loop (see below) in the path of the input signal, which forces the sum of the potentials of the input signal to a fixed value. The optimization algorithm may, for example, assign greater importance to reducing CM2DM in conditions where the sum of the potentials of the input electrodes is close to this fixed value, and give less importance or no importance in conditions where the sum differs from the predicted value.

[0101] As an example, Figure 6 shows an exemplary probability distribution for the offset of a set of input channels having only a first input channel (Channel A) and a second input channel (Channel B), where the system setup includes a driving right leg (DRL) circuit. (Channel A + Channel B) / 2=0.5 1 shows the scaled probability density function for the system where

[0102] To further explain, electrophysiological measurement devices often implement a feedback circuit that feeds back the negative sum (a fixed offset, positive or negative) of the potential of the input electrodes to the patient via a designated electrode. In ECG, this is often the right leg electrode, so the circuit is called a Driven Right Leg "DRL" circuit or a Driven Right Leg "RLD" circuit, but in general, an electrode attached to any body part can be used. In other measurements, the terms "active electrode", "reference electrode" or "drive electrode" may be used, and the term "feedback circuit" may be used instead of the DRL circuit.

[0103] The main purpose of the DRL circuit is to reduce common mode signals, which generally works very effectively for low frequencies, but its effectiveness decreases at higher frequencies due to instabilities in the control loop and limitations on the current that can be drawn from the device to the patient.

[0104] Another effect of the DRL circuit is to establish an operating point. The DRL circuit forces the potentials of the input electrodes to a state where the sum of their potentials is approximately equal to a constant offset. Under normal conditions, this operating point is reached quickly (within a second). Thus, in this scenario, the voltages of the input channels are assumed to be close to the calibration points of (1.0V, 0V), (0.75V, 0.25V), (0.5V, 0.5V), (0.25, 0.75) and (0V, 1.0V) for a constant offset of 0.5V in this example.

[0105] This means, for example, that any positive integer power of x is monotonic for x>=0 (where x is the value of the input signal to the input channel), making the use of a polynomial as the linearizing function a reasonable choice.

[0106] However, note that the ADC connected between the input port and the processor often uses bipolar sampling, and the midpoint of the ADC range is 0 V. This needs to be taken into account when selecting and applying the linearization function.

[0107] Referring to FIG. 6, the measurement range is 0 to 1, with a midpoint of 0.5. The Right Leg Drive (RLD) operates to maintain the average of the two channels at 0.5. In this particular case, this means that a combination of offsets of the input channels that sum to zero is more likely, and a combination of offsets of the input channels that sum to a non-zero value is less likely. This is because the latter combinations only occur during settling of the DRL control loop (which is a short, temporary period) or during abnormal operating conditions. In some embodiments, this is taken into account when determining the probability distribution of the offsets. For example, the optimization process may ignore the quality of the linearization for the above situation, especially if the linearization would be further improved for more normal situations.

[0108] Furthermore, if all electrodes are well and similarly installed and used for the same length of time, the DC offsets they generate are approximately equal. On the other hand, if the electrodes have different aging or installation quality, their DC offsets are more likely to be different. The optimization process can optimize the linearization more strongly for the situation where x1≈0.5, x2≈0.5 (where x1 and x2 are the signals of the first and second input channels), but the situation where this is not true indicates a poor measurement setup, but should not be completely ignored since it does not indicate an abnormal operating condition.

[0109] The probability distribution function of the offset is determined in advance and stored for later use. It can be determined by empirical testing or by theoretical / analytical modeling or simulation.

[0110] It is not essential that the fitting of the linearization function takes into account the probability distribution of the offsets of the input signal channels. However, if the calculation of the linearization parameters does not take into account the probability distribution function, the result may be that the linearization results are (paradoxically) worse in more likely conditions and better in less likely conditions.

[0111] This is shown, for example, in Figures 7 and 8. Each graph in each figure shows the "true" input signal 82 from the sensor element, the actual recorded (uncorrected) input signal 84, and the corrected input signal 86 after application of a linearization function.

[0112] FIG. 7 shows the results for a series of offset conditions with different probabilities in the case where a linearization function is not fitted to take into account the expected probability distribution of the signal offset. FIG. 8 shows the results for the same series of offset conditions with a linearization function fitted to take into account the expected probability distribution of the signal offset. It can be seen that in the scenario of FIG. 7, common-mode interference suppression is in fact significantly better for the less likely offset scenario than for the more likely offset scenario. In contrast, in the case of FIG. 8, signal correction is best for the more likely offset scenario and worst for the less likely offset scenario (which is clearly the preferred result).

[0113] A probability density function can be used to fit the linearization function, and more likely operating conditions can be weighted higher and less likely or abnormal operating conditions can be weighted lower in the cost function used for fitting / optimization. Operating conditions in this context refer to, for example, more likely and less likely combinations of input signal offsets and / or more likely or less likely combinations of input signal values.

[0114] These applied weights cause the optimization process to improve the linearization of states with higher weights at the expense of states with lower weights.

[0115] To further illustrate this, although it was mentioned above that certain unlikely combinations of possible input channel signals are completely excluded from the calibration data set in order to speed up the calculation of the fitting of the linearization function, the use of a probability distribution allows a more sophisticated approach, whereby different combinations of input signals and / or offset values ​​are assigned different weights in the optimization operation (i.e., fitting the parameters of the linearization function) according to their estimated probability of occurring under normal operating conditions.

[0116] For example, continuing with the two channel example above, input voltages near the (0.5V, 0.5V) calibration point represent operating conditions with new electrodes and proper attachment to the patient's skin, whereas input voltages near the (1.0V, 0V), (0V, 1.0V), (0.25V, 0.75V), and (0.75V, 0.25V) calibration points occur when the electrodes have deteriorated over time (the latter being generally less likely than the former). Furthermore, input voltages near the (0.25V, 0.5V), (0.75V, 0.5V), (0.5V, 0.25V), and (0.5V, 0.75V) calibration points represent temporary states during which the device should still produce a noise-free output.

[0117] In order to reduce CM2DM due to channel nonlinearities, an optimization algorithm used in the calibration operation can find the parameters of a linearization function that makes, at each calibration point (where a calibration point means a particular combination of input channel signals), the slope of the output measurement (or some approximation of that slope) as a function of the set of applied input channel signals as similar as possible.

[0118] One way to mathematically describe this cost function is the sum of the absolute differences of these slopes at each calibration point.

[0119] For example, the calibration procedure first records a calibration data set obtained by applying a calculation algorithm to each set of calibration input signals (i.e. at each calibration point) without applying a linearization function, this calibration data set comprising a respective calibration output value for each applied calibration input signal and for each of the various possible offset values. The calibration procedure then comprises, by way of example, generating a cost function calculated as the sum of absolute differences in slopes of the calibration output values ​​as a function of the calibration input values ​​for all possible offset combinations. In other words, for each possible combination of offsets of the input channels, a respective set of calibration output values ​​is obtained as a function of the applied calibration input signal. Each of these sets of calibration output values ​​defines a slope for (as a function of) the applied calibration input value. A cost function is calculated based on the differences in these slopes for the various combinations of offsets, and the optimization (fitting procedure) is based on minimizing this cost function (thereby linearizing the input channels).

[0120] To subject the optimization process to the most common operating points where CM2DM is most likely to reduce bias, the absolute difference in slope at each calibration point can be multiplied by a weighting factor that correlates to the probability of operating near this calibration point. This probability can be expressed as a probability density function (PDF). The probabilities used in the PDF can be estimated.

[0121] Each calibration point corresponds to a set of applied calibration input signals, where each calibration input signal comprises, for example, the sum of a main signal component and a calibration offset component. In this way, the calibration can take into account various possible (differential mode) input signal values ​​and various possible combinations of offsets.

[0122] With regard to the probability distribution of the offsets, this can be determined prior to the measurement and calibration operations. Different embodiments make different assumptions regarding the probability density functions of these offsets. In some cases, when no additional data is available, a normal (i.e., Gaussian) distribution of the offsets is assumed. In other cases, more complex probability distributions (e.g., various functions, including asymmetric distributions) can be used. The probability distribution utilized may be calculated based on theoretical assumptions, or may be based on an empirically obtained data set of the signal offsets, which is then statistically analyzed to identify the probability distribution.

[0123] The values ​​of the probability density function at the calibration points are used directly as weighting factors when calculating the calibration coefficients, or the weighting factors are derived as functions of the probability density function.

[0124] When more than one output vector is applied in calculating the output measurement, it is advantageous to use slightly different linearization functions (or at least different fitted / optimized versions of the same linearization function) for the different output vectors. For example, depending on the particular mapping operation applied with a given output vector, the resulting non-linearity in the output measurement error will be different. Thus, having a linearization function that is specific to a given one or more of the different output vectors improves the error reduction in the output measurement.

[0125] Thus, according to some embodiments, a measurement operation may reference a data set of multiple linearization functions (or multiple different fitted / optimized versions of the same linearization function, i.e., with different sets of fitted parameters), where each linearization function is associated with only a subset of the multiple output vectors, and where only the linearization function associated with a given output vector is applied to a given input channel before applying the respective output vector.

[0126] Additionally or alternatively, in some examples, the measurement operation may use multiple different linearization functions to apply to different subsets of one or more input channels, with a different respective linearization function for each input channel, allowing differences in nonlinear transfer functions along different input channel paths to be taken into account.

[0127] By way of example, Figures 9 and 10 show two exemplary process flows of a measurement operation. In the example of Figure 9, there are two input signals provided to the measurement device, a first input signal 54a and a second input signal 54b. Each input signal is assumed to be constrained by a respective nonlinear transfer function 102a, 102b, which introduces an error into said signal that is a nonlinear function of the input signal itself. An analog-to-digital converter (ADC) 60 is applied to the signals received at the measurement device. In the example of Figure 9, each received input signal is processed with a different respective linearization function 62a, 62b. These two signals are then provided as inputs to a calculation algorithm 64 that generates an output measurement 38 consisting of a linear combination of the corrected input signals.

[0128] The example of Fig. 10 is similar, except that there are three input signals 54a, 54b, 54c, each of which is assumed to be constrained by a different respective nonlinear transfer function 102a, 102b, 102c. In this example, two different output measurements 38a, 38b are obtained by applying two different calculation algorithms 64a, 64b. The first calculation algorithm receives only a subset of the input signals, in particular the first input signal 54a and the second input signal 54b (after linearization). The second calculation algorithm 64b also receives only a subset of the input signals, in particular the second input signal 54b and the third input signal 54c (after linearization). Each calculation algorithm 64a, 64b is associated with a different subset of the multiple linearization functions 62a, 62, 62c, 62d. In particular, the linearization functions 62a and 62b are associated with a first computation algorithm 64a, where the first input signal 54a is processed with the first linearization function 62a before application to the first computation algorithm 64a, and the second input signal 54b is processed with the second linearization function 64b before application to the first computation algorithm 64a. The linearization functions 62c and 62d are associated with a second computation algorithm 64b, where the second input signal 54b is processed with a third linearization function 62c before application to the second computation algorithm 64b, and the third input signal 54c is processed with a fourth linearization function 64d before application to the second computation algorithm 64b.

[0129] For example, mentioned above is the fact that the output measurement vector is taken into account when performing said calibration in order to minimize the error between the predicted output and the actual output by applying the measurement vector to one or more input calibration signals.

[0130] The exemplary embodiments described so far have only specified systems with two input channels: if there are only two input channels, then only one vector is possible to calculate the measurement, which corresponds to calculating the difference between the two input channels.

[0131] As a further illustrative example, one can consider a system with three input channels, labeled x1, x2, and x3. In this case, three calculation vectors are possible for calculating the difference between each individual signal and each of the other two signals. However, the calculation vectors can also use "virtual" points, such as x1-(0.5*x2-0.5*x3), so that in fact an infinite number of calculation vectors are theoretically possible. Which vectors are used depends on the application, i.e., which physiological signals are measured. For example, in the context of a 12-lead ECG measurement device, 12 vectors are typically calculated, corresponding to the difference signals between different combinations of the nine input electrodes (the three limb electrodes RA, LA, LL and the six chest electrodes V1...V6). Other measurement modalities, such as EEG, can calculate vectors between all pairs of electrodes.

[0132] Thus, knowledge of the vectors used in the calculation procedure can be used to reduce the set of calibration points that must be considered for each vector during the calibration operation: if two calibration points (here calibration points means a particular set of input channel signals) differ only with respect to the input channels utilized by a given vector, then for this vector only one of these calibration points needs to be considered in the cost function.

[0133] For example, in an ECG with multiple chest electrodes (V1, V2, ...), a vector calculating the difference between two different chest electrodes is not used.

[0134] The principles of the present invention can be applied to any kind of sensing or measuring device. Examples include, for example, electro-medical measuring devices such as ECG measuring devices, electro-anatomical imaging systems, EEG recorders, AED devices, fetal / obstetric ECG recorders, electro-anatomical imaging systems. However, the application is not limited to electro-medical devices, but is used in other fields where differential measurements are obtained. For example, the embodiments are advantageously used in applications outside of clinical situations, such as smart watches or fitness trackers with ECG capabilities. The embodiments of the present invention are advantageously used in any differential measuring device where common-mode to differential-mode conversion via non-linearities in the transfer function of the input channels is problematic.

[0135] By way of summary, one particularly advantageous (although not exhaustive) set of features of an embodiment of the present invention is summarized below.

[0136] An object of at least one set of embodiments is to address the problem of common-mode to differential-mode conversion due to non-linearities in the transfer functions of the input channels by providing a measurement device that applies a linearization function h(x) to the input signals before calculating the output difference or vector. The linearization function uses parameters that are determined in a calibration procedure by applying a sequence of constant input signals to the inputs of the device and recording the (raw / uncalibrated) output. Information on the sets of input and output values, together with information on the vectors used by the device and the statistical distribution of the offset values ​​(or combinations of offset values), is used to calculate linearization parameters that provide optimal linearization for likely combinations of channel offset values ​​and less optimal linearization for rare combinations. Since the rare combinations usually indicate some problem with the measurement, such as poor contact of the skin electrodes, this provides graceful degradation of the output measurements as offset conditions change from good / common to poor / uncommon.

[0137] The above-described embodiments of the invention employ a processing device. The processing device may generally have a single processor or multiple processors. The processing device may be located within a single containing device, structure or unit, or may be distributed among multiple different devices, structures or units. Thus, reference to the processing device being adapted or configured to perform a particular step or task may correspond to a step or task performed by any one or more of multiple processing components, alone or in combination. Those skilled in the art will understand how such a distributed processing device may be implemented. The processing device includes a communication module or input / output for receiving data and outputting data to further components.

[0138] The one or more processors of the processing unit may be implemented in many ways using software and / or hardware to perform the various functions required. A processor typically uses one or more microprocessors that are programmed using software (e.g., microcode) to perform the required functions. The processor may also be implemented as a combination of dedicated hardware to perform some functions and one or more programmed microprocessors and associated circuitry to perform other functions.

[0139] Examples of circuitry that may be used in various embodiments of the present disclosure include, but are not limited to, conventional microprocessors, application specific integrated circuits (ASICs), and field programmable gate arrays (FPGAs).

[0140] In various implementations, the processor may be associated with one or more storage media, e.g., volatile and non-volatile computer memory such as RAM, PROM, EPROM, and EEPROM. The storage media may be encoded with one or more programs that, when executed on the one or more processors and / or controllers, perform the required functions. The various storage media may be attached within the processor or controller, or may be transportable such that one or more programs stored on the storage media are loaded into the processor.

[0141] Variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the term "comprising" does not exclude other elements or steps, nor does a recitation of a plurality of elements exclude the presence of a plurality of the elements.

[0142] A single processor or other unit may fulfill the functions of several items recited in the claims.

[0143] The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

[0144] The computer program may be stored / distributed on a suitable medium, such as an optical storage medium or a solid-state medium, for example supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunications systems.

[0145] When the term "adapted for" is used in the claims or specification, it is intended to be synonymous with the term "configured to."

[0146] Any reference signs in the claims should not be construed as limiting the scope.

Claims

1. 1. A computer-implemented method for performing on a measurement device, the method comprising: reading signals from at least two input channels of the measuring device, the signal from each of the input channels being received from a respective sensor element; applying a linearization function to each of the input channels, the linearization function having adjustable parameters; applying a computational algorithm to the input channels after applying the linearization function to derive at least one output measurement; and outputting a data signal indicative of said output measurement. a differential measurement operation having applying a plurality of sets of constant value calibration input signals to the input channels of the measurement device; applying the computational algorithm to each set of the calibration input signals without applying the linearization function and recording each output measurement to form a calibration data set; and fitting the adjustable parameters of the linearization function based on the calibration data set. having a calibration operation that is performed at a different time than the differential measurement operation; 10. A computer-implemented method comprising:

2. The method of claim 1 , wherein the linearization function is a polynomial function.

3. The signal received at each input channel is assumed to represent the true sensed signal processed by a nonlinear transfer function; 3. The method of claim 1, wherein the step of fitting the adjustable parameters of the linearization function comprises minimizing an error between a theoretical true output measurement for each calibration input signal, as would be obtained if the nonlinear transfer function had not been applied to the input signal, and the actual output measurement recorded in the calibration data set.

4. 2. The method of claim 1, wherein the computational algorithm comprises application of one or more vectors to the input channels, each vector defining a mapping from the set of input channels to an output measurement, the output measurement being a linear combination of the input channels with weights defined by elements of the vector, and wherein calibration is based in part on the one or more vectors.

5. The method of claim 4 , wherein the differential measurement operation comprises applying a plurality of the vectors to derive a plurality of different output measurements.

6. The method of claim 5 , wherein the measurement device has three or more input channels, and each of the plurality of vectors defines a mapping from only a subset of the input channels.

7. 7. The method of claim 6, wherein the differential measurement operation comprises reference to a data set of a plurality of linearization functions, each linearization function being associated with only a subset of the plurality of vectors, and wherein only the linearization function associated with a given vector is applied to a given input channel before applying each of the vectors.

8. 2. The method of claim 1, wherein the input channels are each assumed to have a differential mode component, a common mode component and an offset, and the calibration procedure comprises reference to a predetermined probability distribution for the offset of the input channel.

9. 9. The method of claim 8, wherein the linearization function and the calibration operation are configured such that the calibrated linearization function provides a more optimal linearization for a set of offsets having the highest probabilities in the probability distribution and a less optimal linearization for a set of offsets having low probabilities in the probability distribution.

10. The signal received at each input channel is assumed to represent the true sensed signal processed by a nonlinear transfer function; fitting the adjustable parameters of the linearization function comprises an optimization process that minimizes an error between true output measurements for a set of calibration input signals, as would be obtained if the nonlinear transfer function were not applied to the input signals, and actual output measurements recorded in the calibration data set; A more optimal linearization for a set of possible offsets means that, after calibration, there is a smaller average error in the output measurements for input signals with the set of possible offsets; and a less optimal linearization for the set of possible offsets means that after calibration, there is a larger average error in the output measurements for input signals with the set of possible offsets; 10. The method of claim 9.

11. A computer program product comprising code means configured to, when executed on a processor, cause said processor to perform the method of claim 1.

12. Input / output section, and one or more processors In a processing device having The one or more processors are operable in a first mode in which the one or more processors perform differential measurement operations, the first mode comprising: reading signals from at least two input channels of a measuring device, the signal from each said input channel being received from a respective sensor element; applying a linearization function to each of the input channels, the linearization function having adjustable parameters; applying a computational algorithm to the input channels after applying the linearization function to derive at least one output measurement; and outputting a data signal indicative of said output measurement. and The one or more processors are operable in a second mode in which the one or more processors are configured to perform a calibration operation, the second mode comprising: applying a plurality of sets of constant value calibration input signals to the input channels of the measurement device; applying the computational algorithm to each set of the calibration input signals without applying the linearization function and recording each output measurement to form a calibration data set; and fitting the adjustable parameters of the linearization function based on the calibration data set. A processing device comprising:

13. at least two signal input ports for simultaneously reading at least two input signal channels from respective sensor elements; and The processing device according to claim 12 A measuring device having

14. A measuring device according to claim 13, and a signal measuring device having at least two sensor elements for connection to said signal input port; A system having:

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