Patent Description:
The present invention, in some embodiments thereof, relates to radiolocation and, more particularly, but not exclusively, to a method and system for estimating the location of a source transmitting a spectral-diversity signal.

Mobile communications has changed the way people communicate and mobile phones have been transformed from a luxury item to an essential part of every day life. The use of mobile phones is today dictated by social situations, rather than hampered by location or technology. Aside for voice connections, the mobile Internet continues to filter further into the fabric of everyday life.

Advanced cellular networks have been specifically designed to fulfill demands of the mobile Internet. As these services grow in popularity and usage, factors such as cost efficient optimization of network capacity and quality of service have become desired. These factors may be achieved with careful network planning and operation, improvements in transmission methods, and advances in receiver techniques. In this regard, networks based on wideband code division multiple access (WCDMA) technology make the delivery of data to end users a feasible option.

Locating sources within a wireless communication system enables features such as location-based services and location-aware management. A number of techniques have been proposed for radiolocation. These can be categorized as either direct radiolocation techniques or indirect radiolocation techniques. In the direct radiolocation techniques, also known as Direct Position Determination (DPD) techniques, the location of the source is estimated in one step, directly from the received signals. Indirect radiolocation is done in two stages. In a first stage, signal propagation parameters, such as Received Signal Strength Indication (RSSI), Time of Arrival (TOA) and Time Difference Of Arrival (TDOA) between different receiving stations are estimated. In a second stage, the location is estimated based on the parameters obtained in the first stage.

Some techniques are based on an exact knowledge of the transmitted signal waveform. These techniques are referred to as "known-signal techniques. " Other techniques do not utilize such information, and are referred to as "unknown-signal techniques. " Generally speaking, known-signal techniques perform better than unknown signal techniques, and direct techniques perform better than indirect techniques.

Document XP011567373, POURHOMAYOUN MOHAMMAD ET AL: "Distributed computation for direct position determination emitter location", discloses how to use a cross-ambiguity function for computing a so-called cross ambiguity matrix.

According to an aspect of some embodiments of the present invention, there is provided a system for estimating a location of a source transmitting a spectral-diversity signal having a known form but at least one unknown parameter. The system comprises: a plurality of signal receiving circuits, each configured to receive the spectral-diversity signal and to compute, for each signal carrier component in the spectral-diversity signal, a cross-ambiguity function based on the known form and on the received spectral-diversity signal. The system further comprises a central processor circuit configured to receive data pertaining to a plurality of cross-ambiguity functions computed by the signal receiving circuits, and to estimate the location of the source, wherein the estimation comprises calculating an extremum of an objective function constructed from all the cross-ambiguity functions,.

the estimation is an indirect estimation, and the central processor circuit is configured to calculate, based on the extremum, Time Difference Of Arrival (TDOA) values between pairs of signal receiving circuits, and to estimate the location based on the TDOA values.

According to some embodiments of the invention, the system comprises a reference source transmitting a reference spectral-diversity signal, wherein each signal receiving circuit is configured to compute a cross-ambiguity function corresponding to signal carrier components in the reference spectral-diversity signal, and wherein the central processor circuit is configured to correct a timing offset among the signal receiving circuits based on the cross-ambiguity function.

According to some embodiments of the invention for each pair of signal receiving circuits, the objective function comprises a matrix having an entry for each of cross-ambiguity function as computed by each signal receiving circuit of the pair.

According to some embodiments of the invention, the estimation is a direct estimation, and the central processor circuit is configured to estimate the location directly from the extremum.

According to some embodiments of the invention, the central processor circuit is configured to access a database storing a digital terrain map describing height data of sources and to extract from the map a height of the source, and wherein the estimation based on the extremum is executed in two spatial dimensions and combined with the extracted height.

According to an aspect of some embodiments of the present invention, there is provided a method of estimating a location of a source transmitting a spectral-diversity signal having a known form but at least one unknown parameter. The method comprises: receiving the spectral-diversity signal by a plurality of signal receiving circuits; computing, for each signal carrier component of the spectral-diversity signal and each signal receiving circuit, a cross-ambiguity function based on the known form and on the received signal carrier component. According to some embodiments of the invention, the method comprises estimating the location of the source, wherein the estimation comprises calculating an extremum of an objective function constructed from all the cross-ambiguity functions.

According to some embodiments of the invention, the estimation is an indirect estimation, which comprises calculating, based on the extremum, TDOA values between pairs of signal receiving circuits, and estimating the location based on the TDOA values.

According to some embodiments of the invention, the method comprises transmitting a reference spectral-diversity signal, computing a cross-ambiguity function corresponding to signal carrier components in the reference spectral-diversity signal, and correcting a timing offset among the signal receiving circuits based on the cross-ambiguity function.

According to some embodiments of the invention, the method comprises accessing a database storing a digital terrain map describing height data of sources and extracting from the map a height of the source, wherein the estimation based on the extremum is executed in two spatial dimensions and combined with the extracted height.

According to some embodiments of the invention for each pair of signal receiving circuits, the objective function comprises a multiplication of N by <NUM> matrices, each being constructed from a first plurality of cross-ambiguity functions corresponding to a first signal receiving circuit of the pair and a second plurality of cross-ambiguity functions corresponding to a second signal receiving circuit of the pair, wherein the N is a number of the signal carrier components.

According to some embodiments of the invention, the estimation is executed directly from the extremum.

According to some embodiments of the invention, the objective function comprises a multiplication of N by K matrices, each being constructed from K pluralities of cross-ambiguity functions respectively corresponding to K signal receiving circuits, wherein the N is a number of the signal carrier components.

According to some embodiments of the invention, the unknown parameter(s) comprises a phase of each signal carrier component.

According to some embodiments of the invention, the unknown parameter(s) comprises amplitude of each signal carrier component.

According to some embodiments of the invention, the unknown parameter(s) comprises a clock drift characterizing the source.

According to some embodiments of the invention, the unknown parameter comprise a phase of each signal carrier component, amplitude of each signal carrier component, and at least one additional parameter other than the phase and the amplitude.

According to some embodiments of the invention, the known form comprises a linear chirp form.

Reference is now made to <FIG> which is a schematic illustration of a system <NUM> suitable for estimating a location of a source <NUM> transmitting a spectral-diversity signal <NUM>. Source <NUM> is optionally and preferably static, but embodiments in which source <NUM> is mobile are also contemplated. The signal <NUM> is shown as two arrows in <FIG> to illustrate that it propagates in space (for example, along a spherical wave-front).

As used herein, a "spectral-diversity signal" refers to a signal having a set of signal carrier components each carried by a different carrier, wherein the carrier frequencies vary among different signal carrier components in the set according to a predetermined time-frequency schedule.

Typically, the time-frequency schedule does not specify absolute times and frequencies, but only differences between times and differences between frequencies. Nevertheless, embodiments in which the time-frequency schedule includes absolute times and frequencies are also contemplated.

Representative examples of spectral-diversity signals suitable for the present embodiments include, without limitation, the, GSM standard, the standard offered by an alliance named LoRa™ and the standard offered by the SIGFOX company.

Other examples include, without limitation, signals of Wireless Local Access Network (WLAN), such as, but not limited to, IEEE <NUM>, IEEE <NUM>. 11a-g, IEEE <NUM>. <NUM>, and derivatives thereof.

Spectral-diversity signals are employed extensively in various communication systems. In such systems, each signal carrier component in the set typically has a narrow bandwidth for a relatively short time. However, the collection of carrier frequencies employed by the signals form an effective bandwidth that is relatively wide, and that in any event is wider than the bandwidth of each individual signal in the set.

Typical bandwidth values of each signal carrier component of a spectral-diversity signal is from about <NUM> to about <NUM>. The effective bandwidth spanned by the collection of carrier frequencies employed by the spectral-diversity signal typically extend from about <NUM> to about <NUM>.

A typical duration of each signal carrier component of a spectral-diversity signal is from about <NUM> msec to about <NUM> msec. The overall duration of a spectral-diversity signal is typically at least <NUM> second or at least <NUM> seconds. In some embodiments the spectral-diversity signal is transmitted continuously.

It was realized by the present Inventor that such a wide effective bandwidth can be used for improving the accuracy of source localization. This is because the accuracy of location increases with the bandwidth. The present Inventor found that even though a set of spectral-diversity signals may in some cases define a sparse spectrum, namely a spectrum that is not continuous and that may be devoid of some frequencies, this is sufficient for improving the accuracy of radiolocation.

The signal carrier components in the set <NUM> typically have a known baseband form denoted herein by sn(t), n=<NUM>, <NUM>,. , N, where N is the number of different signal carrier components in the set <NUM>. Without loss of generality and to ensure correctness of the equations in this description, it is assumed that for each n <MAT> where integral taken over the duration of the nth signal.

Also contemplated are embodiments in which one or more parameters of the signal sn(t) are unknown. For example, a case where the signal carrier components sn(t) are linear frequency modulated (chirps) but the exact rate of change in a chirp is not known. Another example is a case in which the clock rate of the transmitter has an unknown drift compared with the clock rate of the receiver.

The radiofrequency signals that are actually transmitted by source <NUM> based on the baseband forms sn(t) have amplitude and phase which are not necessarily the same for different signal carrier components and are typically unknown to system <NUM>. For example, in some embodiments of the present invention the phase of each signal carrier component is unknown, in some embodiments of the present invention the amplitude of each signal carrier component is unknown, and in some embodiments of the present invention both the phase and the amplitude of each signal carrier component are unknown.

In a representative exemplary embodiment, signal sn(t) has a chirp form, such as, a linear chirp form.

System <NUM> typically comprises a plurality of signal receiving circuits <NUM>, each configured to receive the diversity signals <NUM> and to responsively generate a representation of at least a portion of these signals. Signal receiving circuits <NUM> are optionally and preferably static, but embodiments in which there is a relative motion of circuits <NUM> relative to source <NUM> are also contemplated. Two signal receiving circuits are illustrated in <FIG>, but it is to be understood that the present embodiments contemplate any number of signal receiving circuits. The signal receiving circuits may be physically separate receivers, or receivers tuned to different carrier frequencies at different times, or they may be implemented as a single wideband receiver followed by appropriate digital processing.

Preferably, each of signal receiving circuits <NUM> generates a signal representation for each of the signal carrier components it receives from source <NUM>. The representations generated by circuits <NUM> are denoted herein by xn(t), n=<NUM>, <NUM>,. , N, where N is the number of different representations. When signal receiving circuits <NUM> generate a signal representation for each of the signal carrier components it receives from source <NUM>, the number of representations N is the same as the number of different signal carrier components in the set <NUM>. Typically, each representation xn(t) is a complex signal representation, for example, a complex representation having in-phase component and a quadrature component.

One or more (e.g., each) of signal receiving circuits <NUM> can comprise a representation generating circuit <NUM> that generates the representation xn(t), and a digital signal processing circuit <NUM> that process the representation as further detailed hereinbelow.

Representation generating circuit <NUM> can generate xn(t) in more than one way. In some embodiments of the present invention circuit <NUM> is embodied as a wideband receiver that is sensitive to all the signal carrier components in the set. For example, when all the signals occupy parts of a <NUM> band, then a <NUM> wideband receiver may be used. In these embodiments, circuit <NUM> employs an analog to digital converter (ADC) that digitizes the received diversity signal according to a predetermined sampling rate (e.g., <NUM> Msamples/sec in-phase and <NUM> Msamples/sec quadrature for a <NUM> receiver), and a digital filter bank circuit having a plurality of digital filters each being characterized by a predetermined and different frequency band. The digital filter bank receives the digitized diversity signal and separates it to a plurality of digital representation signals, each being characterized by the frequency band of the respective filter of the bank. The digital filter bank circuit can employ a Fourier transform [e.g., fast Fourier transform (FFT)] and may optionally employ a weighted overlap-add (WOLA) procedure.

In some embodiments of the present invention circuit <NUM> is embodied as a plurality of receivers, each being sensitive to a different signal carrier component of the set. The bandwidth of receiver preferably matches the expected bandwidth of the signal carrier components, e.g., a bandwidth of about <NUM> when each signal carrier component occupies a <NUM> band. In these embodiments, each received signal is transferred to a separate ADC that that digitizes the received signal carrier component according to a predetermined sampling rate (e.g., about <NUM> ksamples/sec in-phase and <NUM> ksamples/sec quadrature for the aforementioned example).

Signal processing circuits <NUM> preferably comprise, or are in communication with, a memory medium <NUM> that stores the forms sn(t). In various exemplary embodiments of the invention signal processing circuit <NUM> computes, for each signal carrier component, a cross-ambiguity function Rn based on the known form sn(t) provided by memory medium <NUM> and on the received signal carrier component (more preferably the representation xn provided by circuit <NUM>). The cross-ambiguity function Rn is typically a time-frequency cross-correlation between sn(t) and xn(t). For example, Rn can be defined, for any time delay d and any frequency shift Ω according to the following equation: <MAT> where the superscripts symbol * denotes a complex conjugate. <NUM> is particularly useful in embodiments in which sn(t) is known (but the phase and the amplitude of the radiofrequency signal based on it are unknown). When one or more additional parameters θ of each baseband signal sn(t) are unknown, the Rn can be defined with the additional unknown parameter as an additional argument, for example, <MAT>.

A representative example of a parameter θ is a chirp rate of sn(t). For example when sn(t) is specified as a linear chirp of known duration T, but with an unknown chirp rate, it may be written as sn(t)=exp(-jθt<NUM>/<NUM>) for |t|<T/<NUM>.

As explained in greater detail below, the arguments of the function Rn are used as optimization variables.

Rn can be computed by circuit <NUM> for any value of the variables d and Ω, using samples of xn(t) and sn(t). This can be done either directly in the time domain, or indirectly in the frequency domain, for example, using a Fourier Transform or FFT.

System <NUM> optionally and preferably comprises a central processor circuit <NUM> that receives from circuits <NUM> data pertaining to the cross-ambiguity functions Rn, and estimates the location of source <NUM>. The data transferred from circuits <NUM> to central processor circuit <NUM> can be of any types that allows central processor circuit <NUM> to obtain the values of the functions Rn, for a plurality of sets of variables (e.g., a plurality of sets {d, Ω}, or a plurality of sets {d, Ω, θ}).

While the embodiments above have been described with a particular emphasis to a situation on which the optimization variables include d and Ω, this need not necessarily be the case. For example, in some embodiments of the present invention the variable Ω is either known or can have an arbitrarily fixed value (e.g., Ω=<NUM>) for all values of n and for all the circuits <NUM>. In these embodiments, the optimization variable or variables do not include Ω. A representative example of such a situation is when the radio frequencies of the signals are known precisely or when the baseband signal sn(t) has a linear chirp form, and thus perfect time-frequency ambiguity.

The estimation performed by central processor circuit <NUM> typically comprises calculating an extremum (maximum or minimum) of an objective function constructed from all the cross-ambiguity functions received from circuits <NUM>. Representative examples of objective functions suitable for the present embodiments are provided hereinbelow. The estimation can be indirect estimation in which case central processor circuit <NUM> calculates, based on the extremum of the objective function, TDOA values between pairs of signal receiving circuits <NUM>, and then estimates the location based on the calculated TDOA values, for example, by least-squares fitting of the TDOA values to distance differences from source <NUM> to circuits <NUM>. The estimation can alternatively be a direct estimation, in which case central processor circuit <NUM> to estimates the location directly from the extremum.

Central processor circuit <NUM> typically provides the location of the source <NUM> as a three-dimensional spatial vector z consisting, for example of latitude, longitude and altitude values, wherein at least one, or more preferably at least two of the components of this vector are estimated based on the extremum of the objective function. When central processor circuit <NUM> estimates two components of z based on the extremum of the objective function, these components typically span a horizontal plane (e.g., perpendicular to the gravitation direction). In these embodiments, central processor circuit <NUM> accesses a database storing a digital terrain map describing height data of sources, extracts from the map the third dimension (e.g., height) of the source, and combine the estimated components with the extracted component to form the three-dimensional vector z. The database storing the digital terrain map can be recorded on a memory medium <NUM> accessible by circuit <NUM>. When central processor circuit <NUM> estimates all three components of z based on the extremum of the objective function, there is no need to extract a component from a digital terrain map. Use of a digital terrain map is advantageous since it reduces the dimensionality of the variable space.

In some embodiments of the present invention system <NUM> comprises one or more reference sources <NUM> transmitting a spectral-diversity signal <NUM>, having a predetermined form. Reference source(s) <NUM> is optionally and preferably static, but embodiments in which there is a relative motion of source(s) <NUM> relative to source <NUM> are also contemplated. The reference spectral-diversity signal <NUM> need not to have the same form as the known form sn(t). Source <NUM> is at a predetermined distance from each of the signal receiving circuits <NUM> so that the expected propagation time of diversity signal <NUM> from source <NUM> to each of circuits <NUM> can be obtained by dividing the distance between source <NUM> and the respective circuit <NUM> by the speed of the signal (typically the speed of light).

Signal receiving circuits <NUM> receive reference signal <NUM> and compute cross-ambiguity functions Rn corresponding to reference diversity signal <NUM>, typically in the same manner as described above with respect to signal <NUM>. Thus, for example, circuits <NUM> can generate a representation (e.g., a complex in-phase and quadrature representation) of the received reference signal and compute a time-frequency cross-correlation between the representation of the received reference signal and the form of the reference signal.

The cross-ambiguity functions Rn of the signal carrier components in the reference spectral-diversity signal set <NUM>, can be used for correcting a timing offset among the signal receiving circuits <NUM>. For example, central processor circuit <NUM> can estimate TDOA values between pairs of signal receiving circuits <NUM> based on the reference diversity signal <NUM>, and compare the estimated TDOA values to the difference between the expected propagation times of signals <NUM> from source <NUM> to the respective signal receiving circuits <NUM>. The difference between the expected and estimated TDOA values can be used by the processor circuit <NUM> to time-shift the cross-ambiguity functions received from the signal receiving circuits thus correcting timing offset among the signal receiving circuits.

<FIG> is a flowchart diagram of a method of estimating a location of a source (e.g., source <NUM>) transmitting diversity signals (e.g., signals <NUM>) according to some embodiments of the present invention. It is to be understood that, unless otherwise defined, the operations described hereinbelow can be executed either contemporaneously or sequentially in many combinations or orders of execution. Specifically, the ordering of the flowchart diagrams is not to be considered as limiting. For example, two or more operations, appearing in the following description or in the flowchart diagrams in a particular order, can be executed in a different order (e.g., a reverse order) or substantially contemporaneously. Additionally, several operations described below are optional and may not be executed.

The method begins at <NUM> and optionally and preferably continues to <NUM> at which the diversity signals are received by a plurality of signal receiving circuits (e.g., circuits <NUM>). The method can continue to <NUM> at which a cross-ambiguity function (e.g., the function Rn) is computed for each diversity signal and each signal receiving circuit, based on the known form and on the received diversity signal, as further detailed hereinabove. In some embodiments of the present invention, the method proceeds to <NUM> at which a reference diversity signal (e.g., signal <NUM>) is transmitted, as further detailed hereinabove. In these embodiments, the method can continue to <NUM> at which a cross-ambiguity function corresponding to the reference diversity signal is computed, and to <NUM> at which a timing offset among the signal receiving circuits is corrected as further detailed hereinabove.

In some embodiments of the present invention the method continues to <NUM> at which a database storing a digital terrain map describing height data of sources is accessed for extracting the third component (e.g., height) of the location vector z as further detailed hereinabove.

The method can then continue to <NUM> at which the location of the source is estimated, as further detailed hereinabove.

Following is a description of objective functions suitable for the present embodiments.

When an indirect estimation is employed, the objective function for each pair of signal receiving circuits optionally and preferably comprises a matrix P of dimensions N×<NUM>, wherein P has an entry (matrix-element) for each of the functions Rn as computed by each signal receiving circuit of the pair. In any of the embodiments of the invention in which indirect estimation is employed it is preferred that each matrix-element P has a form exp(-jωnf(d))Rn, where f is a function, preferably a linear function, of the time-delay variable d. For example, f(d) can be set to ±d/<NUM>. In preferred embodiments, for matrix-elements of P that relate to one signal receiving circuit of the pair the functions Rn are calculated with a positive time-delay variable d, and for matrix-elements of P that relate to the other signal receiving circuit of the pair the functions Rn are calculated with a negative positive time-delay variable d.

A representative example of an expression suitable for a matrix-element corresponding to the kth pair of signal receiving circuits, for the embodiments in which the functions Rn are computed for the sets {d, Ω}, is: <MAT> where, n=<NUM>, <NUM>,. N and l=<NUM>,<NUM>, where k(<NUM>) and k(<NUM>) denote the individual signal receiving circuits of the kth pair, where Rk(<NUM>)n is the cross-ambiguity function Rn as computed by the k(<NUM>)-th signal receiving circuit, and where τ is a temporal optimization variable.

A representative example of an expression suitable for a matrix-element corresponding to the kth pair of signal receiving circuits, for the embodiments in which Ω can have an arbitrary value (e.g., when signals <NUM> have linear chirp form), is: <MAT>.

A representative example of an expression suitable for a matrix-element corresponding to the kth pair of signal receiving circuits, for the embodiments in which the functions Rn are computed for the sets {d, Ω, θ}, is: <MAT>.

A representative example of an expression suitable for a matrix-element corresponding to the kth pair of signal receiving circuits, for the embodiments in which the functions Rn are computed for the sets {d, θ} (e.g., when signals <NUM> have linear chirp form), is: <MAT>.

A representative example of an expression suitable for a matrix-element corresponding to the kth pair of signal receiving circuits, for the embodiments in which the clock drift characterizing the source is unknown and functions Rn are computed for the sets {d, Ω}, is: <MAT> where γ is the unknown clock drift and tn is the center time of the nth diversity signal.

A representative example of an expression suitable for a matrix-element corresponding to the kth pair of signal receiving circuits, for the embodiments in which the clock drift characterizing the source is unknown and Ω can have an arbitrary value (e.g., when signals <NUM> have linear or non-linear chirp form), is: <MAT>.

A representative example of an expression suitable for a matrix-element corresponding to the kth pair of signal receiving circuits, for the embodiments in which the clock drift characterizing the source is unknown and functions Rn are computed for the sets {d, Ω, θ}, is: <MAT>.

A representative example of an expression suitable for a matrix-element corresponding to the kth pair of signal receiving circuits, for the embodiments in which the clock drift characterizing the source is unknown and functions Rn are computed for the sets {d, θ} (e.g., when signals <NUM> have linear or non-linear chirp form), is: <MAT>.

The objective function for the kth pair can optionally and preferably be defined as the highest eigenvalue of the multiplication of the matrix P by its Hermitian conjugate PH. Formally, the objective function for the kth pair can be written as: <MAT> where the notation ||A|| is used to denote the highest eigenvalue. The TDOA of the kth pair can then be estimated as the value of d in the set {v} which maximizes Fk({v}), where {v} denotes the set of optimization variables used to define the matrix P (e.g. sets {d, Ω, θ}).

The calculation of the matrix P and the solution of the optimization problem is preferably repeated for at least a few (e.g., all) the pairs of circuits <NUM>. Thereafter, the location can be estimated based on the calculated TDOA values as further detailed hereinabove.

When a direct estimation is employed, the objective function optionally and preferably comprises a matrix S having an entry for each of the functions Rn as computed by each signal receiving circuit. Thus, the difference between the embodiments in which direct estimation is employed and the embodiments in which indirect estimation is employed, is that when the estimation is indirect, there is a plurality of matrices P, each matrix corresponding to one pair of signal receiving circuit, whereas when the estimation is direct, there is a single matrix S that correspond to more than two signal receiving circuits, more preferably all the signal receiving circuits, of system <NUM>. Thus, the matrix S is preferably an N by K matrix, where K is the number of signal receiving circuits of system <NUM>.

In any of the embodiments of the invention in which direct estimation is employed it is preferred that each matrix-element P has a form exp(-jωnDk(z))Rn, where Dk(z) is the propagation time of the signal from source <NUM> to the kth signal receiving circuit, and can be expressed as the (unknown) distance from source <NUM> to the kth signal receiving circuit divided by the speed of light. When the functions Rn are computed using the time-delay variable d, Dk(z) is preferably substituted for the time-delay variable d during the location estimation.

A representative example of an expression suitable for a matrix-element of S, for the embodiments in which the functions Rn are computed for the sets {d, Ω}, is: <MAT> where Rnk is the cross-ambiguity function as computed by the kth signal receiving circuit.

A representative example of an expression suitable for a matrix-element of S, for the embodiments in which Ω can have an arbitrary value (e.g., when signals <NUM> have linear or non-linear chirp form), is: <MAT>.

A representative example of an expression suitable for a matrix-element of S, for the embodiments in which the functions Rn are computed for the sets {d, Ω, θ}, is: <MAT>.

A representative example of an expression suitable for a matrix-element of S, for the embodiments in which the functions Rn are computed for the sets {d, θ} (e.g., when signals <NUM> have linear or non-linear chirp form), is: <MAT>.

A representative example of an expression suitable for a matrix-element of S, for the embodiments in which the clock drift characterizing the source is unknown and functions Rn are computed for the sets {d, Ω}, is: <MAT>.

A representative example of an expression suitable for a matrix-element of S, for the embodiments in which the clock drift characterizing the source is unknown and Ω can have an arbitrary value (e.g., when signals <NUM> have linear or non-linear chirp form), is: <MAT>.

A representative example of an expression suitable for a matrix-element of S, for the embodiments in which the clock drift characterizing the source is unknown and functions Rn are computed for the sets {d, Ω, θ}, is: <MAT>.

A representative example of an expression suitable for a matrix-element of S, for the embodiments in which the clock drift characterizing the source is unknown and functions Rn are computed for the sets {d, θ} (e.g., when signals <NUM> have linear or non-linear chirp form), is: <MAT>.

The objective function can optionally and preferably be defined as the highest eigenvalue of the multiplication of the matrix S by its Hermitian conjugate SH. Formally, the objective function can be written as: <MAT> where {v} denotes the set of optimization variables used to define the matrix S. When a digital terrain map is employed, the set {v} includes two components of z and one or more elements of the set {τ, Ω, γ, θ}. When a digital terrain map is not employed, the set {v} includes three components of z and one or more elements of the set {τ, Ω, γ, θ}.

The location vector z (or components thereof) is optionally and preferably estimated by maximization of the objective function C over the set {v}. This can be done, for example, by coarse grid search over the relevant domains of the variables in {v}, followed by an iterative maximization algorithm such as, but not limited to, the Nelder-Mead simplex method for fine maximum computation, as described, e.g., in <NPL>.

Stations <NUM> can be deployed in any spatial arrangement. Preferably, the stations are deployed such as to achieve high received power and a variety of reception directions. For example, if the purpose of a system is to locate sources confined to an area which has a square shape, then it is preferred to deploy the stations so they are evenly distributed along the perimeter of this square, and to deploy a reference transmitter in the center of the square area.

Accordingly, it is intended to embrace all such alternatives, modifications and variations that fall within the broad scope of the appended claims.

Claim 1:
A system (<NUM>) for estimating a location of a source (<NUM>) transmitting a spectral-diversity signal (<NUM>) having a known form but at least one unknown parameter, the system (<NUM>) comprising:
a plurality of signal receiving circuits (<NUM>), each configured to receive the spectral-diversity signal (<NUM>) and to compute, for each signal carrier component in the spectral-diversity signal, a cross-ambiguity function using said known form and said received spectral-diversity signal; and
a central processor circuit (<NUM>) configured to receive data pertaining to a plurality of cross-ambiguity functions computed by said signal receiving circuits (<NUM>), and to estimate the location of the source, wherein said estimation comprises calculating an extremum of an objective function constructed from all said cross-ambiguity functions;
wherein said estimation is an indirect estimation, and said central processor circuit (<NUM>) is configured to calculate, based on said extremum, TDOA values between pairs of signal receiving circuits (<NUM>), and to estimate the location based on said TDOA values.