Method for reducing inter-frequency bias effects in a receiver

[0002] This Application is related to Provisional Application Serial No. 60/153,747 filed on Sep. 13, 1999.

[0003] 1. Field of the Invention

[0004] The present invention is related to satellite-based ground-positioning systems and, more particularly, to a method for reducing frequency-related biases in a such a system.

[0005] 2. Background Information

[0006] The Global Navigation Satellite System (GLONASS) is designed to utilize up to twenty four active satellites in earth orbit. Each Global Navigation System (GNS) satellite transmits signals centered on two discrete L-band carrier frequencies, the frequency bands denoted by L1 and L2. The L1 band, for example, includes twenty four transmitting frequencies separated by 0.5625 MHz. A positional system using GLONASS signals employs frequency-division multiplexing to differentiate between the signals of the various satellites. As these signals pass through the RF section of a GLONASS receiver, frequency-related biases are produced, both in the pseudorange and in the carrier phase observations. These biases can arise from, for example, antennas, cables, filters, and various other components in the front end of the receiver.

[0007] One method of reducing the effects of the biases is to directly calibrate the receiver RF section. Unfortunately, this method is very labor intensive and requires specialized equipment. A more preferable method is to calibrate the effects of the inter-frequency biases on the measurements and correct the pseudorange or carrier phase measurements accordingly. For example, the calibration procedure may call for calibrating receivers in pairs, or calibrating a single receiver using a multi-channel GLONASS simulator as a reference. However, such calibration procedures do not readily lend themselves to operation in the field. Further, such calibration methods suffer from the shortcoming that the accuracy of the derived frequency biases are based on the functional attributes of the reference receiver or the simulator. Moreover, the multi-channel GLONASS simulator is an expensive device, and may have uncorrectable biases of its own.

[0008] While the relevant art describes methods for calibrating global positioning devices, there remains a need for a calibration method that offer advantages and capabilities not presently found, and it is a primary object of this invention to provide such a method.

[0009] It is also an object of the present invention to provide a method of calibration which does not require use of supplemental, specialized equipment.

[0010] It is another object of the invention to provide such a method which can be performed in the field.

[0011] Other objects of the invention will be obvious, in part, and, in part, will become apparent when reading the detailed description to follow.

[0012] The invention results from the realization that a significant source of the inter-frequency pseudorange bias in a GPS/GLONASS receiver results from signal group delay in the IF filter. The disclosed calibration procedure includes the steps of i) removing the dynamics of the GPS and the GLONASS satellites by using the ephemeris data for the satellites; ii) estimating the change in receiver clock offset by means of GPS satellite measurements, and iii) acquiring a set of two or more measurements for each satellite frequency of interest to estimate the corresponding inter-frequency bias. The disclosed method utilizes a receiver microprocessor to obtain pseudorange measurements while the GLONASS local oscillator in the receiver is placed at different frequencies. The disclosed method thus allows individual calibration of receivers and advance calibration of frequencies, where the calibration is valid for single point positioning as well as for differential positioning.

[0013] The invention description below refers to the accompanying drawings, of which:

[0014] FIG. 1 is a diagrammatical view of a GPS/GLONASS receiver in accordance with the present invention; and

[0015] FIG. 2 is a flow chart illustrating a three-measurement method for obtaining an inter-frequency bias correction factor in accordance with the present invention.

[0016] FIG. 3 is a flow chart illustrating an alternative two-measurement method for obtaining a correction factor in accordance with the present invention.

[0017] FIG. 1 is a diagrammatical view of a satellite-based ground-positioning receiver system 10 as may be used in the present invention. The receiver system 10 includes an antenna 11 for receiving pseudorandom-noise-encoded signals from, for example, Global Positioning System (GPS) satellites and frequency-division multiple access (FDMA) signals from the GLONASS satellites (not shown) and passing the signals along to a radio frequency (RF) section 13. A local oscillator is used to down-convert the respective RF signal to an intermediate frequency (IF) signal. A receiver clock 15 provides a clock reference.

[0018] In a preferred embodiment, the signals from the GPS satellites are combined at a GPS mixer 21 with the signal from a GPS local oscillator 23. The local oscillator 23 is under the control of a microprocessor 25 which establishes the IF frequency. The resultant GPS IF signal 27 passes to an IF section 31 for filtering and for further processing. The IF section 31 typically includes a filter 33, such as a surface acoustic wave (SAW) filter, and a digital signal processor 35.

[0019] The signals from the GLONASS satellites pass through the RF section 13 and are combined at a GNS mixer 41 with the signal from a GNS local oscillator 43. The local oscillator 43 is controlled by a microprocessor 45. The resultant GNS IF signal 47 passes to the IF section 31 for filtering and processing. As can be appreciated by one skilled in the relevant art, there are frequency-dependent transmission delays incurred by the GLONASS satellite signals in passing through the RF section 13. Moreover, IF signals of varying frequencies enter the IF section 31 and incur further delays, also frequency-dependent, in passing through the SAW filter 33.

[0020] The principal source of the inter-frequency biases in the receiver system 10 is the SAW filter 33. The disclosed method provides a means to calibrate the biases resulting from the frequency-related effects of the SAW filter 33. A preferred calibration procedure suitable for use in the field uses a single GLONASS receiver with ‘live’ GLONASS and GPS signals. An alternative procedure, suitable for factory calibration or screening, uses a GLONASS receiver with a single-channel GLONASS simulator. In brief, the disclosed procedure includes the following steps: i) the dynamics of the GPS and the GLONASS satellites are removed by using the ephemeris data for the satellites; ii) the change in receiver clock offset is estimated by means of GPS satellite measurements, and iii) a set of two or more measurements is made at different satellite frequencies controlled by changing the frequency of the GNS reference oscillator 43 to estimate the corresponding inter-frequency bias.

[0021] The GPS pseudorange measurement P_GPSat each time epoch t_Ncan be expressed as follows:

[0022] P_GPS(t_N)=R_GPS(t_N)+C_R(t_N)−C_GPS(t_N)+ε_SA(t_N)+ε_MP(t_N)+ε_WN(t_N)+ε_AG(t_N)  (1

[0023] where: R_GPS(t_N) is the theoretical range between a GPS satellite and the receiver system 10;

[0024] C_R(tN) is the offset of the receiver clock 15;

[0025] C_GPS(t_N) is the offset of the GPS satellite clock;

[0026] ε_SA(t_N) is the error induced by the selective availability feature;

[0027] ε_P(t_N) is the error due to GPS multipath at the receiver system 10;

[0028] ε_WN(t_N) is the error due to white noise in the receiver system 10; and

[0029] ε_AG(t_N) is the aggregate error which includes atmospheric delay, residual GPS satellite position, and GPS clock errors. The GPS theoretical range R_GPS(t_N) is derived using known position of the user and ephemeris data. In a typical application, the user's position is fixed and known within 100 meters and the ephemeris data is precise enough to provide an accurate bias correction. The GPS satellite clock offset C_GPS(t_N) can be obtained from downlink data.

[0030] In accordance with the inventive method, a receiver clock correction term CLKcorr_GPSis determined as a function of the pseudorange P_GPS, the theoretical range R_GPS, and the GPS satellite clock offset C_GPS. The parameter values are obtained at successive instances of time (t₀, t₁, . . . t_n). The values are averaged and used to estimate inter-frequency biases as explained in greater detail below. In a preferred embodiment, three measured values are obtained at consecutive times t₀, t₁, and t₂. For a set of three values f(t₀), f(t₁), and f(t₂), the average value is given by [f(t₀)−2f(t₁)+f(t₂)]. These averaged values provide a receiver clock correction term CLKcorr_GPSin accordance with the expression: $\begin{array}{cc}\begin{array}{c}{\mathrm{CLKcorr}}_{\mathrm{GPS}}\left(t_2\right)=\left[P_{\mathrm{GPS}}\left(t_0\right)-2P_{\mathrm{GPS}}\left(t_1\right)+P_{\mathrm{GPS}}\left(t_2\right)\right]-\\ \left[R_{\mathrm{GPS}}\left(t_0\right)-2R_{\mathrm{GPS}}\left(t_1\right)+R_{\mathrm{GPS}}\left(t_2\right)\right]+\\ \left[C_{\mathrm{GPS}}\left(t_0\right)-2C_{\mathrm{GPS}}\left(t_1\right)+C_{\mathrm{GPS}}\left(t_2\right)\right]\end{array}& (2\end{array}$

[0031] It has been determined that three measurements are adequate to offset the effects of selective availability (where present) and multipath. Preferably, the measurements are performed within ten to twelve seconds to assure good pull-in without compromising measurement accuracy. Because the value of the aggregate error ε_AG(t_N) changes little during the measurement period (t₂−t₀), the term [ε_AG(t₀)−2ε_AG(t₁)+ε_AG(t₂)] becomes negligible over this period and equation (2) reduces to the expression:

[0032] CLKcorr_GPS(t₂)=ε_CORRGPS+[C_R(t₀)−2C_R(t₁)+C_R(t₂)]  (3

[0033] where

[0034] ε_CORRGPS=ε_SA+ε_MP+ε_WN  (4

[0035] and

[0036] ε_SA=ε_SA(t₀)−2ε_SA(t₁)+ε_SA(t₂)

[0037] ε_MP=ε_MP(t₀)−2ε_MP(t₁)+ε_MP(t₂)  (5

[0038] ε_WN=ε_WN(t₀)−2ε_WN(t₁)+ε_WN(t₂)

[0039] The correction term CLKcorr_GPSfor the GPS signal is thus expressed as a function of selective availability (when present), multipath, white noise, and the offset of the receiver clock 15. It should be noted that the standard deviation of the error, σ_CORRGPS, can be reduced to $\frac{{\sigma }_{\mathrm{CORRGPS}}}{\sqrt{n}}$

[0040] by averaging the estimates from a plurality of n GPS satellites.

[0041] With respect to the GLONASS satellite signals, the pseudorange measurement P_GNSfor a satellite operating at a frequency f_Mcan be represented by the expression:

[0042] P_GNS(t_N,f_M)=R_GNS(t_N)+b_GPSGNS+C_R(t_N)−C_GNS(t_N)+b_U(f_M)+b_L(f_M)+ε′_MP(t_N)+ε′_WN(t_N)+ε′_AG(t_N)  (6

[0043] where R_GNS(t_N) is the theoretical range between the GLONASS satellite and the receiver system 10;

[0044] b_GPSGNSis the essentially constant difference between GPS and GLONASS clocks and includes the RF delay difference between GPS and GLONASS satellite signals in the receiver system 10;

[0045] C_GNS(t_N) is the offset of the GLONASS satellite clock;

[0046] b_U(f_M) is the pseudorange bias for frequency M caused by receiver components located in the signal path upstream of the GNS mixer 41;

[0047] b_L(f_M) is the pseudorange bias for frequency M caused by receiver components located in the signal path downstream of the GNS mixer 41;

[0048] ε′_MP(t_N) is the error due to GLONASS multipath at the receiver system 10;

[0049] ε′_WN(t_N) is the error due to white noise in the receiver system 10; and

[0050] ε′_AG(t_N) is the aggregate error which includes atmospheric delay, residual GLONASS satellite position, and related clock errors.

[0051] As stated above, because the downstream bias parameter b_L(f_M) is considered to be the principal contributor to the inter-frequency biases, the upstream parameter b_U(f_M) is not determined in the preferred embodiment and, accordingly, is not included in subsequent derivation.

[0052] In the preferred embodiment, the difference in bias at a satellite frequency f_Kand a reference frequency f_REFis computed by obtaining a series of three measurements from a selected satellite transmitting at frequency f_M. Preferably, the reference frequency f_REFis one of the twenty-four defined GLONASS satellite operating frequencies, but it should be understood that a reference frequency utilized in the present invention is not limited to GLONASS frequencies. The GNS local oscillator 43 is used to place the satellite signal at the IF frequencies normally used by f_REFand f_K, as needed. Two measurements, at times t₀and t₂, are obtained at the reference frequency f_REF, and the third measurement, at time t₁, is obtained at IF frequencies corresponding to the satellite frequency f_Kas explained in greater detail below.

[0053] The following equation is used for estimating the difference in pseudorange bias Δ{circumflex over (b)}_Lfor the satellite frequency f_Kand the reference frequency f_REF: $\begin{array}{cc}\begin{array}{c}\Delta {\hat{b}}_L\left(f_{\mathrm{REF}},f_K\right)=0.5*\{[P_{\mathrm{GNS}}\left(t_0,f_{\mathrm{REF}}\right)-2P_{\mathrm{GNS}}\left(t_1,f_k\right)+\\ P_{\mathrm{GNS}}\left(t_2,f_{\mathrm{REF}}\right)]-[R_{\mathrm{GNS}}\left(t_0\right)-2R_{\mathrm{GNS}}\left(t_1\right)+\\ R_{\mathrm{GNS}}\left(t_2\right)]+[C_{\mathrm{GNS}}\left(t_0\right)-2C_{\mathrm{GNS}}\left(t_1\right)+\\ C_{\mathrm{GNS}}\left(t_2\right)]-{\mathrm{CLKcorr}}_{\mathrm{GPS}}\}\end{array}& (7\end{array}$

[0054] where R_GNS(t) and C_GNS(t) are computed from the GLONASS ephemeris data and the fixed position of the receiver system 10. This can be explained in greater detail with reference to FIG. 2 in which the three-measurement procedure for computing a value for the pseudorange bias difference Δ{circumflex over (b)}_L(f_REF,f₁) for the GLONASS satellite frequency f₁includes the following operations:

[0055] 1. Obtain GPS satellite pseudorange measurements at times t₀, t₁, and t₂to give P_GPS(t₀), P_GPS(t₁), and P_GPS(t₂), in boxes 101, 103, and 105.

[0056] 2. Compute GPS theoretical range measurements at times t₀, t₁, and t₂to give R_GPS(t₀), R_GPS(t₁), and R_GPS(t₂), in boxes 101, 103, and 105.

[0057] 3. Determine GPS satellite clock offset at times t₀, t₁, and t₂to give C_GPS(t₀), C_GPS(t₁), and C_GPS(t₂), in boxes 101, 103, and 105.

[0058] 4. Use the values from operations 1 through 3 in equation (2) to obtain a value for the receiver clock correction term CLKcorr_GPS(t₂), in box 107.

[0059] 5. Obtain GLONASS satellite pseudorange measurements at times t₀, t₁, and t₂to give P_GNS(t⁰,f_REF), P_GNS(t₁,f₁), and P_GNS(t₂,f_REF), in boxes 111, 113, and 115. Preferably, one GLONASS satellite is used and the frequency of the GNS IF signal 47 is changed between f_REFand f₁by means of the GNS local oscillator 43.

[0060] 6. Compute GLONASS theoretical range measurements at times t₀, t₁, and t₂to give R_GNS(t₀), R_GNS(t₁), and R_GNS(t₂), in boxes 111, 113, and 115.

[0061] 7. Determine GLONASS satellite clock offset at times t₀, t₁, and t₂to give C_GNS(t₀), C_GNS(t₁), and C_GNS(t₂), in boxes 111, 113, and 115.

[0062] 8. Use the values from operations 4 through 7 in equation (7) to obtain a value for the bias difference Δ{circumflex over (b)}_L(f_REF,f₁), in box 109.

[0063] The value for Δ{circumflex over (b)}_L(f_REF,f₂) can be found by performing the following additional operations:

[0064] 9. Retain the most recent values for P_GPS(t₂), R_GPS(t₂), C_GPS(t₂), P_GNS(t₂,f_REF), R_GNS(t₂), and C_GNS(t₂) from operations 1 through 8.

[0065] 10. Obtain GPS satellite pseudorange measurements at times t₃and t₄to give P_GPS(t₃) and P_GPS(t₄), in boxes 121 and 123.

[0066] 11. Compute GPS theoretical range measurements at times t₃and t₄to give R_GPS(t₃) and R_GPS(t₄), in boxes 121 and 123.

[0067] 12. Determine GPS satellite clock offset at times t₃and t₄to give C_GPS(t₃) and C_GPS(t₄), in boxes 121 and 123.

[0068] 13. Use the retained values from operation 9 and the values obtained in operations 10 through 12 to obtain a value for the receiver clock correction term CLKcorr_GPS(t₄), in box 127.

[0069] 14. Obtain GLONASS satellite pseudorange measurements at times t₃and t₄to give P_GNS(t₃,f₂) and P_GNS(t₄,f_REF), in boxes 131 and 133.

[0070] 15. Compute GLONASS theoretical range measurements at times t₃and t₄to give R_GNS(t₃) and R_GNS(t₄), in boxes 131 and 133.

[0071] 16. Determine GLONASS satellite clock offset at times t₃and t₄to give C_GNS(t₃) and C_GNS(t₄), in boxes 131 and 133.

[0072] 17. Use the retained values from operation 9 and the values obtained in operations 13 through 16 to obtain a value for the bias difference Δ{circumflex over (b)}_L(f_REF,f₂) in box 129.

[0073] To compute a value for bias difference Δ{circumflex over (b)}_L(f_REF,f₃), the calibration process continues to box 125, for derivation of P_GPS(t₅), R_GPS(t₅), and C_GPS(t₅) and to box 135 for derivation of P_GNS(t₅,f₃), R_GNS(t₅), and C_GNS(t₅), and follows a procedure similar to operations 9 through 17 above, as indicated by arrows 137 and 139.

[0074] This procedure is repeated for any of the GLONASS satellite frequencies of interest. In way of example, the calibration for the four satellite frequencies f_a, f_b, f_c, and f_dis performed by making an estimate of Δb_L(f_REF,f_a), Δb_L(f_REF,f_b), Δb_L(f_REF,f_c), and Δb_L(f_REF,f_d). This is done by selecting the signals of a particular GLONASS satellite and adjusting the GNS local oscillator 43 to obtain a series of measurements on the selected satellite signals at GLONASS frequencies f_REF, f_a, f_REF, f_b, f_REF, f_c, f_REF, f_d, and f_REF. Then, for derivation of the respective inter-frequency bias correction terms, the results are preferably combined into groups of three measurements each: (f_REF,f_a,f_REF), (f_REF,f_b,f_REF), (f_REF,f_c,f_REF), and (f_REF,f_d,f_REF).

[0075] A time interval of about ten to twelve seconds between each set of measurement groups assures good pull-in with out excessive error due to factors such as selective availability. When all the differences have been estimated once, the process starts again from f_REF, f_a, and f_REFso that a set of bias difference estimates for each frequency can be averaged together to form the final bias estimate. The resultant values are stored in a nonvolatile memory as correction values.

[0076] The disclosed method provides an accurate estimate of the inter-frequency biases. This can be shown by noting that, if the expressions for P_GNS(t_N) from equation (6) and CLKcorr_GPSfrom equation (3) are substituted in equation (7), the pseudorange bias estimate can be expressed as:

[0077] Δ{circumflex over (b)}_L(f_REF,f_K)=0.5*{ε_GNS−ε_CORRGPS+2[b_L(f_REF)−b_L(f_K)]}  (8

[0078] where,

[0079] ε_GNS≡[ε′_MP(t₀)−2ε′_MP(t₁)+ε′_MP(t₂)]+[ε′_WN(t₀)−2ε′_WN(t₁)+ε′_WN(t₂)]  (9

[0080] The pseudorange bias estimate error is thus on the order of 0.5*(ε_GNS−ε_CORRGPS).

[0081] For an environment in which multipaths effects are at a reduced level, or where the selective availability feature is not a factor, the pseudorange bias estimate can be obtained by using only two measurements for each GLONASS satellite frequency of interest. Accordingly, for a set of two values f(t₀) and f(t₁), the average value is given by [f(t₀)−f(t₁)]. In the alternative, two-measurement method, the pseudorange bias Δ{circumflex over (b)}_Lis then given by: $\begin{array}{cc}\begin{array}{c}\Delta {\hat{b}}_L\left(f_{\mathrm{REF}},f_K\right)=\left[P_{\mathrm{GNS}}\left(t_0,f_{\mathrm{REF}}\right)-P_{\mathrm{GNS}}\left(t_1,f_K\right)\right]-\\ \left[R_{\mathrm{GNS}}\left(t_0\right)-R_{\mathrm{GNS}}\left(t_1\right)\right]+\\ \left[C_{\mathrm{GNS}}\left(t_0\right)-C_{\mathrm{GNS}}\left(t_1\right)\right]-{\mathrm{CLKcorr}}_{\mathrm{GPS}}\end{array}& (10\end{array}$

[0082] where

[0083] CLKcorr_GPS(t₁)=[P_GPS(t₀)−P_GPS(t₁)]−[R_GPS(t₀)−R_GPS(t₁)]+[C_GPS(t₀)−C_GPS(t₁)]  (11

[0084] In the alternative two-measurement method, the procedure for computing a value for the pseudorange bias differences Δ{circumflex over (b)}_L(f_REF,f₁), Δ{circumflex over (b)}_L(f_REF,f₂) . . . Δ{circumflex over (b)}_L(f_REF,f_N) for the GLONASS satellite frequencies f₁, f₂. . . f_Nincludes the following operations, as shown in FIG. 3:

[0085] 1. Obtain GPS satellite pseudorange measurements at times t₀and t₁to give P_GPS(t₀) and P_GPS(t₁), in boxes 141 and 143.

[0086] 2. Compute GPS theoretical range measurements at times t₀and t₁to give R_GPS(t₀) and R_GPS(t₁), in boxes 141 and 143.

[0087] 3. Determine GPS satellite clock offset at times t₀and t₁to give C_GPS(t₀) and C_GPS(t₁), in boxes 141 and 143.

[0088] 4. Use the values from operations 1 through 3 in equation (11) to obtain a value for the receiver clock correction term CLKcorr_GPS(t₁), in box 151.

[0089] 5. Obtain GLONASS satellite pseudorange measurements at times t₀and t₁to give P_GNS(t₀,f_REF) and P_GNS(t₁,f₁), in boxes 161 and 163, using one GLONASS satellite where the frequency of the GNS IF signal 47 is changed from f_REFto f₁by means of the GNS local oscillator 43.

[0090] 6. Compute GLONASS theoretical range measurements at times t₀and t₁to give R_GNS(t₀) and R_GNS(t₁), in boxes 161 and 163.

[0091] 7. Determine GLONASS satellite clock offset at times t₀and t₁to give C_GNS(t₀) and C_GNS(t₁), in boxes 161 and 163.

[0092] 8. Use the values from operations 4 through 7 in equation (10) to obtain a value for the bias difference Δ{circumflex over (b)}_L(f_REF,f₁), in box 153.

[0093] 9. Obtain GPS satellite pseudorange measurements at times t₂and t₃to give P_GPS(t₂) and P_GPS(t₃), in boxes 145 and 147.

[0094] 10. Compute GPS theoretical range measurements at times t₂and t₃to give R_GPS(t₂) and R_GPS(t₃), in boxes 145 and 147.

[0095] 11. Determine GPS satellite clock offset at times t₂and t₃to give C_GPS(t₂) and C_GPS(t₃), in boxes 145 and 147.

[0096] 12. Use the values obtained in operations 9 through 11 to obtain a value for the receiver clock correction term CLKcorr_GPS(t₃), in box 155.

[0097] 13. Obtain GLONASS satellite pseudorange measurements at times t₂and t₃to give P_GNS(t₂,f_REF) and P_GNS(t₃,f₂), in boxes 165 and 167.

[0098] 14. Compute GLONASS theoretical range measurements at times t₂and t₃to give R_GNS(t₂) and R_GNS(t₃), in boxes 165 and 167.

[0099] 15. Determine GLONASS satellite clock offset at times t₂and t₃to give C_GNS(t₂) and C_GNS(t₃), in boxes 165 and 167.

[0100] 16. Use the values obtained in operations 12 through 15 to obtain a value for the bias difference Δ{circumflex over (b)}_L(f_REF,f₂), in box 157.

[0101] 17. Repeat operations 1 through 4, as indicated by arrow 149, to compute a value for CLKcorr_GPS(t₅) by deriving P_GPS(t₄), P_GPS(t₅), R_GPS(t₅), R_GPS(t₅), C_GPS(t₄), and C_GPS(t₅).

[0102] 18. Repeat operations 5 through 8, as indicated by arrow 169, to compute a value for bias difference Δ{circumflex over (b)}_L(f_REF,f₃) by deriving values for P_GNS(t₄,f_REF), P_GNS(t₅,f₃), R_GNS(t₄), R_GNS(t₅), C_GNS(t₄), and C_GNS(t₅).

[0103] Invoking the above two-measurement procedure for the four satellite frequencies f_a, f_b, f_c, and f_d, an estimate is made of the expressions Δ{circumflex over (b)}_L(f_REF,f_a), Δ{circumflex over (b)}_L(f_REF,f_b), Δ{circumflex over (b)}_L(f_REF,f_c), and Δ{circumflex over (b)}_{L (fREF},f_d). In one embodiment, this is done by obtaining a series of measurements on the selected satellite signals at GLONASS frequencies f_REF, f_a, f_REF, f_b, f_REF, f_c, F_REF, f_d, and f_REF. Then, for derivation of the respective inter-frequency bias correction terms, the results are preferably combined into groups of two measurements each: (f_REF, f_a), (F_REF, f_b), (F_REF, f_c), and (f_REF, f_d) In another embodiment, computational resources may be decreased by making the measurements in the following order: F_REF, f_a, f_b, f_REF, f_c, f_d, and f_REF. For derivation of the respective inter-frequency bias correction terms, the results are combined into groups of two measurements each: (f_REF, f_a), (f_b, f_REF), (f_REF, f_c), and (f_REF, f_d) where the same f_REFvalue is used in derivation with both f_band f_c.

[0104] In yet another alternative embodiment, a GLONASS single-channel simulator is set up to transmit on a specified GLONASS frequency with zero Doppler frequency. If the simulator and the receiver system 10 are set up to operate from the same clock, the theoretical pseudorange will not be changing, and there will be no relative change between the simulator and the receiver system 10 as a consequence of clock drift. The receiver system 10 then cycles through a series of twenty-four measurements, adjusting the GNS local oscillator 43 each time to move it ahead by one frequency interval. Each measurement set is taken over a time interval suitable for ‘smoothing’ the pseudorange such that the accuracy can be brought to the desired level of the calibration. To obtain the final result, each smoothed pseudorange is differenced with that taken at the specified frequency to obtain the bias difference at all the frequencies.

[0105] While the invention has been described with reference to particular embodiments, it will be understood that the present invention is by no means limited to the particular constructions and methods herein disclosed and/or shown in the drawings, but also comprises any modifications or equivalents within the scope of the claims.