Method and apparatus for navigation using a reduced number of transmitters
View Patent ↗A system for determining a position of a receiver from as few as two or three transmitters. The receiver may be stationary or moving with a known velocity. The system includes a receiver clock having a clock bias and a clock drift relative to a reference clock and may also include a motion sensor. A decoder receives transmitted signals from a number of transmitters and determine pseudo-ranges and transmitter frequencies therefrom and a processing unit receives the pseudo-ranges, the transmitter frequencies and the receiver velocity and determines the position of the receiver therefrom. When only two transmitters are available, the position of the receiver is determined dependent upon a known receiver clock drift. The system may also determine clock bias and, when three or more transmitters are available, receiver clock drift. The processing unit uses ranging and Doppler equations in combination, and may also use a measured velocity.
1. A method for determining a location of a receiver having a known velocity, the method comprising:
for each of three transmitters:
receiving a measured pseudo-range from the receiver to the transmitter, where the measured pseudo-range, a position of the transmitter, the velocity of the receiver, which are known, are related to the location of the receiver and a clock bias of a receiver clock, which are unknown, through a first relationship;
for each of at least two transmitters of the three transmitters:
receiving a measured frequency of a signal transmitted from the transmitter, where the measured frequency, the position of the transmitter, the velocity of the transmitter, the velocity of the receiver and the measured pseudo-range, which are known, are related to the position of the receiver, the clock bias, and a clock drift of the receiver clock, which are unknown, through a second relationship; and
determining the position of the receiver from each of the first relationships for the three transmitters and each of the second relationships for the at least two transmitters.
2. A non-transient, computer readable medium containing processing instructions that, when executed on one or more processors, perform the method of claim 1 .
3. The method of claim 1 , further comprising measuring the velocity of the receiver.
4. The method of claim 1 , further comprising:
generating, by the receiver clock, a timing signal from oscillations of a crystal or a chip-scale atomic clock; and
for each of the three transmitters:
determining the measured pseudo-range dependent upon the timing signal, a time encoded in a signal transmitted from the transmitter and a propagation model.
5. The method of claim 1 , further comprising:
generating, by the receiver clock, a timing signal from oscillations of a crystal; and
for each of the at least two transmitters, determining the measured frequency dependent upon the time signaling.
6. The method of claim 1 , where determining the position of the receiver from each of the first relationships for the three transmitters and each of the second relationships for the at least two transmitters comprises executing a program of instructions on one or more processors.
7. The method of claim 1 , where determining the position of the receiver from each of the first relationships for the three transmitters and each of the second relationships for the at least two transmitters comprises executing a program of instructions on one or more processors is performed in hardware.
8. The method of claim 1 , where the at least two transmitters are moving relative to the receiver.
9. A method for determining a location of a receiver having a known velocity, the method comprising:
for each of two transmitters that are moving relative to the receiver:
receiving a measured pseudo-range from the receiver to the transmitter, where the measured pseudo-range, a position of the transmitter, the velocity of the receiver, which are known, are related to the location of the receiver and a clock bias of a receiver clock, which are unknown, through a first relationship;
receiving a measured frequency of a signal transmitted from the transmitter, where the measured frequency, the position of the transmitter, the velocity of the transmitter, the velocity of the receiver, a clock drift of the receiver clock and the measured pseudo-range, which are known, are related to the position of the
receiver, the clock bias, and, which are unknown, through a second relationship; and
determining the position of the receiver from each of the first relationships for the three transmitters and each of the second relationships for the at least two transmitters.
10. A non-transient, computer readable medium containing processing instructions that, when executed on one or more processors, perform the method of claim 9 .
11. The method of claim 9 , further comprising measuring the velocity of the receiver.
12. The method of claim 9 , further comprising determining the clock drift of the receiver clock from a computer model of the receiver clock.