Method and apparatus for locating the source of an unknown signal

• US 6,618,009 B2
• Filed: 09/19/2001
• Issued: 09/09/2003
• Est. Priority Date: 08/19/1999
• Status: Expired due to Term

• Current Assignee: Kratos Integral Holdings, LLC (Kratos Defense & Security Solutions Incorporated)
• Original Assignee: Qinetiq Limited (QinetiQ Group PLC)
• Inventors: Griffin, Christopher, Edmonds, Paul R., Duck, Simon R.
• Primary Examiner(s): Phan, Dao
• Application Number:
  US09/955,224
• Publication Number:
  US 20020070889A1
• Time in Patent Office: 720 Days
• Field of Search: 342/174, 342/352, 342/358, 342/432, 342/444, 342/453
• US Class Current: 342/432
• CPC Class Codes: G01S 1/026 of associated receivers
• CPC Class Codes: G01S 1/045 Receivers
• CPC Class Codes: G01S 5/0009 Transmission of position information to remote stations involving assistance data G01S5/0236
• CPC Class Codes: G01S 5/0246 involving frequency difference of arrival or Doppler measurements G01S5/02685 takes precedence
• CPC Class Codes: G01S 5/06 Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements G01S5/12 takes precedence

Abstract

A method of determining the location of an unknown source 10 transmitting a signal to satellite relays 14 and 16 comprises receiving replicas of the signal from the relays at receivers 18. The receivers 18 also transmit and receive reference signals via respective relays 14 and 16. All signals are downconverted, digitized and correlated with one another in pairs using a correlation function including a term which compensates for time varying differential frequency offset (DFO). Compensation for time varying differential time offset or time dilation is achieved by replicating or adding to signal samples and applying phase corrections. This procedure enables a correlation maximum and associated measurement results to be obtained despite the effects of relay satellite motion which mitigate against this. Results are used in a prior art geometrical technique to locate the unknown transmitter.

Claims

1. A method of locating the source of an unknown signal received by a plurality of signal relays, the method including the steps of:

(a) arranging for a plurality of receivers to receive replicas of the unknown signal via respective signal relays; and

(b) subjecting the replicas to correlation processing;

wherein step (b) is preformed with data sets adapted in phase and subject to sample adjustments to counteract time dilation.

2. A method according to claim 1 wherein samples in one of two data sets to be correlated are adapted in phase by samples following a removed sample being multiplied by a phase factor or by samples including and following a replicated sample being multiplied by such a factor, the phase factor being either e^2π

i fΔ

t or e<sup>−

π

ifΔ

t</sup> according to which of the two data sets is adapted and to the sign of DTO change with time, and wherein f is a signal band centre frequency of the samples after downconversion for sampling and Δ

t is an interval between successive samples.

3. A method according to claim 1 wherein samples are selected for removal or replication as the case may be on the basis of the correlation function'"'"'s time dimension spread over an interval in which the samples were obtained.

4. A method according to claim 1 wherein samples are selected for removal or replication as the case may be on the basis of at least a linear approximation to the following quadratic equation for t_m:

${\mathrm{\tau <br><br>}}_m=-\frac{\mathrm{\lambda <br><br>}}{c}<br><br>b_1^{\mathrm{\prime <br><br>}}<br><br>t_m-\frac{\mathrm{\lambda <br><br>}}{c}<br><br>b_2<br><br>{\mathrm{\tau <br><br>}}_m^2=\mathrm{m\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>t$

where t_m is the time to the mth replicated or removed sample, m is the number of replicated or removed samples up to time t_m,96_m is the total time dilation up to time t_m Δ

t is the time interval between successive samples and λ

is the free space wavelength at the centre frequency of the sampling band, b′

₁ is an estimate of DFO at initiation of sampling corrected for any systematic error in frequency, and b₂ is half of the rate of change of DFO with time.

5. A method according to claim 1 wherein step (b) is performed with a complex correlation function (CCF) at least partly compensated for change in the replicas'"'"' Differential Frequency Offset (DFO) with time due to relay motion relative to the source and receivers.

6. A method according to claim 5 wherein the correlation function is a complex correlation function referred to as a CCF given by:

$\mathrm{CCF}\equiv <br><br>A<br><br>\left({\mathrm{\tau <br><br>}}_0,b_1,b_2\right)={\int <br><br>}_0^T<br><br>z_1^{*}<br><br>\left(t\right)<br><br>z<br><br>\left(t+{\mathrm{\tau <br><br>}}_0\right)<br><br>{\mathrm{<br><br>}}^{-2<br><br>\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>i<br><br>\left(b_1+2<br><br>b_2<br><br>t\right)<br><br>t}<br><br>\text{\hspace{1em}<br><br>}<br><br><br><br>t$

where z₁ and z₂ are data sets representing two signals being correlated, the asterisk denotes the complex conjugate of z₁, T is the time over which samples are taken, τ

₀ is a time invariant component of Differential Time Offset (DTO), and b₁ and b₂ are constants in an expression for change in DFO with time t as follows;

DFO≡

ν

=b₁ +2 b₂t, and wherein the CCF is at least partly maximized by inserting therein trial values of b₂ and versions of z₁ and z₂ adapted to contain added or removed sample values to counteract time dilation.

7. A method according to claim 4, wherein after each iteration of step (b) the product of z₁*(t)z₂(t=τ

₀)exp(−

2π

ib₂t²) is Fourier transformed to the frequency domain, in order to provide for DFO b₁ to be obtainable as the frequency offset at which the CCF maximum occurs.

8. A location device for locating the source of an unknown signal received by a plurality of signal relays, and including:

(a) a plurality of receivers for receiving replicas of the unknown signal via respective signal relays;

(b) a correlation processor for correlating the replicas and obtaining a correlation maximum indicating at least one of their DTO and DFO;

wherein the correlation processor is arranged to perform correlation with data sets adapted in phase and subject to sample adjustments to counteract time dilation.

9. A location device according to claim 8 wherein the correlation processor is arranged to adapt in phase one of two sets of data samples to be correlated by multiplying samples following a removed sample by a phase factor or multiplying a replicated sample and samples following it by a such a factor, the phase factor being either e^2π

ifΔ

t or e<sup>−

2π

ifΔ

t</sup> according to which of the two data sets is adapted and to the sign of DTO change with time, and wherein f is a signal band centre frequency of the samples after downconversion for sampling and Δ

t is an interval between successive samples.

10. A location device according to claim 8 wherein the correlation processor is arranged to select samples for removal and replication on the basis of the correlation function'"'"'s time dimension spread over an interval in which the samples were obtained.

11. A location device according to claim 8 wherein the correlation processor is arranged to select samples for removal and replication on the basis of at least the linear term of the following quadratic equation in t_m²:

${\mathrm{\tau <br><br>}}_m=-\frac{\mathrm{\lambda <br><br>}}{c}<br><br>b_1^{\mathrm{\prime <br><br>}}<br><br>t_m-\frac{\mathrm{\lambda <br><br>}}{c}<br><br>b_2<br><br>{\mathrm{\tau <br><br>}}_m^2=\mathrm{m\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>t$

where t_m is the time from initiation of sampling to the mth replicated or removed sample, m is the number of replicated or removed samples up to time t_m, τ

_m is the total time dilation up to time t_m, Δ

t is the time interval between successive samples, λ

is the free space wavelength at the centre frequency of the sampling band, b′

₁ is an estimate of DFO at initiation of sampling corrected for any systematic error in frequency, and b₂ is half of the rate of change of DFO with time.

12. A device according to claim 8 wherein the correlation processor is arranged to perform correlation with a complex correlation function (CCF) at least partly compensated for change in DFO with time due to relay motion relative to the source and receivers.

13. A device according to claim 12 wherein the correlation processor is arranged to employ a CCF which contains an exponent of a function of time having a first term which is a constant DFO value and a second term which is a product of time and a constant value for rate of change of DFO with time, comprising a constant differential frequency rate offset (DFRO) value, and wherein the correlation processor is also arranged to introduce trial values of DFRO and to iteratively evaluate correlation for pairs of trial values of DTO and DFRO to determine a DFRO value enabling a correlation maximum to be obtained.

14. A device according to claim 13, wherein the CCF is given by:

$\mathrm{CCF}\equiv <br><br>A<br><br>\left({\mathrm{\tau <br><br>}}_0,b_1,b_2\right)={\int <br><br>}_0^T<br><br>z_1^{*}<br><br>\left(t\right)<br><br>z<br><br>\left(t+{\mathrm{\tau <br><br>}}_0\right)<br><br>{\mathrm{<br><br>}}^{-2<br><br>\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>i<br><br>\left(b_1+2<br><br>b_2<br><br>t\right)<br><br>t}<br><br>\text{\hspace{1em}<br><br>}<br><br><br><br>t$

where z₁ and z₂ are data sets representing two signals being correlated, the asterisk denotes the complex conjugate of z₁, T is the time over which samples are taken, τ

₀ is a time invariant component of DTO, and b₁ and b₂ are constants in an expression for DFO for change in DFO with time t as follows;

DFO≡

ν

=b₁+2b₂t, and wherein the correlation processor is arranged to maximise the CCF by evaluating it with trial values of b₂ in addition to those of τ

₀ together with versions of z₁ and z₂ adapted to contain replicated or removed sample values to counteract time dilation.

15. A device according to claim 14 wherein the correlation processor is arranged to Fourier transform successive products z₁*(t)z₂(t+τ

₀)exp(−

2π

ib₂t²) to the frequency domain in order to obtain DFO b₁ as a frequency offset at which a CCF maximum occurs.