Doppler ambiguity resolution via high order phase terms
A vehicle, radar system for the vehicle and method of operating the vehicle is disclosed. The radar system includes a transmitter, a receiver and a processor. The transmitter transmits a source signal into a region proximate the vehicle. The receiver receives a reflected signal formed by reflection of the source signal from an object in the region. The processor obtains non-linear terms of a phase from the reflected signal and resolves a Doppler ambiguity of the object using the non-linear terms. A navigation system navigates the vehicle with respect to the object based on the resolved Doppler ambiguity.
1. A method of operating a vehicle, comprising:
transmitting a source signal into a region proximate a vehicle;
receiving a reflected signal due to a reflection of the source signal from an object in the region;
sampling the reflected signal at a sampling interval to obtain a plurality of velocity hypotheses, each velocity hypothesis having a phase that is non-linear in at least a sample index of the sampling interval;
determining a likelihood function for the plurality of velocity hypotheses;
selecting a velocity hypothesis for which the likelihood function has a maximum value; and
operating the vehicle using the selected velocity hypothesis.
2. The method of claim 1 , further comprising obtaining a product of the reflected signal and the source signal, performing a low pass filter on the product, and sampling the filtered signal to obtain a sampled signal having the phase with non-linear terms.
3. The method of claim 1 , wherein the phase is further non-linear in at least one of: (i) a chirp index; and (ii) a combination of the chirp index and the sample index.
4. The method of claim 1 , further comprising selecting the velocity hypothesis for which the likelihood function has a global maximum value.
5. The method of claim 4 , further comprising locating the global maximum value of the likelihood function by searching along one of a range and a velocity dimension of a likelihood grid during a first one-dimensional search and searching along the other of the range and velocity dimension during a second one-dimensional search.
6. The method of claim 1 , further comprising navigating the vehicle with respect to the object based on the selected velocity hypotheses.
7. A radar system for a vehicle, comprising:
a transmitter configured to transmit a source signal into a region proximate the vehicle;
a receiver receptive to a reflected signal formed by reflection of the source signal from an object in the region; and
a processor configured to:
sample the reflected signal at a sampling interval to obtain a plurality of velocity hypotheses, each velocity hypothesis having a phase that is non-linear in at least a sample index of the sampling interval;
determine a likelihood function for the plurality of velocity hypotheses;
select a velocity hypothesis for which the likelihood function has a maximum value; and
operate the vehicle using the selected velocity hypothesis.
8. The radar system of claim 7 , wherein the processor is further configured to obtain a product of the reflected signal and the source signal, perform a low pass filter on the product, and sample the filtered signal to obtain a sampled signal having the phase with non-linear terms.
9. The radar system of claim 7 , wherein the phase is further non-linear in at least one of: (i) a chirp index; and (ii) a combination of the chirp index and the sample index.
10. The radar system of claim 7 , wherein the processor is further configured to select the velocity hypothesis for which the likelihood function has a global maximum value.
11. The radar system of claim 10 , wherein the processor is further configured to locate the global maximum value of the likelihood function by searching along one of a range and a velocity dimension of a likelihood grid during a first one-dimensional search and searching along the other of the range and velocity dimension during a second one-dimensional search.
12. The radar system of claim 7 , wherein the processor is further configured to navigate the vehicle with respect to the object based on the selected velocity hypotheses.
13. A vehicle, comprising:
a transmitter configured to transmit a source signal into a region proximate the vehicle;
a receiver receptive to a reflected signal formed by reflection of the source signal from an object in the region;
a processor configured to:
sample the reflected signal at a sampling interval to obtain a plurality of velocity hypotheses, each velocity hypothesis having a phase that is non-linear in at least a sample index of the sampling interval;
determine a likelihood function for the plurality of velocity hypotheses; and
select a velocity hypothesis for which the likelihood function has a maximum value;
a navigation system configured to navigate the vehicle with respect to the object using the selected velocity hypothesis.
14. The vehicle of claim 13 , wherein the processor is further configured to obtain a product of the reflected signal and the source signal, perform a low pass filter on the product, and sample the filtered signal to obtain a sampled signal having the phase with non-linear terms.
15. The vehicle of claim 13 , wherein the phase is further non-linear in at least one of: (i) a chirp index; and (ii) a combination of the chirp index and the sample index.
16. The vehicle of claim 13 , wherein the processor is further configured to select the velocity hypothesis for which the likelihood function has a global maximum value.
17. The vehicle of claim 16 , wherein the processor is further configured to locate the global maximum value of the likelihood function by searching along one of a range and a velocity dimension of a likelihood grid during a first one-dimensional search and searching along the other of the range and velocity dimension during a second one-dimensional search.