WO2005080099A1 - Interrogation method for passive sensor monitoring system - Google Patents

Interrogation method for passive sensor monitoring system Download PDF

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WO2005080099A1
WO2005080099A1 PCT/GB2005/000387 GB2005000387W WO2005080099A1 WO 2005080099 A1 WO2005080099 A1 WO 2005080099A1 GB 2005000387 W GB2005000387 W GB 2005000387W WO 2005080099 A1 WO2005080099 A1 WO 2005080099A1
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frequencies
method according
frequency
interrogation
determined
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PCT/GB2005/000387
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French (fr)
Inventor
Victor Alexandrovich Kalinin
Mark Lee
John Peter Beckley
David W. Clarke
George Edward Bown
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Transense Technologies Plc
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Priority to GB0403481.5 priority
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Publication of WO2005080099A1 publication Critical patent/WO2005080099A1/en

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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B60VEHICLES IN GENERAL
    • B60CVEHICLE TYRES; TYRE INFLATION; TYRE CHANGING OR REPAIRING; REPAIRING, OR CONNECTING VALVES TO, INFLATABLE ELASTIC BODIES IN GENERAL; DEVICES OR ARRANGEMENTS RELATED TO TYRES
    • B60C23/00Devices for measuring, signalling, controlling, or distributing tyre pressure or temperature, specially adapted for mounting on vehicles; Arrangement of tyre inflating devices on vehicles, e.g. of pumps, of tanks; Tyre cooling arrangements
    • B60C23/02Signalling devices actuated by tyre pressure
    • B60C23/04Signalling devices actuated by tyre pressure mounted on the wheel or tyre
    • B60C23/0408Signalling devices actuated by tyre pressure mounted on the wheel or tyre transmitting the signals by non-mechanical means from the wheel or tyre to a vehicle body mounted receiver
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B60VEHICLES IN GENERAL
    • B60CVEHICLE TYRES; TYRE INFLATION; TYRE CHANGING OR REPAIRING; REPAIRING, OR CONNECTING VALVES TO, INFLATABLE ELASTIC BODIES IN GENERAL; DEVICES OR ARRANGEMENTS RELATED TO TYRES
    • B60C23/00Devices for measuring, signalling, controlling, or distributing tyre pressure or temperature, specially adapted for mounting on vehicles; Arrangement of tyre inflating devices on vehicles, e.g. of pumps, of tanks; Tyre cooling arrangements
    • B60C23/02Signalling devices actuated by tyre pressure
    • B60C23/04Signalling devices actuated by tyre pressure mounted on the wheel or tyre
    • B60C23/0408Signalling devices actuated by tyre pressure mounted on the wheel or tyre transmitting the signals by non-mechanical means from the wheel or tyre to a vehicle body mounted receiver
    • B60C23/0422Signalling devices actuated by tyre pressure mounted on the wheel or tyre transmitting the signals by non-mechanical means from the wheel or tyre to a vehicle body mounted receiver characterised by the type of signal transmission means
    • B60C23/0433Radio signals

Abstract

A method of determining the frequency of a plurality of resonant devices (for example three SAW devices) comprises determiníng optimal interrogation frequencies for each of the devices, the optimal interrogation frequencies having maximum power spectral densities, accumulating a plurality of responses for each sensor, performing discrete Fourier transforms on the sampling results to estimate the three resonant frequencies, and averaging the results of the Fourier transforms to provide an indication of resonant frequencies. The averaging step may include the calculation of a standard deviation and the rejection of any results which fall more than a pre-determined multiple of the standard deviation from the average frequency result. The frequency is determined by the method may be employed to calculate the pressure and temperature of the sensor devices. The sensor devices may be located in a vehicle tyre.

Description

INTERROGATION METHOD FOR PASSIVE SENSOR MONITORING SYSTEM

This invention relates to a method for interrogating sensor systems based on wirelessly interrogated passive sensors-transponders as used, for example, for measuring pressure and temperature of air in vehicle tires. More specifically, the preferred embodiment of the invention provides a passive sensor interrogation algorithm which allows high accuracy of measurement of pressure and temperature. A number of solutions for the problem of a wireless interrogation of passive pressure and temperature sensors are known in the prior art. The sensors utilise either one-port delay lines or one-port resonators, preferably based on SAW technology, although other approaches are also possible (bulk acoustic wave devices or dielectric resonators, for instance). The use of the delay lines [see F. Schmidt and G. Scholl, Wireless SAW identification and sensor systems. In a book "Advances in Surface Acoustic Wave Technology, Systems and Applications". Ed. C. W. C. Ruppel and T. A. Fjeldly, Singapore, World Scientific, 2001 , p. 287.] or the resonators [see W. Buff, S. Klett, M. Rusko, J. Ehrenpfordt, and M. Goroll. Passive remote sensing for temperature and pressure using SAW resonator devices. IEEE Trans. On Ultrasonics, Ferroelectrics, and Frequency Control, vol. 45, No. 5, 1998, pp. 1388 - 1392.] is dictated by a necessity to distinguish a passive sensor response on the one hand and a direct feed-through signal together with environmental echo signals on the other hand. This is achieved by employing the fact that the impulse response of the delay lines and the resonators is considerably longer than any parasitic signal. Interrogation of passive SAW sensors based on delay lines is usually performed by means of very short (typically, 0.1 σs) RF pulses. As a result, the interrogation system requires relatively wide bandwidth of 10 MHz or even more, which is not available in licence-free industrial-scientific-medical (ISM) bands below 1 GHz. Sensors based on high Q-factor one-port resonators are more appropriate for these bands due to their narrowband response. For this reason, we shall concentrate on interrogation of resonator-type passive sensors, preferably based on SAW resonators but possibly on surface transverse wave resonators (STW), thin film bulk acoustic wave resonators (FBAR) or dielectric resonators. The main purpose of the interrogation is to measure the frequency of natural oscillations in the resonators (resonant frequencies) excited by relatively long and narrowband RF interrogation pulses. Since the resonant frequencies can be made to depend on temperature and pressure, knowing the resonant frequencies allows temperature and pressure to be calculated. In order to exclude influence of varying antenna impedance on the resonant frequency the prior art [see W. Buff, S. Klett, M. Rusko, J. Ehrenpfordt, and M. Goroll mentioned above] proposes that a difference between the frequencies of natural oscillations of two similar resonators (possibly with slightly different resonant frequencies) connected to one antenna, is measured. If both resonators are at the same temperature and have different pressure sensitivity, the pressure can be found from the frequency difference and the influence of temperature will be greatly reduced. The two resonators can be very efficiently interrogated by bi- harmonic RF pulse exciting natural oscillations in both resonators simultaneously [see GB9925538.2]. When the interrogation pulse is over the response will present an exponentially decaying beat signal with the beat frequency equal to the measured frequency difference. The beat frequency can be accurately determined by means of amplitude detection and period count. In the case of simultaneous measurement of both pressure and temperature, at least three resonators connected to one antenna are required and two frequency differences need to be measured in order to calculate the two unknowns, the pressure and the temperature [see W. Buff, M. Rusko, M. Goroll, J. Ehrenpfordt, and T. Nandahl. Universal pressure and temperature SAW sensor for wireless applications. 1997 IEEE Ultrasonics Symp. Proceedings, 1997, pp. 359 - 362]. Measuring the beat frequency is impossible in this case. The following interrogation techniques are known from literature. 1. The resonators are excited by RF pulses in turn. The exponentially decaying response of each resonator is picked up by antenna is used as an input signal for a gated PLL tracking variations of the resonant frequency [see A. Pohl, G. Ostermayer, and F. Seifert. Wireless sensing using oscillator circuits locked to remote high-Q SAW resonator. IEEE Trans. On Ultrasonics, Ferroelectrics, and Frequency Control, vol. 45, No. 5, 1998, pp. 1161 - 1168]. This technique is more appropriate for a single resonator and becomes too cumbersome and unreliable in the case of three resonators, especially if their frequencies are close to each other.

2. The resonators are excited by RF pulses in turn. The exponentially decaying response of each resonator is picked up by antenna is down- converted to a lower intermediate frequency and then the period of the natural oscillation is counted [see GB9925538.2]. This method also works well either for a single resonator or when the distance between the resonant frequencies is much larger than the resonator bandwidth. However, if it is less than 10 times the bandwidth (which is the case in ISM band), then more than one resonator will be excited by the RF pulse causing parasitic frequency modulation in the sensor response and drastically reducing accuracy of measurement.

3. All three resonators are excited in one go. The spectrum of the sensor response is analysed in the receiver by means of discrete Fourier transfonn and all resonant frequencies are measured [see L. Reindl, G. Scholl, T. Ostertag, H. Scherr, and F. Schmidt. Theory and application of passive SAW radio transponders as sensors. IEEE Trans. On Ultrasonics, Ferroelectrics, and Frequency Control, vol. 45, No. 5, 1998, pp. 1281 - 1291]. This approach allows interrogation of a large number of resonators. However it requires the use of a broadband RF pulse covering the whole frequency range of operation of the sensor. Bearing in mind that the peak power of the interrogation pulse is limited in ISM band (usually it is not more than 10 mW) it is clear that spreading the spectrum of the pulse reduces efficiency of resonator excitation. It adversely affects signal-to- noise ratio (SNR) and hence accuracy of measurements. The object of the present invention is to provide an interrogation method that preserves the advantages of spectral analysis and at the same time provides high efficiency of resonator excitation and high accuracy of measurements. In accordance with one aspect of the present invention a method of interrogating a plurality of resonant devices to determine the respective resonant frequencies of the devices comprises the steps of: (1) determining, for each resonant device, an optimal interrogation frequency; (2) repeating the interrogation of each resonant device a plurality of times at its respective optimal interrogation frequency as determined by step (1) (3) performing parametric modelling on the data accumulated as a result of step (2) and (4) determining the average of the frequencies derived from step (3). The parametric modeling for spectral estimation, which estimates parameters that contain frequency information, can take a variety of foπns. The Yule- Walker method estimates parameters using an estimate of the autocorrelation function of the time series data and minimizes the forward prediction error in a least squares sense and has the advantage of producing a stable model. The Burg method minimizes the forward and backward prediction error with the auto- regression (AR) coefficients constrained to satisfy the Levinson-Durbin recursion and has the advantage of producing high resolution for short data records. The covariance method minimizes the forward prediction error in a least squares sense and can distinguish between many sinusoids. The modified covariance method also minimizes the backward prediction error in a least squares sense and does not suffer from spectral line splitting. These methods offer the basis for improvements in frequency estimation resolution for particular signal conditions. A special class of spectral estimators which are particularly suited to estimating the frequencies of multiple sinusoids in additive white noise come under the heading of subspace methods. Of particular relevance are the multiple signal classification (MUSIC) and eigenvector method, and methods based on these. The MUSIC algorithm estimates the pseudospectrum from a signal or a correlation matrix by performing eigenspace analysis using Schmidt's method. The eigenvector method uses a weighted version of the MUSIC algorithm, and, if the correlation matrix is unavailable, the eigenvalues and eigenvectors can be estimated using singular value decomposition (SND). Both parametric methods and subspace methods may use Fourier techniques to estimate spectral density from the parameters (parametric techniques) or eigenvectors (subspace techniques) but this is distinct from the use of Fourier transforms in a periodogram method where transforms are used to estimate frequency components directly from the time series. The parametric modelling used in the present invention may be suited to the signal produced by the sensor so as to enhance resonant frequency estimation compared with to existing system such as Fourier analysis. Examples of preferred parametric modelling systems are autoregressive modelling and Kumaresan-Tufts methods. The invention would be better understood from the following description of a preferred embodiment thereof, given by way of example only, reference being had to the accompanying drawings wherein: Figure 1 illustrates schematically a pressure and temperature monitoring system for use in a vehicle tyre; Figure 2 illustrates the interrogation algorithm proposed by the present invention; Figure 3 is a graph showing variation in root mean square error with order of modified covariance method; and Figure 4 is a graph showing changes in Frequency Estimation Standard Deviation with signal time for a number of different analytical methods. Referring firstly to Figure 1 , the present invention is particularly applicable to a system for monitoring the temperature and pressure in a vehicle tyre. However, it is to be understood that the invention is not limited to this application and may be applied to other circumstances where pressure and temperature are to be monitored, or indeed to other circumstances where a plurality of other parameters are to be measured by a passive sensor system. The preferred embodiment of the present invention includes three surface acoustic wave devices SAW1, SAW2 and SAW3 which are connected to a common antenna 12. Whilst the use of SAW devices is preferred as a means of generating signals indicative of the sensed condition, it is to be understood that the invention is not limited to such devices and other passive sensors capable of providing appropriate indications by means of resonant frequency may be employed. In the particular preferred application of the present invention (vehicle tyre pressure and temperature sensing) the SAW devices SAW1, SAW2, SAW3 and the antenna 12 are mounted as a unit A within a vehicle tyre. An excitation and monitoring unit B is located on the vehicle in order to provide excitation signals to the tyre mounted unit and to receive response signals from it. For this purpose, the unit B includes an antenna 11 for communicating with the antenna 12 of the package A. An interrogation pulse is generated by a power amplifier 8 that is excited by a transmitter synthesiser 10. The pulse goes through an RF switch 1 to the antenna 11 of the interrogation unit B. The radiated electromagnetic wave is picked up by the antenna 12 of the sensor unit A thus exciting the three SAW resonators in the sensor. Re-radiated sensor response is transmitted by the sensor antenna and received by the antenna 11. The signal goes through a front-end low- noise amplifier 2 to the frequency converter where it is mixed with the signal of the receiver synthesiser 3. The frequency difference between the receiver synthesiser 3 and the transmitter synthesiser 10 is equal to the intermediate frequency, e.g. 1 MHz. The mixer can be IQ mixer producing two IF signals with the phase difference of 90°. The IF signal (or I and Q signals) goes/(go) through a filter 4 and a limiting amplifier (which increases the dynamic range of the receiver) to an 8-bit or 10-bit analog-to-digital converter 6 with the sampling rate sufficiently high in comparison with the IF, e.g. 10 or 20 MHz. The sensor response in digital format is stored in the internal memory of a DSP chip 7 where it is accumulated in a coherent way during the interrogation process. The chip then performs spectral analysis of the data for all three SAW resonators, calculates three resonant frequencies, performs averaging procedure and calculates the pressure and the temperature. The DSP chip 7 also controls the operation of the synthesisers 3 and 10, RF switch 1, and the ADC 6. Besides, it can also enable and disable the power amplifier 8 and the LNA 2 in order to increase an isolation between the receiver and the transmitter. As one of the measures to ensure coherent accumulation of the sensor responses the same quartz crystal oscillator 9 is preferably used as a reference for both synthesisers and for the DSP chip. The above system can also be implemented by using a double frequency conversion receiver that increases image channel rejection. An alternative receiver architecture can be based on a direct frequency conversion. This would cause the removal of one of the synthesizers and addition of the second mixer and ADC to produce a quadrature channel. Referring now to Figure 2, the preferred method of the present invention will be described. The three resonators SAW1, SAW2, SAW3 have slightly different resonant frequencies and different temperature and pressure sensitivities. The frequencies are chosen in such a way that the minimum distance between them is not less than the resonator bandwidth at any pressure and temperature. As a result, the whole operational frequency band (ISM band, for instance) is divided into three sub-bands occupied by the three resonators. The sensor A is interrogated by rectangular RF pulses with the spectral width equal to or less than the resonator bandwidth. This ensures efficient excitation of the resonator in the case if the interrogation frequency is close to the resonant frequency of the resonator. In each sub-band, there are several discrete interrogation frequencies chosen in such a way that the distance between them is equal to or less then the bandwidth of the resonators. The number of the discrete interrogation frequencies depends on the Q-factor of the SAW resonators. For instance, in the case of the unloaded Q = 5000 it would be enough to have nine interrogation frequencies within the 434 MHz ISM band. As a result, whatever the temperature and pressure is, there will always exist three interrogation frequencies from the set of the chosen discrete frequencies that ensure optimal excitation of the three resonators. The excitation is optimal in the sense that the amplitude of oscillation in the resonator will be close to maximum possible one for a given excitation amplitude by the end of the interrogation pulse. The interrogation procedure consists of five main stages as illustrated by the flow chart in Fig. 2. 1. Determination of the three optimal interrogation frequencies maximising power spectral density of the sensor response. At this stage, the sensor is interrogated at all discrete interrogation frequencies one after another. Each time, after launching the interrogation pulse, the sensor response is received and analysed. It can be done, for instance, by frequency down-conversion, sampling the response at the intermediate frequency and either estimation of the signal peak value or calculating discrete Fourier transform. After that, three optimal frequencies are chosen, one in each sub-band, giving maximum peak value of either the signal itself of its spectral density. Alternatively, if a linear amplifier with automatic gain control is used in the receiver, the three frequencies can be chosen that maximise the ratio of the peak value of the spectral density to the average level of its sidelobes. Alternatively, if the limiting amplifier is used in the receiver, the three frequencies can be chosen that maximise the length of the sensor response or minimizes the difference between the position of the peak of the spectral density and the nominal value of the intermediate frequency. At this stage we can already determine the three resonant frequencies by measuring the peak frequencies of the spectral density. However, this would give us just a rough estimate of the actual frequencies of natural oscillations because of the presence of noise and finite resolution of Fourier analysis. 2. Coherent accumulation of sensor responses At this stage we repeat interrogation of the sensor N times at each optimal interrogation frequency in turn. The signals picked up by the receiver are down- converted, sampled and accumulated in a coherent way in three data arrays in a system memory. The aim of the coherent accumulation is to increase SNR by a factor of VN. Coherent accumulation can be ensured, for instance, by using a common quartz-stabilised oscillator both in receiver and transmitter synthesisers and as a clock generator in the DSP chip. In other words, the time between the interrogation pulses is chosen to be an integer number, of the period of the interrogation signal at the intermediate frequency and, at the same time, it needs to be an integer number of the sampling period (alternatively, the start of the sampling needs to be synchronised with the interrogation pulse). Besides, the number of accumulated pulses N is chosen to be sufficiently small (N = 10...30) so that the total time needed for coherent accumulation (approximately 1...2 ms) is small enough in comparison with the period of a vehicle tire rotation (1/40, for instance). As a result, a change in a position of the sensor antenna will not cause a large variation in the phase of the sensor response during accumulation. It is also important from the point of view of minimising a variation of the frequency differences between the three resonators caused by the antenna impedance variation as a result of the tire rotation. Before doing coherent accumulation the presence of interference is also checked at each of the three optimal interrogation frequencies. This can be done for instance by comparing maximum of the spectral density of the signal received in the absence of the interrogation pulse with an appropriate threshold level. If it exceeds the threshold level then the system repeats interrogation after some delay. A simpler interference detection procedure can also be used within the coherent accumulation cycle. In this case, the interference can be detected by measuring the peak value of the received signal during 1 - 2 μs before launching each interrogation pulse. 3. Parametric estimation of frequency components

At this stage the three data arrays obtained as a result of the coherent accumulation are used to calculate the frequency content by means of parametric estimation. Each array contains a time series with a frequency component due to the response of a single resonator although there may also be other frequency components due to the excitation of the two other resonators. However, the main frequency component can be decoupled from the minor components and these minor components can be discarded. The main frequency component corresponds to the relevant frequency of natural oscillation. The parametric method may be based on autoregressive (AR) modelling which involves estimating usually six AR parameters (two for each decaying sine wave corresponding to the SAW sensor response). A system of equations of order p equal to the number of parameters that relates the AR parameters to the time series autocorrelations are solved. A z-domain polynomial can be constructed from these parameters, the roots yielding information on the frequency components present in the time series. In the presence of additive white noise, the associated bias and variance in frequency estimates when using AR modelling is high (it is worse than in the case of discrete Fourier transform) but can be reduced by a number of methods including the use of an autoregressive moving average (ARMA) procedure, or manipulation of the time series to remove the moving average components, for example through recursive filtering.

Autoregressive (AR) methods (such as Burg, Yule-Walker, covariance and modified covariance methods) estimate the all-pole (denominator) parameters of the filter that accurately reproduces the time series data when the filter is driven by white noise with the correct model order being twice the number of sinusoids present. If the data is autoregressive moving average (ARMA), that is, the linear predictor needs previous inputs as well as previous outputs, then a high model order using AR modelling will achieve the same frequency estimation, hence ARMA models are included under the same heading.

AR methods are typically used with undamped data. Further, it is unusual to use these methods with limited signals. One might expect interpolated DFT to give superior results for limited data because no model structure is assumed, and that if AR methods do perform well, a model of high order might be expected to show better performance.

It is shown that AR modelling can give better results, that is, lower root mean square error (RMSE), in this case using the modified covariance method, than that using the DFT. Fig.3 shows that the greatest improvement at short signal length is given with AR order 4. A lower or higher order quickly results in root mean square error increasing above that obtained by DFT.

The data suggests model order 2 is appropriate, or that due to the unusual envelope shape, a very high order would give a good result. Unexpectedly, for a data length 7μs, an intermediate model order gives the lowest root mean square error, performing 35% better than DFT.

Eigenvector methods (such as Pisarenko Harmonic Decomposition, Eigenvector and the MUSIC and ESPRIT algorithms) may alternatively be used within the invention and are based on eigen decomposition of the data correlation matrix and partitioning into signal and noise subspaces. For this reason the methods are also known as subspace methods. In the case of limited damped signals a non- parametric method would be expected to perform better. This is because Eigenvector methods assume a set of complex exponentials exist in white noise and the structure means the model is less suitable for the case of limited damped signals; a non-parametric technique is more flexible and makes no assumptions on the signal properties.

However, in the case of a limited damped signal where the first 3 cycles have approximately constant amplitude, an eigenvector method shows superior results - an outcome which is both novel and unexpected. Fig.2 shows that the Eigenvector method performs better than the DFT. For comparison the modified covariance results for the data used with the Eigenvector method are also shown.

For certain time series characteristics, for example when the received signal from the sensor is weak and the correspondent intermediate frequency signal is not limited by the limiting amplifier, it is desirable to use a technique based on the Kumaresan-Tufts method. This involves setting up a system of linear prediction equations that relates past time series values to predicted future value. Singular value decomposition (SND) is then used to reduce the noise components present and increase accuracy of frequency estimation by retaining the p dominant values where p is the model order. Improvements can be made on the Kumaresan-Tufts method to further enhance frequency estimation.

4. Statistical processing and analysis of the resonant frequency data Stages 1 to 3 (or 2 and 3 only if the resonant frequency variation is slow and a frequent repetition of stage 1 is not required) are continuously repeated and the data on the three resonant frequencies are stored in three data arrays in the system memory. After M cycles of interrogation (M can vary in a wide range, for instance, from 10 to 300) average values fι;2,3 and standard deviations σι>2,3 of each of the three resonant frequencies are calculated. As a result, the standard deviations of f1?2; are further decreased in comparison with σ1>2>3 approximately by a factor of M. Then all the frequencies fs in the relevant arrays not satisfying the condition

Figure imgf000014_0001
(where k may have values from 1 to 3) are excluded from consideration and the average frequencies are re-calculated again. The last procedure is performed in order to exclude possible influence of interference and sudden decrease in the signal amplitude during coherent accumulation causing rough errors in the resonant frequencies. The standard deviations σι>2> can also be used as a measure of validity of the information about the resonant frequencies.

5. Calculation of pressure and temperature

After averaging two difference frequencies are calculated and then the pressure and the temperature are found using, for instance, approach described in Ref. [4]. The proposed interrogation method is aimed to achieve the accuracy of the resonant frequency measurement better than 5x 10"6 . In the case of SAW resonators working in 434 MHz ISM band it should give the accuracy of pressure measurement better that 1 psi and the accuracy of temperature measurement better than 1°C.

Claims

CLAIMS:
1. A method of interrogating a plurality of resonant devices to determine the respective resonant frequencies of the devices comprising the steps of: (1) determining, for each resonant device, an optimal interrogation frequency; (2) repeat the interrogation of each resonant device a plurality of times at its respective optimal interrogation frequency as determined by step (1) (3) perform frequency estimation on the data accumulated as a result of step (2) by means of spectral analysis based on parametric signal modelling and (4) determine the average of the frequencies derived from step (3).
2. A method according to Claim 1 wherein step (4) includes determining the standard deviation for each of the average frequencies determined; rejecting any frequencies which vary from the average frequency by more than a pre-determined multiple of the standard deviation; and re-calculating the average frequency after exclusion of the rejected data.
3. A method according to claim 1 or claim 2 wherein the optimal interrogation frequencies are determined by establishing the frequencies at which the signals from the resonant devices have a maximum peak value or maximum power spectral density.
4. A method according to claim 3 wherein the maximum power spectral density is determined by frequency down-conversion, sampling the response at an intermediate frequency, and calculating discreet Fourier transforms.
5. A method according to claim 3 wherein the maximum power spectral density is determined by means of a linear amplifier with automatic gain control, the optimal frequencies being chosen to maximise the ratio of peak value of the spectral density to average level of its side lobes.
6. A method according to claim 3 wherein the maximum power spectral density is determined by use of a limiting amplifier, the frequencies being chosen to maximise the length of sensor response or minimize the difference between the frequency of the maximum of power spectral density and the IF.
7. A method according to any preceding claim wherein the optimal interrogation frequencies lie within respective sub-bands of an ISM band.
8. A method according to any preceding claim wherein during the repetition of step 2 of claim 1 each signal received is down-converted, sampled and coherently accumulated at optimal interrogation frequencies.
9. A method according to claim 8 wherein coherent accumulation is achieved by using a common clock generator oscillator both in the receiver and transmitter synthesizers and in a DSP chip.
10. A method according to any preceding claim wherein the number of repetitive interrogations in step 2 and the speed at which such interrogations are conducted is such that the total interrogation period is small in comparison with the period of any cyclical movement of the sensors relative to the interrogation equipment.
11. A method according to any preceding claim wherein the determined frequencies are used to calculate pressure and temperature.
12. A method according to any of the preceding claims, wherein said spectral analysis based on parametric signal remodelling is carried out by Autoprogessive methods.
13. A method according to claim 12, wherein said Autoregressive method is drawn from the group comprising Burg Yule- Walker, covariance and modified covariance methods and variants of these methods.
14. A method according to any of claims 1 to 11, wherein said spectral analysis based on parametric signal modelling is carried out using Eigenvector methods.
15. A method according to claim 14, wherein said eigenvector method is chosen from the group comprising Pisarenko, Harmonic, Decomposition, Kumaresan Tufts, Eigenvector and the MUSIC and ESPIRIT altorithms.
16. A method according to any preceding claim wherein the resonant devices are SAW devices.
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