Systems and methods for de-noising GNSS signals
Certain implementations of the disclosed technology may include systems and methods for reducing noise in dual-frequency GNSS signal observation. The method can include: receiving, at a GNSS receiver, a first signal and a second signal. At least the second signal includes noise. The first signal is characterized by a first carrier frequency, and the second signal is characterized by a second carrier frequency. The method includes: down converting, sampling, cross-correlating, accumulating, determining ambiguous instantaneous phases, determining non-ambiguous instantaneous phases, producing normalized non-ambiguous instantaneous first phase samples, constructing a normalized first counter rotation phasor, generating a counter-rotated second observable, applying a low pass filter to remove noise; and outputting the filtered second observable.
1. A method for reducing noise in dual-frequency signal observation, the method comprising:
receiving a first signal and a second signal, wherein the first signal is characterized by a first carrier frequency, and wherein the second signal is characterized by a second carrier frequency;
down converting and sampling the first and second signals to produce complex first samples and complex second samples;
de-spreading the complex first samples and the complex second samples;
determining ambiguous instantaneous first phase samples and a non-ambiguous instantaneous first phase samples of de-spread complex first samples and complex second samples;
producing normalized non-ambiguous instantaneous first phase samples by multiplying the non-ambiguous instantaneous first phase samples by the second carrier frequency divided the first carrier frequency;
constructing a normalized first counter-rotation phasor by taking a complex exponential of a negated version of the normalized non-ambiguous instantaneous first phase samples;
generating a counter-rotated second observable by multiplying the complex second samples by the normalized first counter-rotation phasor; and
applying a low pass filter to the counter-rotated second observable to remove noise to produce a filtered second observable.
2. The method of claim 1 , wherein the de-spreading comprises cross-correlating and accumulating the complex first samples and the complex second samples.
3. The method of claim 1 , further comprising outputting the filtered second observable.
4. The method of claim 1 , wherein the de-spreading comprises accumulating over an interval selected from a range of 1 ms to 100 ms.
5. The method of claim 1 , wherein the first carrier frequency is 1.227 GHz and wherein the second carrier frequency is 1.57 GHz.
6. The method of claim 1 , wherein the first carrier frequency is 1.57 GHz and wherein the second carrier frequency is 1.227 GHz.
7. The method of claim 1 , wherein the ambiguous instantaneous phase of one or more of the complex first samples and complex second samples are 2π ambiguous.
8. The method of claim 1 , wherein the first signal includes more noise than the second signal.
9. The method of claim 1 , wherein the second signal includes more noise than the first signal.
10. The method of claim 1 , wherein the first signal and a second signal are in coherence.
11. A system comprising:
an antenna;
an RF to baseband converter;
one or more analog to digital (A/D) converters;
a digital signal processing (DSP) processor; and
memory in communication with the DSP processor;
wherein the system is configured to:
receive, at the antenna, a first signal and a second signal, wherein the first signal is characterized by a first carrier frequency, and wherein the second signal is characterized by a second carrier frequency;
down convert, with the RF to baseband converter, the first and second signals to respective first baseband and second baseband signals;
sample, with the one or more A/D converters, the first baseband and second baseband signals to produce complex first samples and complex second samples;
de-spread the complex first samples and the complex second samples determine, with the DSP processor, ambiguous instantaneous first phase samples and non-ambiguous instantaneous first phase samples of the de-spread complex first samples and the de-spread complex second samples;
produce normalized non-ambiguous instantaneous first phase samples by multiplying the non-ambiguous instantaneous first phase samples of the result by the second carrier frequency divided the first carrier frequency;
construct a normalized first counter-rotation phasor by taking a complex exponential of a negated version of the normalized non-ambiguous instantaneous first phase samples;
generate a counter-rotated second observable by multiplying the complex second samples by the normalized first counter-rotation phasor;
apply a low pass filter to the counter-rotated second observable to remove noise to produce a filtered second observable; and
output the filtered second observable.
12. The system of claim 11 , further comprising a front end, wherein the front end is configured to filter at least a portion of the received first and second signals.
13. The system of claim 11 , wherein the DSP processor is configured to de-spread the complex first samples and the complex second samples by cross-correlating and accumulating the complex first samples and the complex second samples.
14. The system of claim 11 , wherein the DSP processor is configured to de-spread the first and second complex samples by accumulating over an interval selected from a range between about 1 ms and about 100 ms.
15. The system of claim 11 , wherein the first carrier frequency is 1.227 GHz and wherein the second carrier frequency is 1.57 GHz.
16. The system of claim 11 , wherein the first carrier frequency is 1.57 GHz and wherein the second carrier frequency is 1.227 GHz.
17. The system of claim 11 , wherein the second signal includes more noise than the first signal.
18. The system of claim 11 , wherein the first signal includes more noise than the second signal.
19. The system of claim 11 , wherein the DSP processor is configured to output the filtered second observable.
20. A non-transitory computer readable storage medium storing instructions for use with one or more processors in communication with a memory, and wherein the instructions are configured to cause the one or more processors to perform a method comprising:
receiving a first signal and a second signal, wherein the first signal is characterized by a first carrier frequency, and wherein the second signal is characterized by a second carrier frequency;
down converting and sampling the first and second signals to produce complex first samples and complex second samples;
de-spreading the complex first samples and the complex second samples;
determining ambiguous instantaneous first phase samples and a non-ambiguous instantaneous first phase samples of de-spread complex first samples and complex second samples;
producing normalized non-ambiguous instantaneous first phase samples by multiplying the non-ambiguous instantaneous first phase samples by the second carrier frequency divided the first carrier frequency;
constructing a normalized first counter-rotation phasor by taking a complex exponential of a negated version of the normalized non-ambiguous instantaneous first phase samples;
generating a counter-rotated second observable by multiplying the complex second samples by the normalized first counter-rotation phasor; and
applying a low pass filter to the counter-rotated second observable to remove noise to produce a filtered second observable.