Method and apparatus for measuring characteristics of a particle flow

Abstract

In the presented solution characteristics of a particle flow is measured. A sample flow (Q) comprising electrically charged particles is guided through a passage (2). A mobility analyser (8) having a particle cut-off size is provided. An electrical current carried by the charged particles penetrated through the mobility analyser (8) is measured. The cut-off size of the mobility analyser (8) is alternated. A dynamic model provides a simulated signal (Sim) describing the behaviour of the electrical current during the state of change as a response to alternating the cut-off size of the mobility analyser (8). Similarity between the simulated signal (Sim) and measured electrical current (Iem) is optimized. A value of a particle size parameter (pS) is updated. Concentration quantities (C1-Cn) of the particle flow are determined using the updated parameter value (pS) and the measured electrical current (Iem).

Description

[0001] METHOD AND APPARATUS FOR MEASURING CHARACTERISTICS OF A PARTICLE

[0002] FLOW

[0003] FIELD OF THE INVENTION

[0004] The invention relates to a method of measuring characteristics of a particle flow and to an apparatus for measuring characteristics of a particle flow.

[0005] BACKGROUND OF THE INVENTION

[0006] Particles suspended in gaseous carrier i.e. aerosols play a significant role in ambient and indoor air quality and in many technical processes. An important task lies in detecting the concentration of the particles by way of measurement technology. Particles in the size range of smaller than 10 micrometers diameter may be breathed in by humans and may have a detrimental effect on health. The most recent research results indicate that the usual protective functions of humans are no longer effective for nanoparticles <100 nm in diameter. Nanoparticles arise mainly in combustion processes such as in motor vehicles, coal-fired power stations, wood heating installations, etc. The increased awareness of the adverse health effect of the air pollutants has led to a growing need for up-to-date information on the air quality. Thus, there is an increased need for improved solutions for measuring characteristics of a particle flow.

[0007] Previous state of the art includes detection methods where the detection instrument changes state of the response between two states to gain advanced information about the particle flow, such as particle size. The problem with this approach is that as the instrument state is changed, the response has a time period where it is transient between these two states and a period of measurement signal is lost. When reaching for faster response time of the device, by increasing the frequency of state changes, an increasing amount of measurement time is lost to settling time between these different states. At the limit, no measurement time is used when the half cycle is as long as the response time of the instrument.

[0008] BRIEF DESCRIPTION OF THE INVENTION

[0009] An object of the present invention is to provide a new method and apparatus. The invention is characterized by what is stated in the independent claims. Some embodiments of the invention are disclosed in the dependent claims.

[0010] In the presented solution characteristics of a particle flow is measured. A sample flow comprising electrically charged particles is guided through a passage. A mobility analyser having a particle cut-off size is provided. The mobility analyser allows particles having a size larger than the cut-off size to penetrate through the mobility analyser. An electrical current carried by the charged particles penetrated through the mobility analyser is measured. The cut-off size of the mobility analyser is alternated. Alternating the cut-off size of the mobility analyser forms a state of change for the resulting measured electrical current. A dynamic model provides a simulated signal describing the behaviour of the electrical current during the state of change. The model comprises as input parameters a variable alternating the cut-off size of the mobility analyser, and a particle-size parameter of the sample flow. Similarity between the simulated signal and measured electrical current is optimized. A value of the particle-size parameter is updated based on adequate similarity between the simulated signal and measured electrical current. Concentration quantities of the particle flow are determined already during the state of change using the updated parameter value and the measured electrical current.

[0011] Similarity between the simulated signal and measured electrical current may be optimized by performing similarity calculations between the measured current and the simulated signal.

[0012] The definition that the model is dynamic means that the model comprises a at least one time dependent factor.

[0013] Alternating and controlling the cut-off size is continuous and dependent on measurement result such as measured particle size, flow rate, and / or other factors, and thereby regenerative. The alternating and controlling is so fast that an automatic control device is required. The length of measurement cycle of repeating instrument state is according to an embodiment smaller that 5 seconds and according to another embodiment smaller than 1 second. According to another embodiment the length of the measurement cycle is less than five times and according to another embodiment two times a response time of the device for the change in the cut-off size. The response time is the time duration in which the change in the measured electrical current to 90 % of the final change takes as a result of cut-off size change.

[0014] In the presented solution in parallel with the measured signal a comparison or simulated signal corresponding to the size factor(s) of the particles is simulated. The idea is that the comparison or simulated signal is as similar as possible with the measured signal when the same particle size is used in the measurement and in the simulation. In the presented solution the similarity between the comparison or simulated signal and the measured signal is frequently or continuously compared and the particle size parameter(s) which is / are a starting value(s) to the simulation calculation is / are amended such that the result of the calculated similarity criteria is as good as possible. Continuously meaning with every discrete measurement value of measured electrical current. Frequently meaning twice every measurement cycle or slower.

[0015] In the presented solution it is possible to use a simple and inexpensive mobility analyser, because the underlying model allows for calculating a more accurate result even with limited resolution of a simple analyzer. The mobility analyser may be a zeroth-order mobility analyser. The zeroth-order mobility analyser only has one aerosol input and output flow and no particle guiding sheath flow.

[0016] According to an embodiment an effect of alternating the cut-off size of the mobility analyser to the measured electrical current is eliminated by dividing the measured electrical current or its derivative by the simulated signal or its derivative. Thereby a reformed signal is formed.

[0017] According to an embodiment, in addition to or instead of similarity calculations it is possible to optimize the similarity between the simulated signal and measured electrical current by minimizing the influence of cut-off size modulation on the reformed signal.

[0018] The presented solution provides a very accurate measurement result. The time response of the measurement is very fast. In prior art after alternating the cut-off size a stationary state has to be achieved before reliable measurement results are achieved. In the presented solution instead of or in addition to utilizing stationary states, the changing measurement signal following the alternating of the cut-off size is utilized to provide continuous and instantaneous measurement results. It has been noticed that in addition to particle flow-rate also particle size affects the dynamical behaviour of the state of change. Therefore it is extremely difficult to provide measurement results during the state of change. However, in the presented solution this is achieved.

[0019] BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In the following the invention will be described in greater detail by means of some embodiments with reference to the attached drawings, in which

[0021] Figure 1 shows schematically an apparatus for measuring characteristics of a particle flow;

[0022] Figures 2, 3, and 4 show block diagrams of methods for measuring characteristics of a particle flow; and Figures 5, 6, and 7 show diagrams of signals utilized in a method for measuring characteristics of a particle flow.

[0023] DETAILED DESCRIPTION OF THE INVENTION

[0024] Figure 1 shows an apparatus 1 for measuring characteristics of a particle flow. The apparatus 1 comprises a passage 2 with an inlet 3 and an outlet 4 for guiding a sample flow Q through the apparatus 1. The sample flow Q comprises electrically charged particles. The flow through passage 2 may be realized in various ways such as by using a pump, by using chimney effect, or by using ion wind.

[0025] In the embodiment shown in Figure 1 the apparatus 1 is provided with a clean gas channel 5. A clean gas flow is provided to flow along a clean gas channel 5. The clean gas forming the clean gas flow may be clean air, for example.

[0026] A charger 6 is provided in the clean gas channel 5. The charger is powered by a high voltage source 7. The charger 6 may be a corona discharge needle, for example. The charger 6 ionizes the clean gas flowing in the clean gas channel 5 thereby forming an ionized clean gas flow.

[0027] The ionized clean gas flow C may form a main flow of an ejector thereby forming an ejector flow. The ejector flow may generate an under pressure for driving a gas flow comprising small particles into the apparatus 1 via the inlet 3. Another solution, however, is to provide the system with one inlet flow and one outlet flow and form the flow with a pump. In such case, the operation of the ejector would be redundant and would not affect the flow.

[0028] The ionized clean gas flow and the gas flow comprising small particles are mixed in the passage 2. Thereby the ions in the ionized clean gas flow charge particles in the gas flow and the sample flow Q comprising electrically charged particles.

[0029] Instead of mixing an ionized gas flow with the gas flow comprising particles the sample flow Q comprising electrically charged particles may be formed by other means, also. Examples of these other means are photoionization, radioactive ionization and x-ray ionization.

[0030] The apparatus 1 further comprises a mobility analyser 8. The mobility analyser 8 allows particles having a size larger than the cut-off size to penetrate through the mobility analyser 8. The mobility analyser 8 removes excess ions and / or a part of the charged particles from the sample flow Q, for example.

[0031] In the embodiment disclosed in Figure 1 the mobility analyser 8 is an electrostatic ion and particle trap, referred to as a trap. The trap removes small, charged particles due to their high electrical mobility in an electrical field. Thus, the trap 9 may remove free ions from the sample flow Q. The trap may also remove charged particles having a particle size smaller than a trap cut-off size.

[0032] The trap cut-off size may be controlled by adjusting the voltage of the trap, for example. The embodiment shown in Figure 1 comprises a power source 9, which generates the necessary trap voltage for the trap. The power source 9 is controlled by a control unit 10 for controlling the trap voltage.

[0033] It is also possible to control the trap cut-off size by adjusting the distance between electrodes in the ion trap, or adjusting the total flow through the trap, for example.

[0034] The apparatus 1 further comprises a measuring device 11. The measuring device 11 measures an electrical current carried by the charged particles penetrated through the mobility analyser 8. The measuring device 11 may measure an electrical current escaping from the apparatus 1 with the particles. However, the measurements may be implemented using other current measurement techniques, such as electrodes or a particle filter collecting at least a fraction of the charged particles.

[0035] The measurement results are guided to the control unit 10. The measurement results are converted to mass concentration or any other characteristics of the particle flow. The conversion may be performed by the control unit 10 or the control unit may forward the measurement results to another unit performing the conversion. The control unit controlling the apparatus and providing the measurement results may be the control unit 10 in direct connection with the apparatus. Alternatively, the control unit may comprise the control unit 10 in direct connection with the apparatus and a separate unit such as a separate computer. According to a further embodiment the control unit controlling the apparatus and providing the measurement results is a separate unit such as a separate computer that is functionally connected to the apparatus.

[0036] The cut-off size of the mobility analyser 8 is alternated. Alternating the cut-off size of the mobility analyser 8 forms a state of change for the resulting measured electrical current. The cut-off sizes of the mobility analyser 8 are set on basis of determined particle size and / or flow-rate related parameters. According to an embodiment the optimal cut-off size criteria is typically that the measured signal is half compared to a situation in which the current caused by all particles is measured.

[0037] Even though the cut-off size of the mobility analyser 8 is alternated the characteristics of the particle flow may be measured or determined continuously or at least without waiting the output signal to settle into a stationary state. A dynamic model provides a simulated signal describing the behaviour of the electrical current during the state of change. The model is included in the control unit 10 or in a separate computer, for example. The model corresponds to static and dynamic features of the apparatus. Model parameters depending on external or variable features are left as variable parameters of the model.

[0038] The model comprises as input parameters a variable alternating the cutoff size of the mobility analyser, and a particle-size parameter of the sample flow. Similarity between the simulated signal and measured electrical current is optimized by performing similarity calculations between the measured current and the simulated signal. A value of the particle-size parameter is updated based on adequate similarity between the simulated signal and measured electrical current. Concentration quantities of the particle flow are determined already during the state of change using the updated parameter value and the measured electrical current. According to an embodiment characteristics of the particle flow are determined using the determined parameter value, the measured electrical current, and the simulated signal.

[0039] According to an embodiment the dynamic model comprises differential equations or difference equations as a function of time. According to an embodiment the simulated signal of the dynamic model is achieved by computing the results of the equations over time.

[0040] According to an embodiment the similarity calculations utilize covariance, correlation, or essentially same kind of statistical measure between the measured electrical current and the simulated signal.

[0041] According to an embodiment optimal parameter values are chosen by interpolation.

[0042] In the following the solution for measuring characteristics of a particle flow is discussed with reference to Figures 2 to 4. Figures 2 to 4 show simplified block diagrams of methods for measuring characteristics of a particle flow.

[0043] In Figures 2, 3, and 4 the double line denotes a signal path which is a continuous or semicontinuous signal from measurement to output. The single solid line denotes feeding a continuous or semicontinuous parameter for algorithm functioning. The dotted line denotes how a parameter to be updated according to algorithm internal calculations is fed.

[0044] Block 100 denotes that the cut-off size of the mobility analyser is alternated. In this embodiment the mobility analyser is an electrostatic trap. The alternating trap voltage Ut may be a predetermined trap voltage sequence, a trap voltage controlled by an algorithm, or a random change of the trap voltage, or any combination of the above. According to an embodiment the trap voltage values are based on the model results and are calculated in block 105 shown in Figures 3 and 4.

[0045] Block 101 denotes simulation of the model signals. Thus, a simulated signal Simis formed. Block 101 has inputs of the trap voltage Ut and a parameter describing at least one parameter describing the size properties of particles to be measured. The size properties of particles may be electrical mean mobility or mean size, for example. Optionally, a parameter describing the flow rate through the trap may also be an input. Typically, the input concentration in simulation is assumed to stay constant. Typically, the input concentration has a value 1. One or more simulated signals Simmay be computed in parallel using different values for parameters.

[0046] Block 102 denotes determination of similarity parameter values. The similarity parameter is used for estimating the similarity between the simulated signal (s) Simand the measured current signal Iem. Inputs for the calculations are the measured signal Iemand the simulated current signal Sim. Outputs are similarity value values for each Sim(i) and Iempair, where each Sim(i) signal corresponds to one parameter vector, having at least one parameter, used for signal simulation.

[0047] The computational estimate can be based on determination of covariance, correlation, or their derivatives, or in general calculation, which include as an essential procedure the multiplication of signals to be compared or their derivatives, for example. Another alternative is based on determination of the cumulated difference of signals to be compared or derivatives of those signals or / and derivatives of the differences. A typical derivative of the difference is its square. In that case commonly used term is least square fit. The disadvantage of this solution based on cumulated differences is that, in addition to the signal shape, also the amplitude of the model signal should be estimated.

[0048] Block 103 denotes updating size and / or flow parameter values. Reference marking pS relates to a parameter relating to particle size or size distribution. Reference marking pQ relates to a parameter relating to sample flow (or flow through a mobility analyser (e.g. a trap)). Updating the estimation of particle-size and / or flow-rate parameters is based on similarity calculation. Inputs are the similarity value vectors from block 102. The output is the adjustment for parameters pQ, pS, such that maximum similarity is achieved between simulated and measured signals.

[0049] According to an embodiment the particle-size parameter is taken into account but the flow-rate parameter is not taken into account. In such case the flow-rate parameter may be defined to be constant. According to an embodiment both the flow-rate parameter and the particle-size parameter are taken into account. Thereby an extremely accurate measurement result is achieved.

[0050] Block 104 denotes derivation of the concentration quantities. As a result calculates block 104 the concentration quantities. Inputs for the block 104 are measured current and derived size and / or flow parameters. The outputs are concentration quantities Cl - Cn. The concentration quantities Cl - Cn can be i.e. particle number concentration, mass concentration, and / or LDSA (Lung Deposited Surface Area), for example. Inputs may also comprise reformed measured and simulated signals (see block 106 in Figure 4) and / or concentration coefficients (see block 105 in Figures 3 and 4).

[0051] Block 105 in Figures 3 and 4 denotes trap voltage determination and concentration coefficient derivation. According to particle-size and optionally flowrate parameters block 105 calculates optimal trap voltages. In typical case the trap voltage sequence has two voltages; the lower voltage is kept constant while the higher one is varied. Block 105 may also calculate coefficients for concentrationresult calculations. Inputs for the block 105 are size parameter pS and optionally flow-rate parameter pQ.

[0052] According to an embodiment the voltage of the electrostatic trap is modulated between at least two voltages, corresponding to different particle cutoff sizes. This modulation of the cut-off size produces modulation of the measured current. The modulated measured current values depend on the aerosol size distribution. From this modulation a modulation ratio can be calculated. The modulation ratio means the ratio of the modulated currents. The modulation ratio between two voltages corresponds directly to a ratio of the aerosol population above the corresponding cut-off sizes. For example, median size corresponds to a ratio of 0.5, but other ratios may be useful for other characteristic sizes.

[0053] According to an embodiment alternating the cut-off size of the mobility analyser is controlled such that a resulting modulation ratio is kept essentially constant. The controlling may be based on the particle-size parameter and / or the flowrate parameter, or on feedback control of the measured electrical current, for example. The resulting modulation ratio may be a ratio between the measured electrical current on a higher cut-off size and the measured electrical current on a lower cut-off size. In this connection the definition that the resulting modulation ratio is kept essentially constant means that the resulting modulation ratio does not deviate more than 20 % of the average resulting modulation ratio. When the cut-off size is adjusted to produce an essentially constant resulting modulation ratio, the characteristic cut-off size corresponds to the same characteristic size of the size distribution and the characteristic size can be quickly and accurately measured over a wide particle size range.

[0054] It is rather demanding to take both the flow-rate parameter and the particle-size parameter into account whereby both of them are variables. In such case both the parameters affect on the signal and the correlation and similarity values. An excellent and surprising solution for solving or determining both the flow-rate parameter and the particle-size parameter is to utilize both low and high cut-off states of the mobility analyser (low and high voltages of the trap). The flow-rate parameter is determined or solved in low cut-off state (practically after falling edge of the trap voltage or on the rising edge of the measured current), because in this phase the particle-size parameter has a relatively low contribution to the result. In this phase the particle-size parameter is set to an existing (previously determined) value. Correspondingly the particle-size parameter is determined or solved in high cut-off state (after rising edge of the trap voltage or on the falling edge of the measured current), because in this phase the particle-size parameter has the highest contribution to the result. In this phase the flow-rate parameter is set to an existing (previously determined) value.

[0055] Block 106 denotes signal reforming. In block 106 the signal modulation caused by modulated trap voltage is eliminated. The simplest measure for this is to divide the measured current signal by the optimal simulated signal Sim. Inputs for block 106 are measured and simulated signals. Output of the block 106 is re- formed / demodulated signal.

[0056] Thus, according to an embodiment an effect of alternating the cut-off size of the mobility analyser 8 to the measured electrical current Iemis eliminated by dividing the measured electrical current Iemor its derivative by the simulated signal Simor its derivative.

[0057] Figures 5 to 7 illustrate how the parameter values for the simulated signal are chosen. In the Figures the dotted line 200 denote how the trap voltage is altered. The dashed line 201 denotes a noiseless measured signal Iem. The line 202 denotes a first simulated signal Siml, the line 203 denotes a second simulated signal Sim2, and the line 204 denotes a third simulated signal Sim3.

[0058] Simulated signals Siml, Sim2, Sim3 have been derived with varied dynamic parameter. For sake of simplicity in the presented example only one parameter value has been varied. Dynamic parameters of the second simulated signal Sim2 are equal compared to the reference signal (noiseless measured signal Iemin Figure 6), while varied rate parameter is lower in the case of the first simulated signal Siml and higher for the third simulated signal Sim3.

[0059] R2values (correlation power 2) between simulated signals (Siml, Sim2, Sim3) and noiseless measured signal Iemduring altered trap voltage sequence are listed in table below.

[0060]

[0061] In Figures 6 and 7 the line 205 denotes a noisy measured signal Iem. Noisy measured signal Iemis formed by adding random changes (noise) into the noiseless measured signal Iem. Corresponding R2values are listed below. Random deviation (noise) decreases R2values, but the signal with equal dynamic parameters (Sim2) with compared signal yield still highest R2value.

[0062] In Figure 7 of the simulated signals only the second simulated signal Sim2 is shown because it gives the best results. The effect of trap-voltage modulation to the measured signal Iemcan be eliminated by dividing the measured signal lem by the optimal simulated signal Sim2. The resulting signal is a reformed noisy signal Si_refor. In Figure 7 the line 206 denotes the reformed noisy signal Si_refor.

[0063] In the following some examples for calculating similarity between two data sets are given.

[0064] A well-known criteria for similarity of two data sets are their covariance or correlation (Pearson’s correlation).

[0065] One form of correlation equation for two data sets to be compared can be written as

[0066] For covariance correspondingly:

[0067] Practical experience has indicated that the result of correlation or covariance calculation does not yield best possible similarity criteria between bmeas- ured signal modulated by electrical mobility analyser and ^corresponding simulated signal. This is due to the fact that those calculations utilize only dynamically changing components ("AC component") of the signals to be compared, but not constant values ("DC component", base value). A possible method of utilizing also the constant values ("DC component") is fitting the simulated signal to the measured one. This takes in account completely the constant values ("DC components"). In this case both signal shape and magnitude are fitted. This kind of fitting procedures are complicated, less sta- ble and need much more computing power than covariance or correlation calculations. A drawback is also that fitting two components (magnitude and shape) compromises the accuracy between two features (magnitude and shape) compared to one-feature (shape) estimation in the case of covariance or correlation calculation. Especially, if there are any considerable offset in the measured signal, this kind of "two-feature" fitting may yield more inaccuracy in "shape parameters".

[0068] It will be obvious to a person skilled in the art that, as technology advances, the inventive concept can be implemented in various ways. The invention and its embodiments are not limited to the examples described above but may vary within the scope of the claims.

Claims

CLAIMS1. A method of measuring characteristics of a particle flow, the method comprising guiding a sample flow comprising electrically charged particles through a passage; providing a mobility analyser having a particle cut-off size, the mobility analyser allowing particles having a size larger than the cut-off size to penetrate through the mobility analyser; measuring an electrical current carried by the charged particles penetrated through the mobility analyser; alternating the cut-off size of the mobility analyser thereby forming a state of change for the resulting electrical current; providing a dynamic model providing a simulated signal describing the behaviour of the electrical current during the state of change, the model comprising as input parameters a variable alternating the cut-off size of the mobility analyser, and a particle-size parameter of the sample flow; optimizing similarity between the simulated signal and measured electrical current; updating a value of the particle-size parameter based on adequate similarity between the simulated signal and measured electrical current; and determining, already during the state of change, concentration quantities of the particle flow using the updated parameter value and the measured electrical current.

2. A method as claimed in claim 1, wherein the model comprises as an input parameter also a flow-rate parameter of the sample flow and also a value of the flow-rate parameter is updated based on adequate similarity between the simulated signal and the measured electrical current.

3. A method as claimed in claim 1 or 2, wherein the concentration quantities of the particle flow are determined using the updated parameter value, the measured electrical current, and the simulated signal.

4. A method as claimed in claim 3, comprising eliminating an effect of alternating the cut-off size of the mobility analyser to the measured electrical current by dividing the measured electrical current or its derivative by the simulated signal or its derivative, thereby forming a reformed signal.

5. A method as claimed in claim 4, wherein similarity between the simulated signal and measured electrical current is optimized by minimizing theinfluence of cut-off size modulation on the reformed signal.

6. A method as claimed in any one of the preceding claims, comprising controlling alternating the cut-off size of the mobility analyser such that a resulting modulation ratio is kept essentially constant, the resulting modulation ratio being a ratio between the measured electrical current on a higher cut-off size and the measured electrical current on a lower cut-off size.

7. A method as claimed in any one of the preceding claims, wherein the dynamic model comprises differential equations or difference equations as a function of time.

8. A method as claimed in claim 7, wherein the simulated signal of the dynamic model is achieved by computing the results of the equations over time.

9. A method as claimed in any one of the preceding claims, wherein similarity between the simulated signal and measured electrical current is optimized by performing similarity calculations between the measured current and the simulated signal.

10. A method as claimed in claim 9, wherein the similarity calculations utilize covariance, correlation, or essentially same kind of statistical measure between the measured electrical current and the simulated signal.

11. A method as claimed in claim 9 or 10, wherein the similarity calculations comprise interpolation.

12. A method as claimed in any one of the preceding claims, wherein a zeroth-order mobility analyser is used as the mobility analyser.

13. An apparatus for measuring characteristics of a particle flow, the apparatus comprising a passage guiding a sample flow comprising electrically charged particles; a mobility analyser having a particle cut-off size, the mobility analyser allowing particles having a size larger than the cut-off size to penetrate through the mobility analyser; a measuring device measuring an electrical current carried by the charged particles penetrated through the mobility analyser; and a control unit, the control unit being arranged to alternate the cut-off size of the mobility analyser thereby forming a state of change for the resulting electrical current; comprising a dynamic model providing a simulated signaldescribing the behaviour of the electrical current during the state of change, the model comprising as input parameters a variable alternating the cut-off size of the mobility analyser, and a particle-size parameter of the sample flow ; being arranged to optimize similarity between the simulated signal and measured electrical current; being arranged to update a value of the particle-size parameter based on adequate similarity between the simulated signal and measured electrical current; and being arranged to determine, already during the state of change, concentration quantities of the particle flow using the updated parameter value and the measured electrical current.

14. An apparatus as claimed in claim 13, wherein the control unit being arranged to determine the characteristics of the particle flow using the determined parameter value, the measured electrical current, and the simulated signal.

15. An apparatus as claimed in claim 13 or 14, wherein the dynamic model comprises differential equations or difference equations as a function of time.

16. An apparatus as claimed in claim 15, wherein the control unit is arranged to compute the results of the equations over time to achieve the simulated signal of the dynamic model.

17. An apparatus as claimed in any one of the claims 13 to 16, wherein the mobility analyser is a zeroth-order mobility analyser.

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