Radio Science

Interferometric meteor radar phase calibration using meteor echoes

Authors


Abstract

[1] A technique for the phase calibration of interferometric meteor radar systems is presented. This technique uses phase differences of meteor echoes measured between spaced receiving antennas. The technique can be applied to data collected during routine observations, effectively allowing self phase calibration without the need for additional hardware or scheduled down time for off-line phase calibration measurements. The technique can also be used to correct data collected using erroneous phase calibration estimates. Simulations of typical range and angle of arrival distributions are used to illustrate the technique and verify its performance. The results reveal that the phase offsets can be estimated to within 2° using realistic simulation parameters. The technique is also applied to data collected using the Buckland Park meteor radar, with the standard deviation of the daily phase offsets estimated over a four month period found to be less than 3°.

1. Introduction

[2] Radar techniques have been used for meteor observations for over 50 years [e.g., Elford, 2001]. Recent advances in personal computers and digitization technology have resulted in a suite of instruments used for online meteor observations. Three recent examples are the meteor detection and collection (MEDAC) system [e.g., Valentic et al., 1996], the SkiYMet all-sky interferometric meteor radar [e.g., Hocking et al., 2001], and the Buckland Park all-sky interferometric meteor radar (BPMR) [e.g., Holdsworth et al., 2004]. The SkiYMet and BPMR make use of an antenna configuration (hereafter referred to as the JWH configuration) designed to yield unambiguous meteor angle of arrival while minimizing mutual antenna coupling [e.g., Jones et al., 1998].

[3] Knowledge of any receive path phase offsets introduced by the antennas, feeder cables, and receivers, are critical to the accuracy of interferometric radar angle of arrival (AOA) estimates, and parameters deduced directly and indirectly from the AOAs. Phase calibration techniques with varying degrees of complexity have been implemented to achieve this aim. One simple and commonly used technique uses partial reflection returns, where the mean scattering position over a suitably long observation period is assumed to be centered on the zenith [e.g., Kudeki et al., 1990]. A related technique applied for MF radar observations uses total reflection E region echoes [e.g., Brosnahan and Adams, 1993]. Other techniques include the use of stellar sources [e.g., Palmer et al., 1996], distant transmitters at known locations [e.g., Djuth and Elder, 1993; Valentic et al., 1997], echo transponders [e.g., Baggaley and Webb, 1980], satellite beacon [e.g., Clark, 1978], aircraft [e.g., Robertson et al., 1953; Chen et al., 2002], injection of test signals into various system components [e.g., Holdsworth and Reid, 2002], and correction for estimated phase offsets throughout the receiving system (antennas, feeder cables, receivers) [e.g., Röttger and Ierkic, 1985; Hocking et al., 2001]. Meek and Manson [1990] attempted phase calibration by transmitting on one antenna and receiving on the remaining antennas, but found the estimated phase offsets did not agree with those obtained using partial reflection returns, possibly due to ground reflections. Solomon et al. [1998] describe the use of meteor echoes for complete calibration of an “over the horizon” radar. Since variations in atmospheric conditions have been reported to result in relative phase offset fluctuations of up to 8° between day and night conditions [e.g., Djuth and Elder, 1993], phase calibration is ideally performed routinely, such as is possible through various receiver path components for the Buckland Park MF radar [e.g., Reid et al., 1995].

[4] This paper describes a technique for phase calibration of interferometric meteor radar systems using antenna configurations based on the JWH antenna configuration. The technique is derived from that implemented for meteor observations using the MU radar, which is described in section 2. The theory of the technique is presented in section 3. Simulations using expected height and angle of arrival distributions are used to illustrate the technique. In section 4, the simulations are extended to perform a statistical evaluation of the technique. The application of the technique to data collected using the BPMR is presented in section 5.

2. MU Radar Meteor Phase Calibration

[5] The antenna configuration used for early MU radar meteor observations is illustrated in the work of Nakamura et al. [1991, Figure 1]. Antennas 1, 2 and 3 form an equilateral triangle with spacing 0.697λ, with antenna 4 is located approximately 2λ away. AOAs were first determined using antennas 1, 2 and 3, with antenna 4 then used to improve the accuracy of the AOA. This antenna configuration was subsequently replaced with that shown in the work of Nakamura et al. [1997a, Figure 2], which uses longer antenna baselines to improve AOA accuracy.

[6] MU radar meteor observations are characterized by echo rates of about 10 thousand underdense per day, allowing gravity wave and temperature studies [e.g., Nakamura et al., 1997b]. Since ambipolar diffusion coefficient (D) can be assumed to be azimuth independent under mean state conditions, any tilt in equi-D plane (i.e., the plane of (x, y, z) positions with the same D) obtained using data collected over a few days can usually be attributed to phase offsets between receiver channels. Using antennas i, j, and k, the AOA can be estimated using the phase differences ϕij and ϕik measured between antenna pairs i, j and i, k, respectively. Equi-D plane fitting of the resulting AOAs is then performed by minimizing

equation image

where N is the total number of meteor echoes used, (xn, yn, zn) is the position of the nth echo, Dn is ambipolar diffusion coefficient of the nth echo, and a, b, c and d are “tilt coefficients”. The tilt coefficients are estimated using a least squares fit. Varying a, b and c is analogous to steering the uncalibrated AOAs using poststatistic steering (PSS) [e.g., Kudeki and Woodman, 1990], thereby adjusting the tilt of the equi-D plane. Once the optimal tilt coefficients have been determined, they can be converted into the direction cosine of the equi-D plane tilt using

equation image

The direction cosines can then be used to calculate the phase offsets introduced through receive channels j and k. This procedure is first applied to determine phase offsets of receiving channel 2 and 3 with respect to receiving channel 1. The phase offset for receiving channel 4 are then determined by estimating the mean phase difference required to produce the same AOA for antenna groups 1-2-3, 1-2-4, 1-3-4, and 2-3-4.

[7] A typical example of the results obtained using “uncalibrated” and “calibrated” phase differences for early MU radar meteor observations from 16–18 November 1993 is shown in Figure 1. The “uncalibrated” phase differences produce a tilt of only 2°, but this is sufficient to produce pronounced azimuth dependence of D estimates, increased scatter in the height dependence of D, and a broadening of the height distribution.

Figure 1.

(top) Example of results obtained using uncalibrated and (bottom) calibrated phase estimates for MU radar meteor observations from 16-018 November 1993. (a and c) Scatterplot of the diffusion coefficient versus height, illustrating the uncalibrated diffusion coefficients show greater scatter. (b and e) Local mean diffusion coefficient, illustrating the uncalibrated diffusion coefficients show a pronounced azimuth dependence. (c and f) height distribution, illustrating the uncalibrated height distribution shows lower peak values and higher standard deviation.

[8] It should be noted that the azimuth angles of meteor echoes have a local time dependency resulting from Earth's rotation [e.g., Meek and Manson, 1990]. This can cause a weak azimuth dependence of equi-D plane. The D values are also known to contain local time-dependent temporal variations such as diurnal variations with an amplitude of about a few tens of percent, seemingly caused by atmospheric tides [e.g., Tsutsumi et al., 1994, 1996]. Thus these local time dependencies in AOA may produce slight real azimuth dependency in the equi-D plane. Further, the effect of Earth's magnetic field can also produce further azimuth dependence of equi-D plane above 95 km [e.g., Elford, 2001], suggesting phase calibration using the equi-D plane technique should be limited to heights below 95 km.

[9] An alternative to using equi-D plane fitting is to use information obtained from the height distribution of the meteor echoes. For instance, the antenna phase offsets can be adjusted until the azimuth variation of peak heights is minimized, or alternatively, the standard deviations of the height distribution is minimized.

3. Interferometric Meteor Radar Calibration

3.1. Antenna Configuration

[10] Figure 2 illustrates the typical receiving antenna configuration for an interferometric meteor radar system. The following derivation provides generalized equations describing phase calibration for radar systems using antenna baselines with configurations similar to that shown in Figure 2, without necessarily using the antenna separations for the JWH configuration, in which the separations di between the inner (1) and outer (i) antennas are ∣d2∣ = ∣d4∣ = 2λ and ∣d3∣ = ∣d5∣ = 2.5λ, where λ is the radar wavelength. The resulting equations may therefore also be applicable to radars designed primarily for atmospheric and ionospheric observations. For instance, meteor observations are increasingly being made using SuperDARN radars [e.g., Hall et al., 1997; Yukimatu and Tsutsumi, 2002], ionosondes [e.g., MacDougall and Li, 2001], and MF radars [e.g., Meek and Manson, 1990; Tsutsumi et al., 1999; Holdsworth and Reid, 2004], complementing the measurements for which these radars were originally intended. The equations derived in this paper are directly applicable to the Buckland Park medium frequency (BPMF) radar, where the available antenna spacings are multiples 0.6λ [e.g., Briggs et al., 1969; Holdsworth and Reid, 2004], and to other non-JWH antenna systems, such as those of Djuth and Elder [1993] and Valentic et al. [1997]. With this in mind, the only assumptions we will make are

equation image
equation image

and

equation image

We define baselines 23 and 45 such that antenna 1 is considered the origin, d2 and d4 positive, and d3 and d5 negative.

Figure 2.

Typical antenna configuration for an interferometric meteor radar.

3.2. Simulation Technique

[11] In order to demonstrate the implementation and verification of the phase calibration technique we have used range and AOA distributions based on those typically obtained for an all-sky meteor radar, such as the BPMR [e.g., Holdsworth et al., 2004], to generate a set of N height (hn), zenith (θn), and azimuth (ɛn) combinations, where (n = 1,., N). Examples of zenith, height, and AOA distributions obtained for one simulation realization using N = 1000 are shown in Figure 3. A uniform distribution of azimuth angles has been used. This is usually not the case in practice due to the diurnal azimuth dependence of the AOA azimuths and diurnal variation in count rate, as well as azimuth variations in the receiving antenna polar diagrams, such as those obtained using linearly polarized receiving antenna [e.g., Hocking et al., 2001; Holdsworth et al., 2004]. An example of the AOA skymap produced using these simulations is also shown in Figure 3. The range Rn is calculated according to

equation image

where Re is the radius of Earth. This equation allows for correction due to Earth's curvature. The phases differences between the inner and outer antennas for each echo are calculated using

equation image

where k = 2π/λ is the radar wave number, and (ξi, ηi) is the vector difference of the antenna separations. We then add phase offsets αi, and a random component δin to simulate experimental errors in the phase difference estimates, yielding phase differences

equation image
Figure 3.

Example of (a) zenith angles, (b) height, and (c) AOA distributions generated by the simulation procedure.

[12] The simulations described in this paper use the JWH configuration. Unless otherwise indicated, the simulation parameters used throughout this paper are N = 10000, phase offsets of α2 = 120°, α3 = 80°, α4 = −170° and α5 = −20°, with δin generated according to a Gaussian distribution with RMS values of δ = 10°. The value of N is based on the daily count rates typically observed using the BPMR radar [e.g., Holdsworth et al., 2004]. Analysis is performed assuming pulse repetition frequencies (PRFs) of 500 Hz and 2 kHz. The effects of range aliasing are introduced for the 2 kHz PRF by aliasing the ranges into the interval zero to 75 km. Although use of such PRFs result in an inability to unambiguously resolve the height of approximately 10° of the meteor echoes [e.g., Holdsworth et al., 2004], they are typically used to increase the sampling resolution of the meteor echoes in order to apply techniques for estimation of meteoroid velocities and decelerations [e.g., Cervera et al., 1997; Elford, 2001], or to allow extra coherent integrations to improve the SNR of the meteor echoes and enhance their detectability [e.g., Holdsworth et al., 2004].

3.3. Phase Calibration Theory

[13] Consider a meteor echo with AOA component ψ relative to antenna baseline 23. In the absence of any phase offsets between the inner and outer antennas, the phase differences estimated between the outer and inner antennas are given by

equation image

and

equation image

From equations (9) and (10), it follows that

equation image

[14] In the presence of phase offsets αi between the outer and center antennas, the estimated phase differences become

equation image

and

equation image

Since d2 and d3 exceed λ/2 the estimated phase differences will be aliased into the range ±π. As a result, there will exist an AOA component set Ψ2′ satisfying

equation image

and an AOA component set Ψ3′ satisfying

equation image

Let ψ2′ be an arbitrarily selected AOA from the set Ψ2′. The phase difference required to measure the AOA ψ2′ for antenna spacing d3 is

equation image

Let γ3 = ϕ3 − ϕ3′. Using equations (11)–(14) and (16), we find

equation image

Since α2 and α3 will lie in the range ±π, it follows that γ3 will be in the range (or can be aliased into the range) ±(d3/d2 − 1) π, no matter which AOA ψ2′ of the set Ψ2′ is selected. Rearranging equation (17) and substituting into equation (13) yields

equation image

We can define a further phase difference ϕ3″ by substituting γ3 into equation (18) to yield

equation image

Substituting ϕ3 = ϕ3″ into equation (10), we produce an AOA set Ψ3″.

[15] In equations (12) and (19), we have two phase differences expressed in terms of α2. Since the second term in equation (19) is that obtained by substituting ϕ2 = α2 into equation (11), it necessarily follows from equation (4) that there must exist one coincident AOA in the sets Ψ2′ and Ψ3″, which we denote ψ′. This is illustrated in Figure 4, which shows Ψ2′, Ψ3′, and Ψ3″ obtained using an arbitrarily selected set of simulated phase differences. Furthermore, sin ψ′ is the unambiguous AOA obtained by differencing ϕ3″ and ϕ2

equation image
equation image
equation image

From equation (22), it follows that sin ψ′ is unambiguous within the range ±Δϕ/(k(d3d2)), from which it follows that (an unaliased) α2 must lie within the range ±kd2.

Figure 4.

(a) Ψ2′ and Ψ3′ and (b) Ψ2′ and Ψ3″ obtained using an arbitrarily selected set of simulated phase differences. The diamonds and dotted lines indicate the AOAs for an antenna spacing of 2λ, while the squares and dashed lines indicate the AOAs for an antenna spacing of 2.5λ.

[16] An alternative means of understanding equations (12) and (19) is in terms of the poststatistic steering (PSS) technique [e.g., Kudeki and Woodman, 1990]. In this technique, phase offsets are applied to the receiver outputs from spaced antennas before combining to steer the receive polar diagram. The offsets α2 and α2d3/d2 can be interpreted as those required to steer the receive beam polar diagram from ψ to ψ′. This is illustrated in Figure 5, which shows the AOA obtained by varying α2 within the range ±kd2 for the same phase difference set shown in Figure 4. The effects of varying α2 within the range ±kd2 is to steer the AOA over the range ±Δϕ/(k(d3d2)).

Figure 5.

Variation of AOA ψ as a function of α2 using the same set of phase differences as in Figure 4.

3.4. The γ Estimation

[17] Given n sets of phase differences ϕin′, we obtain n estimates of γ33n) and γ55n) along each antenna baseline. Figure 6 illustrates histograms of the γ3 and γ5 estimates for the simulated data set. The histograms do not show a distinct peak because the values of γ3 and γ5 are aliased into the range ±(d3/d2 − 1)π = 0.25π. In order to determine the optimal value of γ3 we produce revised distributions Γ3n = [γ3n − μ, γ3n, γ3n + μ] and Γ5n = [γ5n − ν, γ5n, γ5n + ν], where μ = 2(d3/d2 − 1)π = 0.5π and ν = 2(d5/d4 − 1)π = 0.5 π, as shown in Figures 6c and 6d. From the revised histograms we can clearly determine optimal values of γ3 and γ5 (hereafter equation image3 and equation image5) using any of a number of fitting procedures, such as by applying a Gaussian or parabolic fit about the peak. The estimates of equation image3 and equation image5 determined from these example using Gaussian fits are −41.22° and −53.1°, respectively, which are in good agreement with the (aliased) input values of −40° and −52.5°, respectively.

Figure 6.

Histograms of (a) γ3, (b) γ5, (c) Γ3n, and (d) Γ5. The values indicated in the plot titles for Figures 6b and 6d represent equation image estimates obtained from application of a Gaussian fit, indicated by the solid line.

3.5. The α Estimation

[18] Once the equation image estimates have been made, the phase offsets αi can be estimated in a number of different ways, without any need to consider use of diffusion coefficient estimates as described in section 2.

[19] The equation image3 and equation image5 estimates can be used to obtain ϕ3n″ and ϕ5n″ using equation (19), which can in turn be used to form α2 and α4 arrays varying between ±kd2 and ±kd4, respectively. For each (α2, α4) pair, a set of revised phase differences ϕ2n′, ϕ3n″, ϕ4n′, and ϕ5n″ can be produced, allowing determination of a set of N AOA components along each antenna baseline using techniques similar to Jones et al. [1998]. The AOA components can then be combined to produce zenith θn and azimuth angle estimates ɛn. In the situation where the direction cosines ln = sin ψ23n and mn = sin ψ45n along each antenna baseline satisfy

equation image

no zenith/azimuth estimate is possible. Such echoes are deemed “AOA unresolvable”.

[20] The height for each meteor with a successfully estimated zenith angle at each (α2, α4) pair is determined by substituting the range (Rn) and zenith angle θn into equation (6). If the radar is operated with a PRF producing range-aliasing it is necessary to apply equation (6) at each unaliased range, therefore producing a number of height candidates [e.g., Holdsworth et al., 2004]. If a single height exists within the appropriate height limits h1 and h2 this is the assumed echo height. If no heights exist within h1 to h2 the candidate is deemed “height unresolvable”. If two or more heights exist within h1 to h2, the candidate is deemed “height ambiguous”. This is sometimes the case for zenith angles exceeding 65° and ranges exceeding 200 km when high PRFs (e.g., 2 kHz) are used. In this case it is sometimes possible to determine the most likely height by comparing the diffusion coefficient, D, with the theoretical estimate, or mean of the existing estimates, at the each possible height. However, for the purposes of the technique described in this paper, such candidates are precluded from further analysis. The height limits used throughout this paper are h1 = 70 km and h2 = 110 km, which are the limits typical for a VHF radar [e.g., Hocking et al., 2001; Holdsworth et al., 2004].

[21] We can make use of different combinations of the phase difference, AOA and height information to determine optimal values of α2 and α4 (hereafter equation image2 and equation image4) using four different methods:

[22] 1. Estimation of the tilt in the height variation as a function of direction cosines along each interferometer baseline. This method is best suited for nonrange aliased data with small phase offsets.

[23] 2. Finding the (equation image2, equation image4) pair which minimizes the standard deviation of the height distribution, as described in section 2.

[24] 3. Using the direction cosines to find the (equation image2, equation image4) pair that maximize the number of meteor echoes satisfying

equation image

This technique is analogous to that described by Valentic et al. [1997], who illustrated that phase offsets produce phase difference (and hence direction cosine) wrapping across to the opposite horizon.

[25] 4. Finding the (equation image2, equation image4) pair which minimizes the percentage of “bad” estimates Nbad, defined as the sum of number of AOA unresolvable, height unresolvable and height ambiguous estimates. These methods have been evaluated, with method 4 found to produce the most stable phase calibration estimates. This is attributed to the variability inherent in estimating the standard deviation of the height distribution as used by method 2, and due to the fact that method 3 does not make use of any height information that could further aid in the determination of the optimal (equation image2, equation image4) pair, as is the case for method 4. As such, minimization of the percentage of “bad” estimates Nbad is the preferred technique, and will be assumed throughout the remainder of the paper.

[26] There are two approaches that can be taken in forming the α2 and α4 arrays. One approach is to define a large array of elements with a small interval to produce accurate estimates of equation image2 and equation image4. The other approach, as used here, is to use a small number of array elements to produce rough estimates of equation image2 and equation image4, and iteratively decrease the range of the α2 and α4 arrays to smaller extents about the previous equation image2 and equation image4 estimates. This approach is illustrated in Figure 7, which shows the variation of Nbad as a function of α2 and α4 for the 2 kHz PRF. Note that the minimum Nbad exceeds 22% because unambiguous heights cannot be obtained from many of the AOAs due to use of range aliasing, as described in section 2.2. From Figure 7a we can determine equation image2 and equation image4 using any of a number of techniques, such as applying a two-dimensional Gaussian or parabolic fit about the peak, or by using the actual values which minimize Nbad. The unaliased estimates of equation image2 and equation image4 determined from this example using a two-dimensional Gaussian fit are 117.9° and −171.7°, which are in good agreement with the model input values of 120° and −170°. The final unaliased estimates of equation image2 and equation image4 from Figure 7d are 118.3° and −171.6°, which are in very good agreement with the model input values of 120° and −170°.

Figure 7.

Image plot of percentage of bad estimates for the 2 kHz PRF using various different ranges of α2 and α4: (a) ±720°, (b) ±180° about minimum position estimated from ±720°, (c) ±90° about minimum position estimated from ±180°, and (d) ±40° about minimum position estimated from ±90°. The square in each plot indicates the position of the minimum Nbad, while the diamond indicates the value estimated using a two-dimensional Gaussian fit about the maximum. The estimate of equation image2 and equation image4 estimated using a two-dimensional parabolic fit is shown at the top of the plot.

[27] Given equation image2, equation image4, equation image3 and equation image5, we can estimate optimal values of α3 and α5 (hereafter equation image3 and equation image5) using equation (17), therefore providing the complete set of the phase offsets. The equation image3 and equation image5 estimates from the simulated data are 80.9° and −60.3°, which are in excellent agreement with the model input values of 80° and −60°.

4. Phase Calibration Evaluation Using Simulated Data

[28] To illustrate the accuracy of the phase calibration technique, the simulation technique has been applied for 250 realizations of 10000 sets of phase differences, with each realization using an independent set of four phase offsets generated according to a uniform random distribution between ±π. The influence of the number of meteors used in the estimation process has been investigated using subsets of the 10000 sets of phase differences. For example, for 100 meteors, the 10000 sets of phase differences is divided into 100 subsets, yielding 250 × 100 × 4 (=100000) α estimates, while for 1000 meteors, 10 subsets produced 250 × 10 × 4 (=10000) α estimates. Typical examples of the resulting histograms of the difference between the model input and estimated values for phase errors of 10° are illustrated in Figure 8, for both non range aliased and range aliased modes. The non range aliased mode produces narrower distributions since no height ambiguous echoes result, thereby increasing the number of echoes used in the calculations. The RMS difference between the model input and estimated using various numbers of meteors for phase errors of 5°, 10° and 20° are shown in Figure 9. These results indicate the RMS difference increases with increasing δin and decreasing numbers of meteors.

Figure 8.

Histogram of differences between estimated and actual phase offsets for simulated data for (a) 500 meteors with 10 RMS phase error, range aliasing, (b) 500 meteors with 10° RMS phase error, no range aliasing, (c) 5000 meteors with 10 RMS phase error, range aliasing, and (d) 5000 meteors with 10° RMS phase error, no range aliasing. The dotted line indicates the results of a Gaussian fit. The first and second moments of the Gaussian fit are indicated at the top of the plot.

Figure 9.

RMS difference between actual and estimated phase offsets: 5° RMS phase error, range aliasing (diamonds, solid line), 5° RMS phase error, no range aliasing (triangles, dotted line), 10 RMS phase error, range aliasing (squares, dashed line), 10° RMS phase error, no range aliasing (crosses, dot dashed line), 20° RMS phase error, range aliasing (plusses, dot-dot dash line), and 20° RMS phase error, no range aliasing (asterics, long dashed line).

[29] In order to deduce appropriate lower limits for numbers of meteors required for successful phase calibration we consider typical values of the RMS phase error, and appropriate values for the upper limit of the maximum acceptable RMS difference. The RMS phase error obtained using the BPMR is typically of the order of 5°, while RMS differences of 10° can reduce the number of ambiguous AOAs in range aliased mode by 10%. Assuming these values, we can deduce from Figure 9 that as little as 100 meteors can provide successful phase calibration estimates for both nonrange aliased and range aliased modes. However, in quoting this limit, we need to recognise that the simulations have been generated assuming typical AOA and height distributions measured using a all-sky meteor radar over the course of one day. However, since Earth's rotation produces diurnal variations in AOA [e.g., Meek and Manson, 1990] and height distributions, it follows that applying phase calibration to a data set collected over a short time interval (e.g., an hour) may not necessarily yield accurate phase offsets due to the limited range of meteor AOAs and heights available. From this point of view, we suggest the use of daily data intervals, where the full distribution of possible AOAs and heights can be expected.

5. Phase Calibration Evaluation Using the Buckland Park Meteor Radar

[30] The phase calibration technique has been applied to data collected using the BPMR [e.g., Holdsworth et al., 2004]. This system operates at 31 MHz, using the JWH antenna configuration. The antenna orientation is similar to that shown in Figure 1, with baselines at azimuths 28° and 118°. The main difference in comparison to Figure 1 is that the dipoles for the center antenna are individually accessible, and the antenna indexing convention differs. Initial phase calibration estimates for this radar were produced by feeding the attenuated transmit pulse into the system at various hardware stages. However, no satisfactory means of measuring the phase offsets introduced by the antennas was found, since the estimated phase offsets were found to vary depending with the position of the feed point upon the antenna. The phase offsets obtained on feeding the attenuated transmit pulse into the receiver front ends and feeder cables are shown in Table 1. The difference in these phase offset estimates represents the phase offsets introduced by the feeder cables. Although care was taken to cut the cables to the same electrical length, offsets of up to 11°, corresponding to an electrical length of 30 cm, are introduced through the cables.

Table 1. Comparison of Phase Calibration Estimates Obtained Using the Attenuated Transmit Signal and Meteor Methods
Antenna PairReceiver Front Ends, degFeeder Cables, degMeteor Echoes
1321.720.125.7° ± 2.8
1418.88.013.6° ± 2.0
1518.725.431.5° ± 2.2°
1632.634.82.6° ± 1.6°

[31] The meteor phase calibration technique was applied to BPMR meteor observations collected between November 1st 2002 and March 23rd 2003. This data set was selected as it represents the longest observation period for which stable experiment and antenna configuration have been used [e.g., Holdsworth et al., 2004]. A PRF of 1980 Hz was employed, resulting in range aliasing. The estimation of α and γ parameters for data recorded on the 23rd of March 2003 (arbitrarily chosen), where 9593 height resolvable meteor echoes were collected, is illustrated in Figure 10. These results are similar to those obtained using simulated data in Figures 6 and 7, although there is some anisometry in the α plots. The anisometry appears to be related to the gamma-matched feeds used for these observations, since it is not evident in subsequent observations when the gamma-matched feed was replaced with a balanced feed. The mean and standard deviations of the daily phase offset estimates over the observation period are shown in Table 1. The phase offset for receiver channel pair 1, 3 increased by around 8° over the observation period, and this increase is the cause of the larger standard deviation reported for this channel. After the removal of the results of a linear fit to the time series of phase offsets for this receiver channel pair, the standard deviation becomes 1.9°. The remaining receiver channel pairs did not exhibit any obvious variations other than statistical fluctuations. Taking into account the phase offset drift for receiver channel pair 1, 3, the standard deviations of the daily phase offset estimates are ≈2°, which is in good agreement with the range aliased simulation results shown in Figure 9. The cause of the increase for receiver pair 1, 3 is not known. Since such drifts were not observed for other pairs using receiver channel 1, it is assumed the drift results solely due to receiver channel 3. No mechanical problems were found in the receive path for receive channel 3, and the antenna impedance remained stable throughout the observation period. The increase is uncorrelated with the daily mean outside ambient temperature measured on site by an automatic weather station, which varied between 20° and 35°, peaking in the middle of the observation period.

Figure 10.

Histogram of reformed (a) Γ3 and (b) Γ6 estimates for the Buckland Park meteor radar (BPMR). The values indicated in the plot titles represent the equation image estimates obtained from application of a Gaussian fit, indicated by the solid line. (c) Image plot of percentage of bad estimates for ±40° ranges of α4 and α5 for the BPMR. The square indicates the position of the minimum Nbad, while the diamond indicates the value estimated using a two-dimensional Gaussian fit about the maximum. The values of equation image4 and equation image5 estimated from the two-dimensional Gaussian fit are shown at the top of the plot.

[32] Since the only difference in the receive path between the meteor and feeder cable phase offsets are the antennas, we assume any difference in the phase offsets represents the phase offsets introduced by the antennas. Table 1 shows the difference for between the meteor and feeder cable phase offsets for receiver pair 1 and 6 are 32°. This seems an excessively large value, ands tend to suggest an antenna problem. However, no mechanical problems were found, and the meteor echo powers measured in receiver 6 were similar to those recorded in other channels. Numerical electromagnetic code (NEC) simulations have shown the use of gamma-matching with crossed dipole antennas can result in significant coupling between the crossed antenna elements, and it is thought that this may contribute to the antenna phase offsets. Although antenna offsets may usually not be so significant, these results illustrate the importance of being able to include antenna introduced phase offsets in any correction for phase offsets introduced throughout the receive path, rather than relying on phase offset estimates made prior to the antennas [e.g., Röttger and Ierkic, 1985; Hocking et al., 2001; Holdsworth and Reid, 2002]. The meteor phase calibration procedure necessarily includes these offsets. The results also illustrate the importance of applying regular phase calibration procedures, for which the meteor phase calibration procedure is especially suited.

6. Summary

[33] A technique for the phase calibration of interferometric meteor radar systems using meteor echoes has been presented. Simulations of typical range and angle of arrival distributions suggest the technique is capable of estimating phase offsets to within 2°. The simulation results are confirmed by results obtained using the Buckland Park meteor radar, where the standard deviation of the daily phase offsets over a four month period were found to be less than 3°.

Acknowledgments

[34] Thanks to Chris Adami, Bruce Johnson, Callum Heinrich, and Daniel Vettori for their contributions toward the work presented in this paper. The Buckland Park meteor radar was supported by Australian Research Council grant 20006300.

Ancillary