Phase correction for object detection including TDMA

1. An object detection system, comprising:

a plurality of first transmitters that respectively transmit a first signal at a first time;

a plurality of second transmitters that respectively transmit a second signal at a second time;

a plurality of receivers that receive the signals; and

a processor that is configured to determine whether a transmission timing phase shift exists between the received first signals and the received second signals based on a relationship between matrices including the received signals, wherein the matrices comprise covariance matrices and the processor is configured to

determine a reference covariance matrix of the received first signals;

determine an unmodified covariance matrix including at least part of the received first signals and at least part of the received second signals;

determine a set of modified second signal values for the part of the received second signals multiplied by −1;

determine a modified covariance matrix including the part of the received first signals and the set of modified second signal values; and

determine the relationship between the matrices based on (i) a relationship between the reference covariance matrix and the unmodified covariance matrix and (ii) a relationship between the reference covariance matrix and the modified covariance matrix.

2. The object detection system of claim 1 , wherein the processor is configured to

determine a reference trace T of the reference covariance matrix;

determine a trace Tu of the unmodified covariance matrix;

determine a trace Tm of the modified covariance matrix;

determine the relationship between the reference covariance matrix and the unmodified covariance matrix based on a relationship between the reference trace T and the trace Tu; and

determine the relationship between the reference covariance matrix and the modified covariance matrix based on a relationship between the reference trace T and the trace Tm.

3. The object detection system of claim 2 , wherein the processor is configured to

determine whether the reference trace T is more similar to the trace Tu or the trace Tm; and

determine whether the transmission timing phase shift exists based on which of the traces Tu or Tm is more similar to the reference trace T.

4. The object detection system of claim 3 , wherein the processor is configured to

determine that the transmission timing phase shift exists when the reference trace T is more similar to the trace Tm than the trace Tu; and

determine that the transmission timing phase shift does not exist when the reference trace T is more similar to the trace Tu than the trace Tm.

5. The object detection system of claim 4 , wherein the processor is configured to use a phase shift value of 180° for processing at least some of the received signals when the transmission timing phase shift exists.

6. The object detection system of claim 1 , wherein

there are four first transmitters;

there are four second transmitters;

there are thirty-two receivers;

there are one hundred twenty-eight received first signals in the reference covariance matrix;

there are sixty-four received first signals in the part of the received first signals; and

there are sixty-four received second signals in the part of the received second signals.

7. The object detection system of claim 1 , wherein

the signals comprise RADAR signals; and

the receivers receive the signals after the signals reflect off an object.

8. The object detection system of claim 1 , wherein

the matrices comprise covariance matrices including at least some of the received signals;

the processor is configured to determine traces of the covariance matrices; and

the relationship between the matrices comprises a relationship between the traces of the covariance matrices.

9. The object detection system of claim 8 , wherein the processor is configured to use a phase shift value of 180° for processing at least some of the received signals when the transmission timing phase shift exists.

10. An object detection method, comprising:

transmitting first signals at a first time from a plurality of first transmitters;

transmitting second signals at a second time from a plurality of second transmitters;

receiving the signals at a plurality of receivers; and

determining whether a transmission timing phase shift exists between the received first signals and the received second signals based on a relationship between matrices including the received signals, wherein the matrices comprise covariance matrices and the method comprises

determining a reference covariance matrix of the received first signals;

determining an unmodified covariance matrix including at least part of the received first signals and at least part of the received second signals;

determining a set of modified second signal values for the part of the received second signals multiplied by −1;

determining a modified covariance matrix including the part of the received first signals and the set of modified second signal values; and

determining the relationship between the matrices based on (i) a relationship between the reference covariance matrix and the unmodified covariance matrix and (ii) a relationship between the reference covariance matrix and the modified covariance matrix.

11. The method of claim 10 , comprising

determining a reference trace T of the reference covariance matrix;

determining a trace Tu of the unmodified covariance matrix;

determining a trace Tm of the modified covariance matrix;

determining the relationship between the reference covariance matrix and the unmodified covariance matrix based on a relationship between the reference trace T and the trace Tu; and

determining the relationship between the reference covariance matrix and the modified covariance matrix based on a relationship between the reference trace T and the trace Tm.

12. The method of claim 11 , comprising

determining whether the reference trace T is more similar to the trace Tu or the trace Tm; and

determining whether the transmission timing phase shift exists based on which of the traces Tu or Tm is more similar to the reference trace T.

13. The method of claim 12 , comprising

determining that the transmission timing phase shift exists when the reference trace T is more similar to the trace Tm than the trace Tu; and

determining that the transmission timing phase shift does not exist when the reference trace T is more similar to the trace Tu than the trace Tm.

14. The method of claim 13 , comprising using a phase shift value of 180° for processing at least some of the received signals when the transmission timing phase shift exists.

15. The method of claim 10 , wherein

there are four first transmitters;

there are four second transmitters;

there are thirty-two receivers;

there are one hundred twenty-eight received first signals in the reference covariance matrix;

there are sixty-four received first signals in the part of the received first signals; and

there are sixty-four received second signals in the part of the received second signals.

16. The method of claim 10 , wherein

the signals comprise RADAR signals; and

the receivers receive the signals after the signals reflect off an object.

17. The method of claim 10 , wherein

the matrices comprise covariance matrices including at least some of the received signals;

the method includes determining traces of the covariance matrices; and

the relationship between the matrices comprises a relationship between the traces of the covariance matrices.

18. The method of claim 17 , comprising using a phase shift value of 180° for processing at least some of the received signals when the transmission timing phase shift exists.