Systems and methods for determining satellite orbit parameters

This application claims the benefit of European Patent Application EP19382556.9 filed on June 28th, 2019.

Field of the Invention

The present disclosure relates to systems and methods for use in satellite orbit determination and/or satellite tracking.

BACKGROUND

A variety of methods for determining the orbit of a satellite are known. However, the known methods of determining a satellite orbit (or determining satellite orbit parameters) suffer a number of drawbacks.

The known methods, for example, require the arrangement of ground sensors at very large distances from each other. Thus, the known techniques are inefficient and cumbersome to implement.

Therefore, there is a need for a system and method that may accurately and reliably determine a satellite orbital trajectory with a reasonable or acceptable error margin.

SUMMARY

In a first aspect, the invention comprises a method for determining at least two Time difference of arrival (TDOA) parameters suitable for determining an orbit of at least one target satellite having a transmitting frequency, the method comprising the steps of:

-Obtaining from at least three receivers at least a portion of a signal transmitted by the target satellite;

-Obtaining a Master Clock signal;

-Obtaining a target satellite transmitting frequency, at least partly on the basis of said Master Clock signal; and

For each receiver: -Obtaining a Radio Frequency (RF) signal corresponding to the at least one portion of the target satellite transmitted signal; and

-For each obtained RF signal:

-Obtaining a baseband In-phase and Quadrature signal at least partly on the basis of the obtained target satellite transmitting frequency;

-Defining at least two different pairs of receivers of the at least three receivers, and -For each defined pair of receivers:

-Obtaining a cross-correlation parameter between the obtained baseband In-phase and Quadrature signals corresponding to each receiver within the defined pair of receivers; and

-Obtaining at least one TDOA parameter for the defined pair of receivers at least partly based on said cross-correlation parameter. The TDOA parameters obtained in this manner may be more precise than those obtained by known methods.

The method(s) according to the present invention use a cross-correlation determination that is partly based on interferometry. Interferometry techniques may be very sensitive to positional changes or displacements (for example, a change in a satellite ^' s orbit) of the elements in respect of which a position is to be determined.

Thus, using a parameter in the form of a phase angle as output data of a cross correlation, interferometry can be highly vulnerable to relatively small phase errors.

Aspects of the present invention, such as synchronizing all elements with a master clock, using at least three receivers, and defining at least two pairs of receivers for determining a cross-correlation may help minimize such potential phase errors. Using the present method, it is possible to obtain precise data on the orbit of a target satellite by obtaining the two potential TDOA values corresponding to the target satellite. In this manner, the present system can be made more compact than known systems.

In other words, the present system(s) and method(s) provide a precision in the TDOA parameter determination that, if using known methods, would require a distance between receiving antennas in the order of hundreds of kilometers. However, the present invention enables the placement or arrangement of the receiving antennas at separation distances, for example, in the order of tens of meters, to attain the same precision in the TDOA parameter(s).

This additionally enables, with the use of fiber optic systems, local gathering of the data, at a single station, which may be advantageously located near the receivers (antennas). This reduction in distance between where the data is received and where it is processed may advantageously reduce the potential introduction of transmission errors.

In general, satellites are assigned a specific frequency band for signal transmission and reception. In the case of receiving the signals from multiple satellites simultaneously, the methods according to the present invention can be performed in parallel for all the satellites, by selecting the transmitting frequencies corresponding to each satellite, without having to change (for example, increase) the number of antennas used.

In this manner, the number of elements the system uses for obtaining the TDOAs of multiple satellites can be reduced or minimized, without introducing phase errors (which can negatively affect the cross-correlation calculations).

Additionally, these methods and systems can be implemented in a local manner without necessitating the installation of long-distance data transmission structures (which can be another source of errors in the received data).

This solution also makes the logistics of the system for tracking satellite orbits more cost-effective. Also, known methods may be more active. That is, the satellite needs to receive a system order or command to send signals and proceed to carry out the orbit determination process.

However, the methods and systems according to the present invention are more versatile, given that the type of data input to the system (the signals or portions thereof picked up by the receivers) can encompass a greater variety, and need not have to be necessarily obtained in an active manner (that is, under command from the system to the satellite), but may also be of exclusively passive origin. According to aspects of the invention, any type of signal emitted by the satellite(s) during its functioning may be used. For example, a content signal or a telemetry beacon may be used to carry out the invention, as long as the satellite transmitting frequency is known.

Alternatively or additionally, a radar-type scheme may be employed (sending a signal to the at least one satellite, wherein the receiving antennas receive the rebound signal) such that the method(s) and system(s) according to the present invention may obtain reliable TDOAs and the satellite orbit may thus be obtained in a reliable manner.

In some embodiments of the invention, determining a cross-correlation parameter between the obtained baseband In-phase and Quadrature signals corresponding to each receiver within the defined pair of receivers comprises:

-Obtaining a complex cross-correlation parameter comprising a phase angle value, and wherein obtaining said at least one TDOA parameter comprises obtaining said at least one TDOA parameter at least partly based on said phase angle value.

In another aspect of the invention, obtaining said at least one TDOA parameter comprises performing a selective calculation comprising the steps of:

-Obtaining a natural number N of iterations to be performed by the selective calculation;

While N>0, Performing the steps of:

-Obtaining at least two Nth input values by adding a number of cycles P to each of the obtained phase angle values of the obtained complex correlation parameters for each receiver pair, wherein P can have a different value for each receiver pair; -Obtaining at least two TDOA parameters for the Nth iteration, one from each previously obtained phase angle value;

-Obtaining an orbit element set output value and an Nth remainder parameter value by performing an Orbital Determination Algorithm on the Nth input values;

-Subtracting 1 from N;

-Determining the input P values resulting in the lowest remainder parameter value, and

-Obtaining the at least two TDOA parameters for each receiver by adding the number of cycles P which generated the lowest remainder parameter value to the at least two phase angle values of the obtained complex cross-correlation parameters for each receiver According to some embodiments, the received RF signal is an analog signal, and the method(s) may further comprise the step of:

-Converting the obtained In-phase and Quadrature signals to digital signals, based at least partly on the Master Clock.

According to further embodiments, a complex Cross-Correlation parameter comprises determining a Cross Ambiguity Function, and the method further comprises the steps of:

-Obtaining the magnitude of the obtained complex cross-correlation parameter, and

-Obtaining a Frequency difference of arrival (FDOA) parameter, suitable for determining an orbiting speed of the target satellite from the obtained magnitude.

According to a further aspect of the invention, the transmitting frequency of the at least one target satellite is obtained by means of a signal synchronization module, using the master clock signal as a reference signal.

In a further aspect of the invention, a signal synchronization module for obtaining the transmitting frequency of each target satellite is provided for each of the at least three receivers, using the master clock signal as a reference signal.

According to some embodiments of the invention, the signal synchronization module comprises a phase-locked loop circuit. In some aspects of the invention, the step of obtaining In-phase and Quadrature signals from the received RF signal comprises the steps of:

-Demodulating the received RF signal to an Intermediate Frequency (IF) signal, based at least partly on the Master Clock signal;

-Obtaining a base band In-phase and Quadrature signal from obtained the IF signal, based at least partly on the corresponding obtained transmitting frequency of the target satellite.

The obtained In-Phase signals may comprise baseband In-Phase signals.

According to a further aspect of the invention, the step of obtaining an RF signal corresponding to the at least one portion of the transmitted signal of each target satellite, further comprises the step of converting the received analog signal into an optical signal, via, for example analog optical transceivers.

In order to perform a coherent demodulation synchronized with the master clock signal, the RF signal from each receiver is transported from its receiving point to a common processing point. Such signal transportation must be performed in a manner which requires, amongst other factors, no previous demodulation or time-discretization of the signal in any form. Otherwise the main purpose of coherency and synchronization would be defeated. Therefore, a digital optical link, typically used for fast data communications, cannot be applied for this matter. The only way to use an optical link while keeping the coherency shall be using a non-distorting low noise analog electro-optical modulation process and its complementary electro-optical demodulation. Such process is not an industry standard application and requires much higher performance and constraints than a digital optical link. Thus, the amplified analog signal(s) are converted directly to optical signal(s) without any prior digitization.

According to a further aspect of the invention, the at least three receivers comprise antennas configured for receiving signals in the radiofrequency spectrum. The antennas may be configured, for example, to receive signals in the K, Ku, C, L and/or S RF bands.

In another aspect, the method(s) according to the invention further comprises the step of associating the at least one TDOA parameter with a time stamp or ^' epoch ^' . Such a time stamp or epoch may be provided by a GPS receptor which provides precise UTC standard time.

A system for determining at least two Time Difference of arrival (TDAO) parameters suitable for determining an orbit of at least one target satellite having a transmitting frequency is also provided.

The system may comprise at least three receivers for obtaining a radiofrequency signal based on at least one portion of a signal transmitted by at least one target satellite;

-means for obtaining In-phase and Quadrature signals of each of the RF signals,

-means for providing a Master Clock signal;

-a signal synchronization module for synchronizing each of the received signals with respect to said Master Clock signal, and

-processing means, wherein the processing means are configured to

-Define at least two different pairs of receivers of the at least three receivers, and

-For each defined pair of receivers:

-Obtaining a cross-correlation parameter between the obtained In-phase and Quadrature signals corresponding to each receiver within the defined pair of receivers; and

-Obtaining at least one TDOA parameter for the defined pair of receivers at least partly based on said cross-correlation parameter.

In some aspects of the invention, performing the selective calculation by the processor of the system may comprise the steps of:

• Obtaining a natural number N of iterations to be performed by the selective calculation; While N>0, Performing the steps of:

-Obtaining at least two Nth input values by adding a number of cycles P to each of the obtained phase angle values of the obtained complex correlation parameters for each receiver pair, wherein P can have a different value for each receiver pair;

-Obtaining at least two TDOA parameters for the Nth iteration, one from each previously obtained phase angle value;

-Obtaining an orbit element set output value and an Nth remainder parameter value by performing an Orbital Determination Algorithm on the Nth input values;

-Subtracting 1 from N;

-Determining the input P values resulting in the lowest remainder parameter value, and

-Obtaining the at least two TDOA parameters for each receiver by adding the number of cycles P which generated the lowest remainder parameter value to the at least two phase angle values of the obtained complex cross-correlation parameters for each receiver.

In some embodiments, the three receivers comprise antennas configured for receiving signals in the radiofrequency spectrum.

The antennas may be configured for receiving signals in the K, Ku, C, L or S RF bands.

Alternatively or additionally, the receivers may be configured to receive signals in other frequency bands.

In some embodiments, the obtained In-Phase signals comprise baseband In-Phase signals.

In some embodiments, the system processing means comprise at least one field- programmable gate array (FPGA).

In some embodiments, the processing means comprise one or more of a central processing unit (CPU), a graphical processing unit (GPU), a configurable processor, a FPGA, and a microprocessor. According to another aspect of the invention, the system may further comprise means for obtaining an optical signal from the at least one portion of the signal transmitted by the at least one target satellite, and means for obtaining an RF signal from said optical signal.

In some embodiments, the means for obtaining an optical signal from the at least one portion of the signal transmitted by the at least one target satellite comprise a fiber optic medium.

According to a further aspect of the invention, a method is provided for determining at least two Time difference of arrival (TDOA) parameters suitable for determining an orbit of at least one target satellite having a transmitting frequency, the method comprising the steps of processor configured for:

-receiving at least three digital representations of an In-Phase and Quadrature signals corresponding to at least three different receivers,

-Defining at least two different pairs of said at least three digital representations, and

-For each defined pair of digital representations:

-Obtaining a cross-correlation parameter between the obtained baseband In- phase and Quadrature signals corresponding to each receiver within the defined pair of receivers; and

-Obtaining at least one TDOA parameter for the defined pair of receivers at least partly based on said cross-correlation parameter.

Determining a cross-correlation parameter between the obtained baseband In-phase and Quadrature signals corresponding to each receiver within the defined pair of receivers comprises:

-Obtaining a complex cross-correlation parameter comprising a phase angle value, and wherein obtaining said at least one TDOA parameter comprises obtaining said at least one TDOA parameter at least partly based on said phase angle value.

Obtaining said at least one TDOA parameter comprises performing a selective calculation comprising the steps of: -Obtaining a natural number N of iterations to be performed by the selective calculation;

While N>0, Performing the steps of:

-Obtaining at least two Nth input values by adding a number of cycles P to each of the obtained phase angle values of the obtained complex correlation parameters for each receiver pair, wherein P can have a different value for each receiver pair;

-Obtaining at least two TDOA parameters for the Nth iteration, one from each previously obtained phase angle value; -Obtaining an orbit element set output value and an Nth remainder parameter value by performing an Orbital Determination Algorithm on the Nth input values;

-Subtracting 1 from N;

-Determining the input P values resulting in the lowest remainder parameter value, and

-Obtaining the at least two TDOA parameters for each receiver by adding the number of cycles P which generated the lowest remainder parameter value to the at least two phase angle values of the obtained complex cross-correlation parameters for each receiver. According to another aspect of the invention, at least one processor is provided which is configured with instructions to carry out one or more method(s) according to the invention.

The at least one processor may comprise one or more of a FPGA, microprocessor, central processing unit (CPU), and Graphical Processing Unit (GPU). In a further aspect of the present invention a method is provided. The method may comprise determining at least two Time difference of arrival (TDOA) parameters, suitable for determining an orbit of at least one objective satellite, the satellite transmitting a signal at a corresponding transmitting frequency, the transmitted signal being received by at least three receiving antennas, the method comprising the steps of:

Obtaining a Master Clock signal; Obtaining the transmitting frequency of the objective satellite, by means of the master clock signal;

Defining at least two different pairs of receiving antennas;

For each receiving antenna within the defined pairs of receiving antennas: o Obtaining a received Radio Frequency (RF) signal comprising the transmitted signal of the objective satellite;

For each obtained received RF signal:

o Obtaining a base band in-phase and quadrature signal from the received RF signal, comprising the transmitted signal of the objective satellite, by means of the obtained transmitting frequency of the objective satellite.

Obtaining a parameter may comprise,

For each defined pair of receiving antennas:

Obtaining a complex correlating parameter by determining a Cross

Correlation between the obtained (baseband) in-phase and quadrature signals corresponding to each antenna, within the defined pair of receiving antennas;

Obtaining a phase angle of the obtained complex correlating parameter.

Obtaining a TDOA parameter, suitable for determining the orbit of the objective satellite, by performing a selective calculation comprising the steps of:

Obtaining a natural number N of iterations to be performed by the selective calculation;

While N>0, Performing the steps of:

Obtaining a possible input parameter by adding P number of cycles to the obtained phase angle value of the obtained complex correlating parameter;

• Obtaining a possible TDOA parameter and a remainder parameter by performing an Orbital Determination Algorithm to the possible input parameter;

• Subtracting 1 from N;

And Obtaining at least two TDOA parameters by adding the lowest remainder parameter to the at least two TDOA parameters obtained from the phase angle value of the obtained complex correlating parameter. Adding a number of cycles P refers to adding a phase value (e.g. in terms of multiples of pi in radian units).

A cross-correlation may comprise a correlation calculation applied for a given frequency of the signals. TDOA is obtained from the phase of the complex number that results of applying Cross Correlation to its input signals. It provides information of the position of the satellite over time.

In order to further obtain FDOA by means of the correlation calculation, a Cross Ambiguity function may be used; which is a correlation calculation that may be applied to a plurality of frequencies of the signals.

FDOA is obtained from the magnitude of the complex number that results of applying Cross Correlation to its input signals. It provides information about the speed of the satellite over time.

Obtaining the number N of iterations to be performed can be achieved in any suitable manner, depending on different criteria. For example, a higher number N of iterations may be selected when accuracy is highly critical, while a lower number of iterations N may be selected when speed or efficiency are critical.

According to an aspect of the invention, a master clock is obtained, which may be used by a system performing a method according to the present invention. The master clock may be obtained by employing a local oscillator at a substantially stable frequency. Such an oscillator may comprise, for example, a crystal oscillator, which delivers a substantially reliable clock signal. The local oscillator may be substantially isolated from any exterior signal, and may not require any external signal to be obtained.

The master clock may synchronize a plurality of elements that may perform steps of the present method(s), achieving a synchronized performance of the method(s), which advantageously minimizes the introduction of time-, frequency- or phase- related errors in the processing of the signal(s).

The term target satellite as used herein refers to a satellite for which a parameter(s) is/are being determined in accordance with one or more aspects of the invention. Each target satellite may transmit a signal to the receivers. This signal may be a signal transmitted actively by the satellite in a substantially autonomous way, or actively in response to a signal sent to the satellite. It may also be a signal sent to the satellite by any other device or system, including the system performing the method of the present invention, which bounces back from the satellite and is received by the receivers (e.g. antennas (as in the case of a radar system)).

In any of the above described cases, the signal is transmitted by the target satellite and received by the receivers in a given or particular transmitting frequency (normally defined by a transmitting frequency band), which is known (or made known) to the system performing the method(s) according to the present invention.

In case of the satellite actively sending the signal, in response or not to another signal it may have received, the satellite may have a predetermined working frequency band in which it is allowed to send data (normally assigned by

communicating authorities), and therefore said working frequency band will be known by (or can be made known to) the system(s) of the present invention.

In case a radar-type transmission and reception scheme is used with the satellite, a signal may have been sent to the satellite and backscattered, the sent signal having a frequency that is known by the present system(s).

This may be achieved by, for example, by obtaining each transmitting frequency by means of a synchronizing element (for each receiver). Such a synchronizing element may comprise a Phase-Locked Loop (PLL) circuits (or other similar circuits which achieve substantially the same result), which synthesize each transmitting frequency using the master clock as a reference signal.

A different PLL circuit may be used to obtain each transmitting frequency. This way, by having or providing a specific PLL circuit per frequency, the system avoids introducing aleatory phases to the transmitting frequencies (which may be introduced by a PLL circuit when it is activated in the case of using a plurality of PLL circuits to obtain one transmitting frequency).

A definition of at least two (different) pairs of receivers (or antennas) is performed. This definition is performed for all the receivers (or antennas) the system may comprise or may have access to. For example, if a given system performing the present method uses three receivers (or antennas), at least two different pairs of receivers (or antennas) from among said three receivers (antennas) in any possible combination. Another possibility could be that a first pair comprises the first and the second antenna, and a second pair comprises the second and the third antenna.

According to a further aspect of the invention, at least three different pairs of receivers are defined in respect to the at least three (different) receivers.

In a preferred embodiment, three receivers are used and three different pairs of receivers are defined. Therefore, a first pair may comprise the first and second receiver, a second pair could comprise the first and the third receiver, while a third receiver pair may comprise the second receiver and the third receiver. The at least two TDOA parameters may thus be obtained taking into account all pair permutations (three pairs) for the three receivers. This would yield a total of six TDOA parameters.

Another possible scenario could be that the system performing the method(s) of the present invention comprises four antennas. In that case, the defined pairs could be any possible combination between said four antennas, as long as at least two pairs (two pairs or more) are defined.

For example, a first pair may comprise a first and second antenna, and a second pair may comprise a first and a fourth antenna.

Another example could be that a first pair comprises a first and second antenna, and a second pair comprises a third and a fourth antenna.

After said definition of pairs of antennas is performed, a received signal of each antenna comprised in each defined pair of antennas is obtained.

Furthermore, each obtained received signal, which may be a Radio Frequency (RF) signal, may be demodulated, and a baseband In-phase and Quadrature signal (l/Q) may be obtained. This demodulation may be performed in one step, or alternatively may be performed in at least two steps, by demodulating the obtained received signal, which is an RF signal, into an Intermediate Frequency (IF) signal, and further lowering the signal from an IF signal to a band base in-phase quadrature signal. In case two or more steps are performed, all the Local Oscillators to be used for obtaining each consecutive signal are obtained.

For each defined pair of receiving antennas, a complex correlating parameter is obtained by performing a Cross Correlation in between the obtained base band in- phase and quadrature signals corresponding to each antenna within the defined pair of receiving antennas.

In this manner, for a first pair of antennas comprising a first and a second antenna, a Cross Correlation is applied between the base band in-phase and quadrature signal of the first antenna and the base band in-phase and quadrature signals of the second antenna.

The Cross Correlation performed in between the two signals is a well-known calculation, widely applied in signal processing, which measures the similarity in between said two signals, and it gives as a result a correlating parameter which is a complex number, and which can be represented in polar form as an amplitude parameter and a phase parameter.

Furthermore, the obtained phase of said obtained complex correlating parameter is used in the following steps. This phase can be used to obtain a TDOA which is considered to be ambiguous, because it only partially delivers information useful for the obtaining of the orbit of a satellite. Since it is a phase, the value of this parameter ranges from values [-TT, +TT], but without knowing a number of cycles corresponding to the phase parameter, the TDOA extracted from said phase may define an infinite number of potential satellite orbits.

Therefore, the system needs to find an approximation of a TDOA from the obtained phase by obtaining a number of cycles which has to be added to the obtained phase, in order to obtain a single TDOA.

In order to obtain a single TDOA for each defined pair of receiving antennas (that is, obtaining a number of cycles to be added to the obtained phase), the system performing the method of the present invention performs an iteration of an Orbital Determination Algorithm, each algorithm resulting in a possible TDOA (from which a possible orbit of the satellite is easily obtained) and a remainder parameter. From all the iterations, the best output is defined to be used to obtain a single TDOA.

There are many different Orbital Determination Algorithms used in the state of the art, and the present method can use any of the ones which deliver as a result a possible orbit of the satellite and try to minimize the remainder parameter while doing so, the remainder parameter giving information about how close to reality or reliable the resulting orbit (easily obtained from the obtained possible TDOA) calculated by the algorithm is. The smaller the remainder parameter, the more reliable (closer to the real orbit) the solution of the Algorithm is.

A natural number N is defined in order to perform N iterations of possible solutions of the algorithm, thus obtaining at least 2N TDOAs, at least 2P plausible number of cycles and at least 2N Orbit Determination remainders.

The definition of P may be based on many different factors, but a good starting point to know the magnitude of P may be the magnitude of the complex correlating parameter. A TDOA can be extracted directly from said magnitude, but its reliability is very low, thus it is a good starting point to define a possible P number. Other information can be used to in addition to the magnitude of the complex correlating parameter, or on its own, related to a rough estimate of the position of the satellite in the sky related to the position of the antennas. That is, a possible range of orbits can be deduced by the fact that the satellite may be of a certain type (geo-stationary, of a certain group of known orbits, etc...) which provides another good starting point to determine a possible definition of P.

More specifically, P refers to the natural number of cycles to be added to the obtained phase of the complex correlating parameter in order to obtain a reliable TDOA.

In case the calculation is performed with the obtained phase, the cycles are in phase units (for example, degrees or radians), and in each of the N iterations, the calculation can be made directly with the phase value. Alternatively, the phase value may be converted to a TDOA value prior to the calculation.

The selective calculation may comprise the following:

If performing the calculation in the phase domain, the number of cycles is

represented in phase units (for example, degrees or radians). And in each iteration the number of cycles is added to the phase in the prescribed phase unit (e.g., degrees or radians).

Alternatively, if performing the selective calculation in the TDOA domain, the number of cycles is represented in time units (for example, seconds), and in each iteration = the conversion of the number of cycles to TDOA domain is added to the existing TDOA.

The output of each iteration represents a potential orbit with an associated remainder value. The number of cycles P which has resulted in the orbit with the lowest remainder or residual value (in (absolute) mathematical terms).

Finally, a TDOA parameter for each defined pair of receiving antennas (at least two TDOA parameters) is obtained by adding the lowest remainder parameter P (number of cycles P) obtained in the iteration (among N possible obtained remainder parameters) to a TDOA obtained from the phase angle of the obtained complex correlating parameter.

The invention is also directed to computer program product comprising program instructions for causing a computing system to perform any one or more of the methods disclosed herein.

The invention is also directed to a computer program product as indicated above, embodied on a storage medium. The invention is also directed to a computer program product as indicated above, carried on a carrier signal. BRIEF DESCRIPTION OF THE DRAWINGS

Non-limiting examples of the present disclosure will be described in the following, with reference to the appended drawings, in which:

Figure 1 is a block diagram of a system according to an exemplary embodiment of the invention.

Figure 2 is a block diagram of a digital converter system according to an exemplary embodiment of the invention.

Figure 3 is a schematic depiction of a synchronization module according to an exemplary embodiment of the invention.

DETAILED DESCRIPTION OF EXAMPLES

Figure 1 illustrates an example of the system for determining an orbit path according to the present invention, in a block diagram form.

The system is connected to a plurality of antennas, in this case three antennas (A1), (A2) and (A3), which receive signals from two objective satellites S1 and S2 (not shown). Each antenna receives said signals and adapts them by means of an Antenna feed system (101), a Low Noise Amplifier (102) which amplifies the signal without demodulating it, and an optical transmitter to convert the amplified electrical signal into an optical signal which is sent through an Optical Transmitting system (200), connected through an optic fiber cable to an Optical Receiver System (RF Front end) (300).

Figure 2 shows a detailed block diagram of the Optical Receiver System (RF Front end) (300), wherein the optical signal is received, which converts the light signal into an electrical signal through its photodetector (301). The converted electrical signal, which is an RF (radio frequency) signal, is further lowered or demodulated to IF (intermediate frequency) by means of a mixer (302), using an RF clock (302CK) signal. No digital signal.

The demodulated signal is further sent into two In-phase and Quadrature mixers (303A) (303B) (hereinafter called l/Q mixers), one for each of the objective satellites. These mixers (303A) (303B) demodulate the same signal into In-phase and Quadrature components, demodulating the signal from one satellite each (Satellites S1 and S2). This is achieved by using an IF clock for each signal corresponding to each satellite S1 and S2, i.e., for obtaining the signal of the first satellite S1 , a first IF clock (303A_CK) is used, and for obtaining the signal of the second satellite S2, a second IF clock (303B_CK) is used. These clocks may be previously known, since they are related to the transmitting frequency designated or allocated to each satellite. Both the ADC clock and the IF clock are generated using the Master Clock and PLLs.

This way, the output of l/Q mixer (303A) is a group of two signals (303A_S1), the two signals being an In-phase component and a Quadrature component corresponding to satellite S1. The same applies to the second l/Q mixer (303B), whose output is a group of two signals (303B_S2), the two signals being an In-phase and a Quadrature component corresponding to satellite S2.

After obtaining the l/Q signals corresponding to each satellite, both (303A_S1) and (303B_S2) are converted into digital signals by means of an Analog-Digital Converter (304) (hereinafter called ADC), using a clock signal (304CK).

The output of the ADC (304) comprises the digitalized versions of (303A_S1) and (303B_S2), and is connected then to the input lines of a Processing means (400), in this case a FPGA (Field Programmable Gate Array) which will be executed in real time.

Likewise, the other two Antennas (A2) and (A3) are connected to an analogous chain of circuits, which use as their corresponding Clock signals (302CK), (303A_S1), (303B_S2) and (304CK), obtaining the same signals as in the case of the first Antenna (A1), but with the input signal of corresponding Antennas (A2) and (A3). The use of the same clock signals ensures that the overall system of the present invention (each part of the system corresponding to each Antenna) is completely synchronized and minimal (if any) time/frequency differences are introduced in the overall system as might be by the use of different clocks.

Each digitalized output from each ADC corresponding to each Antenna is connected to the input of the FPGA (400), which may compute, for example, in real time, a Cross Correlation value. The process of this function may comprise the following:

The selective calculation may comprise the following:

If performing the calculation in the phase domain, the number of cycles is

represented in phase units (for example, degrees or radians). And in each iteration the number of cycles is added to the phase in the prescribed phase unit (e.g., degrees or radians).

Alternatively, if performing the selective calculation in the TDOA domain, the number of cycles is represented in time units (for example, seconds), and in each iteration the conversion of the number of cycles to TDOA domain is added to the existing TDOA.

The output of each iteration represents a potential orbit with an associated remainder value. The number of cycles P which has resulted in the orbit with the lowest remainder or residual value (in (absolute) mathematical terms).

Finally, a TDOA parameter for each defined pair of receiving antennas (at least two TDOA parameters) is obtained by adding the lowest remainder parameter P(number of cycles P which resulted in the lowest remainder during the iteration, among N possible obtained remainder parameters) to a TDOA obtained from the phase angle value of the obtained complex correlating parameter.

The result of said iteration outputs as a result a digital data matrix of complex numbers which is sent by the FPGA to a CPU for further processing of the data.

Figure 3 illustrates a synchronizing module comprised within the system of the present invention, wherein all the clocks needed in the part of the system shown in Fig1 are generated.

The synchronizing module is used to ensure the synchronization of all the parts of system, through their corresponding clocks. Therefore, all the clocks used in it are generated from a master clock. More specifically, the synchronizing module comprises a local oscillator (hereinafter called LO) (500) used as a Master clock, whose output is connected to a plurality of interfaces, which adapt the signal to be compatible with the specifications of each clock, but introducing no variable time delay within any of the resultant clocks, which is important to avoid any

synchronization malfunction of any parts of the system, and for the calculations related to the orbit of the satellite performed within the system to be the closest to the actual value.

The output of the LO (500) is connected to a first interface 501 to generate a clock signal for the processor (for example, an FPGA). The output of the LO (500) is also connected to a second interface 502 to generate various clock signals for the analog- to-digital converters, and to a third interface 503 to generate clock signals for the various mixers.

The methods and systems disclosed herein are not limited to satellite detection and tracking, but may also be employed, for example, for detecting and/or tracking other objects in spatial orbit such as spatial debris, space shuttles, etc.

For reasons of completeness, various aspects of the present disclosure are set out in the following numbered clauses:

Clause 1. Method for determining at least two Time difference of arrival (TDOA) parameters suitable for determining an orbit of at least one target satellite having a transmitting frequency, the method comprising the steps of:

-Obtaining from at least three receivers at least a portion of a signal transmitted by the target satellite;

-Obtaining a Master Clock signal;

-Obtaining a target satellite transmitting frequency, at least partly on the basis of said Master Clock signal; and

For each receiver:

-Obtaining a Radio Frequency (RF) signal corresponding to the at least one portion of the target satellite transmitted signal; and

-For each obtained RF signal:

-Obtaining a baseband In-phase and Quadrature signal at least partly on the basis of the obtained target satellite transmitting frequency;

-Defining at least two different receiver pairs of the at least three receivers, and -For each defined receiver pair:

-Obtaining a cross-correlation parameter between the obtained baseband In-phase and Quadrature signals corresponding to each receiver within the defined pair of receivers; and

-Obtaining at least two TDOA parameters for the defined pair of receivers at least partly based on said cross-correlation parameters.

Clause 2. The method of Clause 1 , wherein determining a cross-correlation parameter between the obtained baseband In-phase and Quadrature signals corresponding to each receiver within the defined pair of receivers comprises:

-Obtaining a complex cross-correlation parameter comprising a phase angle value, and wherein obtaining said at least two TDOA parameters comprises obtaining said at least two TDOA parameters at least partly based on said phase angle value. Clause 3. The method according to Clause 2, wherein obtaining said at least two TDOA parameters comprises performing a selective calculation comprising the steps of:

-Obtaining a natural number N of iterations to be performed by the selective calculation; While N>0, Performing the steps of:

-Obtaining at least two Nth input values by adding a number of cycles P to each of the obtained phase angle values of the obtained complex correlation parameters for each receiver pair, wherein P can have a different value for each receiver pair;

-Obtaining at least two TDOA parameters for the Nth iteration, one from each previously obtained phase angle value;

-Obtaining an orbit element set output value and an Nth remainder parameter value by performing an Orbital Determination Algorithm on the Nth input values;

-Subtracting 1 from N;

-Determining the input P values resulting in the lowest remainder parameter value, and -Obtaining the at least two TDOA parameters for each receiver by adding the number of cycles P which generated the lowest remainder parameter value to the at least two phase angle values of the obtained complex cross-correlation parameters for each receiver. Clause 4. Method according to any of Clauses 1 -3, wherein the received RF signal is an analog signal, and the method further comprises the step of:

-Converting the obtained In-phase and Quadrature signals to digital signals, based at least partly on the Master Clock.

Clause 5. Method according to any of Clauses 2 to 4, wherein determining a complex Cross-Correlation parameter comprises determining a Cross Ambiguity Function, and the method further comprises the steps of:

-Obtaining the magnitude of the obtained complex cross-correlation parameter, and -Obtaining a Frequency difference of arrival (FDOA) parameter, suitable for determining an orbiting speed of the target satellite from the obtained magnitude.

Clause 6. Method according to any of the preceding clauses, wherein the transmitting frequency of the at least one target satellite is obtained by means of a signal synchronization module, using the master clock signal as a reference signal.

Clause 7. Method according to any of the preceding clauses, wherein a signal synchronization module for obtaining the transmitting frequency of each target satellite is provided for each of the at least three receivers, using the master clock signal as a reference signal.

Clause 8. Method according to Clause 6 or Clause 7, wherein the signal synchronization module comprises a phase-locked loop circuit.

Clause 9. Method according to any of the preceding clauses, wherein the step of obtaining a baseband In-phase and Quadrature signal from the received RF signal comprises the steps of:

-Demodulating the received RF signal to an Intermediate Frequency (IF) signal, based at least partly on the Master Clock signal;

-Obtaining a base band In-phase and Quadrature signal from obtained the IF signal, based at least partly on the corresponding obtained transmitting frequency of the target satellite.

Clause 10. Method according to any of the preceding clauses, wherein the step of obtaining an RF signal corresponding to the at least one portion of the transmitted signal of each target satellite, further comprises the step of converting the received analog signal into an optical signal.

Clause 1 1. Method for determining at least two Time difference of arrival (TDOA) parameters suitable for determining an orbit of at least one target satellite having a transmitting frequency, the method comprising the steps of processor configured for: -receiving at least three digital representations of an In-Phase and Quadrature signals corresponding to at least three different receivers,

-Defining at least two different pairs of said at least three digital representations, and -For each defined pair of digital representations:

-Obtaining a cross-correlation parameter between the obtained baseband In-phase and Quadrature signals corresponding to each receiver within the defined pair of receivers; and

-Obtaining at least two TDOA parameters for the defined pair of receivers at least partly based on said cross-correlation parameter.

Clause 12. Method according to Clause 1 1 , wherein determining a cross-correlation parameter between the obtained baseband In-phase and Quadrature signals corresponding to each receiver within the defined pair of receivers comprises:

-Obtaining a complex cross-correlation parameter comprising a phase angle value, and wherein obtaining said at least one TDOA parameter comprises obtaining said at least one TDOA parameter at least partly based on said phase angle value.

Clause 13. Method of Clause 12, wherein obtaining said at least one TDOA parameter comprises performing a selective calculation comprising the steps of:

-Obtaining a natural number N of iterations to be performed by the selective calculation; While N>0, Performing the steps of:

-Obtaining an Nth input value by adding P number of cycles to the obtained phase angle value of the obtained complex correlation parameter;

-Obtaining an Nth TDOA parameter value and an Nth remainder parameter value by performing an Orbital Determination Algorithm to the Nth input value;

-Subtracting 1 from N;

-Determining the input value resulting in the lowest remainder, and -Obtaining the at least two TDOA parameters by adding said lowest remainder to the at least one TDOA obtained from a phase angle value of the obtained complex cross correlation parameter. Clause 14. System for determining at least two Time Difference of arrival (TDOA) parameters suitable for determining an orbit of at least one target satellite having a transmitting frequency, the system comprising:

-at least three receivers for obtaining a radiofrequency signal based on at least one portion of a signal transmitted by at least one target satellite;

-means for obtaining In-phase and Quadrature signals of each of the RF signals,

-means for providing a Master Clock signal;

-a signal synchronization module for synchronizing each of the received signals with respect to said Master Clock signal, and

-processing means, wherein the processing means are configured to

-Define at least two different pairs of receivers of the at least three receivers, and

-For each defined pair of receivers:

-Obtaining a cross-correlation parameter between the obtained In-phase and Quadrature signals corresponding to each receiver within the defined pair of receivers; and

-Obtaining at least one TDOA parameter for the defined pair of receivers at least partly based on said cross-correlation parameter.

Clause 15. The system of Clause 14, wherein performing the selective calculation comprise the steps of: • Obtaining a natural number N of iterations to be performed by the selective calculation;

While N>0, Performing the steps of:

-Obtaining at least two Nth input values by adding a number of cycles P to each of the obtained phase angle values of the obtained complex correlation parameters for each receiver pair, wherein P can have a different value for each receiver pair;

-Obtaining at least two TDOA parameters for the Nth iteration, one from each previously obtained phase angle value;

-Obtaining an orbit element set output value and an Nth remainder parameter value by performing an Orbital Determination Algorithm on the Nth input values;

-Subtracting 1 from N; -Determining the input P values resulting in the lowest remainder parameter value, and

-Obtaining the at least two TDOA parameters for each receiver by adding the number of cycles P which generated the lowest remainder parameter value to the at least two phase angle values of the obtained complex cross-correlation parameters for each receiver.

Clause 16. System of Clause 14 or Clause 15, wherein the at least three receivers comprise antennas configured for receiving signals in the radiofrequency spectrum.

Clause 17. System of any of clauses 13-16, further comprising means for obtaining an optical signal from the at least one portion of the signal transmitted by the at least one target satellite, and means for obtaining an RF signal from said optical signal.

Clause 18. System of Clause 17, wherein the means for obtaining an optical signal from the at least one portion of the signal transmitted by the at least one target satellite comprise a fiber optic medium. Clause 19. System according to the system of any of clauses 13-18, wherein the antennas are configured for receiving signals in K, Ku, C, L and/or S RF bands.

Clause 20. System according to Clause 19, wherein the obtained In-Phase signals comprise baseband In-Phase signals.

Clause 21. System according to any of Clauses 13-20, wherein the processing means comprise at least one field-programmable gate array (FPGA).

Clause 22. System according to any of Clauses 13-21 , wherein the processing means comprise one or more of a central processing unit (CPU), a graphical processing unit (GPU), a configurable processor, a FPGA, and a microprocessor.

Clause 23. Method according to any of the clauses 1-13, wherein the at least three receivers comprise antennas configured for receiving signals in the radiofrequency spectrum.

Clause 24. Method according to any of the clauses 1-13 and 23, further comprising the step of associating the at least one TDOA parameter with a time stamp/epoch.

Clause 25. Processor configured with instructions to carry out one or more of the methods according to clauses 1-13 and 23-24.

Clause 26. Processor according to Clause 25, wherein the processor comprises one or more of a FPGA, microprocessor, central processing unit (CPU), and Graphical Processing Unit.

Clause 27. A computer program product comprising program instructions for causing a computing system to perform any one or more of the methods of claims 1-13 and 23- 24.

Clause 28. The computer program product of Clause 27, embodied on a storage medium.

Clause 29. The computer program product of Clause 27, carried on a carrier signal. Clause 30. The method of Cause 1 , wherein the step of obtaining an RF signal corresponding to the at least one portion of the transmitted signal of each target satellite, further comprises the step of converting the received analog signal into an optical signal without any prior digitization of the received analog signal.

Clause 31. The method of Clause 30, wherein the step of obtaining an RF signal corresponding to the at least one portion of the transmitted signal of each target satellite, further comprises the step of amplifying the received analog signal prior to converting the analog signal into an optical signal.

Clause 32. The system of Clause 14, wherein the at least three receivers for obtaining a radiofrequency signal based on at least one portion of a signal transmitted by at least one target satellite comprise an optical transmitter for converting the at least one portion of a signal transmitted by at least one target satellite to an optical signal.

Clause 33. The system of Clause 32, wherein the at least three receivers for obtaining a radiofrequency signal based on at least one portion of a signal transmitted by at least one target satellite further comprise a low noise amplifier for amplifying the at least one portion of a signal transmitted by at least one target satellite prior to converting the analog signal to an optical signal.

Clause 34. The system of Clause 14, wherein the at least three receivers for obtaining a radiofrequency signal based on at least one portion of a signal transmitted by at least one target satellite comprise a low noise amplifier for amplifying the at least one portion of a signal transmitted by at least one target satellite, and an optical transmitter for converting the amplified at least one portion of a signal transmitted by at least one target satellite to an optical signal.

Although only a number of examples have been disclosed herein, other alternatives, modifications, uses and/or equivalents thereof are possible. Furthermore, all possible combinations of the described examples are also covered. Thus, the scope of the present disclosure should not be limited by particular examples, but should be determined only by a fair reading of the claims that follow. If reference signs related to drawings are placed in parentheses in a claim, they are solely for attempting to increase the intelligibility of the claim, and shall not be construed as limiting the scope of the claim.