Method and system for determining location and velocity of electromagnetic emitters using doppler frequency measurements

A method for determining the position and velocity of an emitter of an electromagnetic signal moving with a substantially constant but unknown velocity and having a substantially constant but unknown frequency, the method comprising the steps of:

• (A) moving two receivers with substantially identical velocities along parallel, substantially straight-line trajectories, each said receiver being responsive to all signals lying in the spectral band of frequencies that are Doppler-shifted by the motion of the source in the receiver's frame of reference and active at all times;
• (B) receiving signals by said receiver;
• (C) for each receiver, measuring a Doppler-shifted frequency of one of said emitted signals received at each of four points along its trajectory, and measuring inter-measurement distances or time spans for each receiver's set of frequency measurements, both receivers having the same sum of inter-measurement distances or time spans;
• (D) for each receiver, calculating two ratios of frequency differences, each ratio involving three frequencies for frequency measurements at four points on the receiver trajectory, there being four possible triples of frequency measurements, each ratio being a function of the bearing angle between the closing velocity vector and the receiver-to-source line-of-sight in the receiver frame of reference at each of the three measurement points or times in the three measurement triples used for the ratio of frequency differences;
• (E) for each receiver, calculating a candidate set of range and closing velocity combinations from the ratios of frequency differences and the inter-measurement distances or time spans;
• and
• (F) resolving ambiguities by finding the closing velocity vector common to both solution fans and lying exactly within the solution fans' boundaries.

A method for determining a position and a velocity of an emitter of an electromagnetic signal moving with a substantially constant but unknown velocity, said signal having a substantially constant but unknown frequency, the method comprising the steps of:

• (A) moving a single receiver at a substantially constant velocity along a first substantially straight-line trajectory, said receiver being responsive to all frequencies in a spectral band of frequencies that are Doppler-shifted by the motion of the source in the receiver's reference frame, and said receiver being active at all times;
• (B) measuring the Doppler-shifted frequency of said received signal at each of at least four points along the receiver's trajectory and measuring the receiver's inter-measurement distances or time spans;
• (C) calculating two ratios of frequency differences, each ratio involving three frequencies and each ratio being a function of a bearing angle between the closing velocity vector and a receiver-to-source line-of-sight in a receiver frame of reference at each of said three measurement points or times in said measurement ratios used for the ratio of frequency differences;
• (D) calculating a candidate set of range and closing velocity combinations from said ratios of frequency differences and said inter-measurement distances or time spans;
• (E) maneuvering said receiver to a second trajectory which is substantially parallel to said first trajectory and moving said receiver with the same velocity as along said first trajectory and along a second substantially straight-line trajectory;
• (F) measuring the Doppler-shifted frequency of the received signal at each of at least four points along the receiver's second trajectory and measuring the receiver's inter-measurement distances or time spans;
• (G) calculating two ratios of frequency differences, each ratio involving three frequencies and each ratio being a function of a bearing angle between a closing velocity vector and a receiver-to-source line-of-sight in said receiver frame of reference at each of said three measurement points or times in said measurements used for said ratio of frequency differences;
• (H) calculating a candidate set of range and closing velocity combinations from the ratios of frequency differences and the inter-measurement distances or time spans;
• (I) creating a phantom set of at least four measurements by iterating forward in time said solution fan derived from the measurement set said receiver collected on said first trajectory, said phantom measurement set having a first frequency measurement made to coincide in absolute time with said first frequency measurement of said second set of at least four frequency measurements;
• and
• (J) resolving ambiguities by finding the closing velocity vector common to both solution fans and lying exactly within the solution fans' boundaries.

A system for determining the position of a stationary emitter of an electromagnetic signal having a substantially constant but unknown frequency, such system comprising:

• a receiver of electromagnetic signals that is responsive to all signals lying in a spectral band of frequencies that are Doppler-shifted by a motion of said receiver relative to the source, said receiver being active at all times;
• means for moving said receiver along a substantially straight-line trajectory;
• means for measuring a Doppler-shifted frequency of a received electromagnetic signal at each of at least three points along said trajectory;
• means for calculating two ratios of three possible Doppler-shifted frequency pairs, each ratio being a function of a bearing angle between a receiver trajectory and a receiver-to-source line-of-sight at the place or time of the measurement of said first frequency of said ratio and the bearing angle at a place or time of the measurement of the second frequency of said ratio;
• and
• means for calculating the position of said emitter relative to said receiver from said frequency ratios and said inter-measurement distances.

A system for determining a position and a velocity of an emitter of an electromagnetic signal moving with a substantially constant but unknown velocity and having a substantially constant but unknown frequency, the system comprising:

• two receivers, each said receiver responsive to all signals lying in the spectral band of frequencies that are Doppler-shifted by the motion of the source in the receiver's frame of reference and being active at all times;
• means for moving said receivers with substantially identical velocities along parallel, substantially straight-line trajectories;
• for each of said two receivers, means for measuring a Doppler-shifted frequency of an emitted signal received at each of at least four points along its respective trajectory, and means for measuring inter-measurement distances (or time spans) for each receiver's set of frequency measurements;
• for each of said two receivers, means for calculating two ratios of frequency differences, each ratio involving three frequencies, and each ratio being a function of a bearing angle between said closing velocity vector and said receiver-to-source line-of-sight at each of said three measurement points or times in said measurements used for said ratios of frequency differences;
• for each of said two receivers, means for calculating a candidate set of range and closing velocity combinations from said ratios of frequency differences and said inter-measurement distances or time spans;
• and
• means for resolving ambiguities by finding a closing velocity vector common to both solution fans and lying exactly within the boundaries of said solution fans.

A system for determining, with a single receiver, a position and velocity of an emitter of an electromagnetic signal moving with a substantially constant but unknown velocity and having a substantially constant but unknown frequency, such system comprising:

• a single receiver, said receiver responsive to all signals lying in said spectral band of frequencies that are Doppler-shifted by said motion of the source in the receiver's frame of reference and active at all times;
• means for moving said receiver at a substantially constant velocity along a substantially straight-line trajectory;
• means for measuring said Doppler-shifted frequency of said received signal at each of at least four points along said receiver's trajectory and means for measuring said receiver's inter-measurement distances or time spans;
• means for calculating two ratios of frequency differences, each ratio involving three frequencies and each ratio being a function of said bearing angle between said closing velocity vector and said receiver-to-source line-of-sight in said receiver frame of reference at each of said three measurement points or times used for the ratio of frequency differences;
• means for calculating a candidate set of range and closing velocity combinations from the ratios of frequency differences and the inter-measurement distances or time spans;
• means for maneuvering the receiver to another trajectory which is substantially parallel to said first trajectory and means for moving said receiver with the same velocity as along said first trajectory and along a second substantially straight-line trajectory;
• means for measuring the Doppler-shifted frequency of the received signal at each of at least four points along said receiver's second trajectory and means or measuring said receiver's inter-measurement distances or time spans;
• means for calculating two ratios of frequency differences, each ratio involving three frequencies and each ratio being a function of a bearing angle between the closing velocity vector and the receiver-to-source line-of-sight in said receiver frame of reference at each of the three measurement points or times;
• means for calculating a candidate set of range and closing velocity combinations from said ratios of frequency differences and said inter-measurement distances or time spans;
• means for creating a phantom set of at least four measurements by iterating forward in time said solution fan derived from said measurement set said collected on an initial trajectory, said phantom measurement set having its first frequency measurement made to coincide in absolute time with a first frequency measurement of said second set of at least four frequency measurements;
• and
• means for resolving ambiguities by finding a closing velocity vector common to both solution fans and lying exactly within said solution fans' boundaries.

A method for determining the location of a source which emits an electromagnetic signal having a substantially constant but unknown frequency, said method being based on at least three points along a trajectory having a substantially straight-line portion, the method comprising the steps of:

• (A) moving a first receiver along said trajectory, said first receiver being responsive to a spectral band including a frequency of said electromagnetic signal that is Doppler-shifted by relative motion between said source and said first receiver;
• (B) measuring said Doppler-shifted frequency of said received electromagnetic signal when said receiver is located at each of said three points on said first trajectory;
• (C) calculating at least two ratios of frequencies, said ratios being functions of bearing angles;
• and
• (D) calculating said location of said source with respect to said first receiver from said frequency ratios at said at-least-three points.

A method for determining the range between a source which emits an electromagnetic signal and a first receiver of said electromagnetic signal at at-least-four points along a portion of a source trajectory, said source trajectory portion being a substantially straight line and having two end points and said emitted electromagnetic signal having a substantially constant but unknown frequency, the method comprising the steps of:

• (A) moving said first receiver along a first receiver trajectory having a substantially straight-line portion, said first receiver being responsive to a spectral band including a frequency of said electromagnetic signal that is Doppler-shifted by relative motion between said source and said first receiver;
• (B) measuring said Doppler-shifted frequency at at-least-four predetermined points on said substantially straight-line portion of said first receiver trajectory while said source is on said substantially straight-line trajectory portion;
• (C) calculating at least two first ratios of frequencies, said frequencies being functions of bearing angles;
• (D) moving a second receiver along a second receiver trajectory having a substantially straight-line portion that is parallel to said first receiver trajectory, said second receiver being responsive to a spectral band including a frequency of said electromagnetic signal that is Doppler-shifted by relative motion between said source and said second receiver;
• (E) measuring said Doppler-shifted frequency at said at-least-four predetermined points on said substantially straight-line portion of said second receiver trajectory and said source is on said substantially straight-line portion of said source trajectory;
• (F) calculating at least two second ratios of frequencies, said frequencies being functions of bearing angles;
• and
• (G) calculating said range between said first receiver and said source from said first and second frequency ratios at said at least four points.

A method for determining the range between a source which emits an electromagnetic signal and a first receiver of said electromagnetic signal at two pairs of points, each pair including at least four points along a distinct portion of a source trajectory, said source trajectory portions including two substantially parallel, straight lines and said emitted electromagnetic signal having a substantially constant but unknown frequency, the method comprising the steps of:

• (A) causing said first receiver to move along a first receiver trajectory, said first receiver being responsive to a spectral band including a frequency of said electromagnetic signal that is Doppler-shifted by relative motion between said source and said first receiver, said first receiver trajectory having a first substantially straight-line portion;
• (B) causing said first receiver to measure said Doppler-shifted frequency at a first set of times including at least four predetermined times having predetermined relative intervals therebetween while said first receiver is on said first substantially straight-line portion of said first receiver trajectory and said source is on said substantially straight-line portion of said source trajectory;
• (C) calculating at least two first ratios of frequencies, said frequencies being functions of bearing angles;
• and
• (D) causing said first receiver to move along a second receiver trajectory, said second receiver trajectory having a second substantially straight-line portion that is parallel to said first substantially straight-line portion;
• (E) causing said first receiver to measure said Doppler-shifted frequency at a second set of times including at least four additional predetermined times while said first receiver is on said first substantially straight-line portion of said second receiver trajectory and said source is on said substantially straight-line portion of said source trajectory, said second set of times being subsequent to said four predetermined times and having predetermined relative intervals substantially equal to the corresponding relative intervals of the first set of times;
• (F) calculating at least two second ratios of frequencies, said frequencies being functions of bearing angles;
• and
• (G) calculating said range between said first receiver and said source from said frequency ratios at said at least four points.

A system for determining the range to a source which emits an electromagnetic signal having a substantially constant but unknown frequency from at least three points along a trajectory having a substantially straight-line portion, the system comprising:

• a first receiver, said first receiver being responsive to a spectral band including a frequency of said electromagnetic signal that is Doppler-shifted by relative motion between said source and said first receiver;
• means for moving a first receiver along said trajectory;
• means for measuring said Doppler-shifted frequency of said received electromagnetic signal when said receiver is located at each of said three points on said first trajectory;
• means for calculating at least two ratios of frequencies, said frequencies being functions of bearing angles;
• and
• means for calculating said range between said first receiver and said source from said frequency ratios at said at-least-three points.

A system for determining the range between a source which emits an electromagnetic signal and a first receiver of said electromagnetic signal at at-least-four points along a portion of a source trajectory, said source trajectory portion being a substantially straight line and having two end points and said emitted electromagnetic signal having a substantially constant but unknown frequency, the system comprising:

• a first receiver, said first receiver being responsive to a spectral band including a frequency of said electromagnetic signal that is Doppler-shifted by relative motion between said source and said first receiver;
• means for moving said first receiver along a first receiver trajectory having a substantially straight-line portion;
• means for measuring said Doppler-shifted frequency at at least four predetermined points on said substantially straight-line portion of said first receiver trajectory while said source is on said substantially straight-line trajectory portion;
• means for calculating at least two first ratios of frequencies, said frequencies being functions of said Doppler-shifted frequencies;
• a second receiver, said second receiver being responsive to a spectral band including a frequency of said electromagnetic signal that is Doppler-shifted by relative motion between said source and said second receiver;
• means for moving said second receiver along a second receiver trajectory having a substantially straight-line portion that is parallel to said first receiver trajectory;
• means for measuring said Doppler-shifted frequency at said at-least-four predetermined points on said substantially straight-line portion of said second receiver trajectory and said source is on said substantially straight-line portion of said source trajectory;
• means for calculating at least two second ratios of frequencies, said frequencies being functions of said Doppler-shifted frequencies;
• and
• means for calculating said range between said first receiver and said source from said first and second frequency ratios at said at-least-four points.

A system for determining the range between a source which emits an electromagnetic signal and a first receiver of said electromagnetic signal at two pairs of points, each pair including at least four points along a distinct portion of a source trajectory, said source trajectory portions including two substantially parallel, straight lines and said emitted electromagnetic signal having a substantially constant but unknown frequency, the system comprising:

• a first receiver, said first receiver being responsive to a spectral band including a frequency of said electromagnetic signal that is Doppler-shifted by relative motion between said source and said first receiver;
• means for moving said first receiver along a first receiver trajectory, said first receiver trajectory having a first substantially straight-line portion;
• means for measuring said Doppler-shifted frequency at a first set of times including at least four predetermined times having predetermined relative intervals therebetween while said first receiver is on said first substantially straight-line portion of said first receiver trajectory and said source is on said substantially straight-line portion of said source trajectory;
• means for calculating at least two first ratios of frequencies, said frequencies being functions of said Doppler-shifted frequencies;
• means for moving said first receiver along a second receiver trajectory, said second receiver trajectory having a second substantially straight-line portion that is parallel to said first substantially straight-line portion;
• means for measuring said Doppler-shifted frequency at a second set of times including at least four additional predetermined times while said first receiver is on said first substantially straight-line portion of said second receiver trajectory and said source is on said substantially straight-line portion of said source trajectory, said second set of times being subsequent to said four predetermined times and having predetermined relative intervals substantially equal to the corresponding relative intervals of the first set of times;
• means for calculating at least two second ratios of frequencies, said frequencies being functions of bearing angles;
• and
• means for calculating said range between said first receiver and said source from said frequency ratios at said at-least-four points.