System and method for interferometrically tracking objects using a low-antenna-count antenna array

• US 20150220488A1
• Filed: 02/05/2015
• Published: 08/06/2015
• Est. Priority Date: 02/05/2014
• Status: Abandoned Application

• Current Assignee: The Government Of The United States As Represented By The Secretary Of The Navy
• Original Assignee: The Government of The US As Represented By The Secretary of The Navy
• Inventors: Healy, Liam M.
• Application Number:
  US14/615,238
• Publication Number:
  US 20150220488A1
• Time in Patent Office: Days
• US Class Current: 1/1
• CPC Class Codes: G01S 13/003 Bistatic radar systems; Multistatic radar systems
• CPC Class Codes: G01S 13/42 Simultaneous measurement of distance and other co-ordinates indirect measurement G01S13/46
• CPC Class Codes: G01S 13/84 for distance determination by phase measurement
• CPC Class Codes: G01S 13/878 Combination of several spaced transmitters or receivers of known location for determining the position of a transponder or a reflector G01S13/874 takes precedence
• CPC Class Codes: G01S 19/43 using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
• CPC Class Codes: G01S 19/44 Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
• CPC Class Codes: G01S 19/54 using carrier phase measurements; using long or short baseline interferometry
• CPC Class Codes: G01S 19/55 Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
• CPC Class Codes: G01S 3/02 using radio waves
• CPC Class Codes: G01S 5/0278 involving statistical or probabilistic considerations G01S5/0252, G01S5/0294 take precedence
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04

Abstract

A radio-frequency interferometry method for determining parameters of motion of a moving object from phase difference information from an antenna baseline formed of two antennas. At each of a plurality of observation events, compute a posterior probability density function from the phase differences from the baseline, separate the modes with a threshold value of probability density, and compute a probability of each mode. For each possible sequence of modes, determine a mode sequence probability as the product of the probabilities of each mode in that sequence, estimate a χ² goodness of fit function based on an assumed type of motion. Determine the net probability of each possible sequence of modes as the product of a relative probability derived from the χ² and the mode sequence probability. Alternately, two or more parallel or colinear baselines are used, and the posterior PDF is a combined PDF over each of the baselines.

Claims

1. A radio-frequency interferometry based method for determining parameters of motion of a moving object from phase difference information from at least one radio-frequency antenna baseline, the baseline including two antennas, the method comprising:

at each of a plurality of observation events, computing a posterior probability density function from the phase differences over the antenna baseline, applying a threshold value of probability density to separate the modes, and computing a probability of each individual separated mode;

for each possible sequence of modes, determining a mode sequence probability as the product of the probabilities of each individual separated mode in that sequence;

estimating a χ

² goodness of fit function based on an assumed type of motion; and

for each of the sequences of modes, determining the net probability of each possible sequence of modes as the product of a relative probability derived from the χ

² and the mode sequence probability.

2. The method according to claim 1, wherein the method determines parameters of motion of the moving object from phase difference information from at least two radio-frequency antenna baselines, each of the baselines including two antennas, each baseline having a length different than the other baselines, each baseline being parallel with the other baselines, and

the posterior probability density function is a combined probability density function over each of the baselines.

3. The method according to claim 2, wherein the method for determining parameters of motion of a moving object from phase difference information is accomplished with phase information from at most two antenna baselines.

4. The method according to claim 1, further comprising:

evaluating several of the sequences of modes with the highest net probability and using the motion parameter estimates that correspond to one of the several sequences of modes with the highest net probability.

5. The method according to claim 1, wherein the parameters of motion include direction of the object relative to the radio frequency antenna baseline.

6. The method according to claim 2, wherein the computing a combined probability density function from the phase differences over each of two antenna baselines comprises solving the multimodal posterior probability function with an assumption of Gaussian distribution of measured arrival times at an observation, as

8. The method according to claim 1, wherein the determining the net probability of each possible sequence of modes as the product of a relative probability derived from the χ

² and the mode sequence probability comprises solving

9. The method according to claim 1, further comprising:

setting an initial threshold by simulating motion and sampling data with a Monte Carlo method,

adjusting the threshold until known correct motion parameters occur with the highest probability weight.

7. The method according to claim 7, wherein the χ

² goodness of fit factor is determined according to

10. A radio-frequency interferometer for determining parameters of motion of a moving object from measured phase differences of signals arriving at at least two antennas forming an antenna baseline, comprising:

at least one radio-frequency antenna baseline, the baseline including two antennas;

a receiver configured to measure a phase difference over the baseline;

a computer having stored instructions thereon configured for

at each of a plurality of observation events, computing a posterior probability density function from the phase differences over the antenna baseline, applying a threshold value of probability density to separate the modes, and computing a probability of each individual separated mode,

for each possible sequence of modes, determining a mode sequence probability as the product of the probabilities of each individual separated mode in that sequence,

estimating a χ

² goodness of fit function based on an assumed type of motion, and

for each of the sequences of modes, determining the net probability of each possible sequence of modes as the product of a relative probability derived from the χ

² and the mode sequence probability.

11. The interferometer according to claim 10, further comprising at least a second receiver and a second radio frequency antenna baseline, the second antenna baseline having a different length and the baselines being parallel, and wherein the stored instructions are configured to determine parameters of motion of the moving object from phase difference information from both baselines, and

the posterior probability density function is a combined probability density function over each of the baselines.

12. The interferometer according to claim 11, wherein the parameters of motion of the moving object are determined with phase information from at most two antenna baselines.

13. The interferometer according to claim 10, wherein the stored instructions are further configured to evaluate several sequences of modes with a highest net probability and selecting the motion parameter estimates that correspond to one of the several sequences of modes with the highest net probability.

14. The interferometer according to claim 10, wherein the parameters of motion include direction of the object relative to the radio frequency antenna baseline.

15. The interferometer according to claim 10, wherein the stored instructions are configured to compute a combined probability density function from the phase differences over each of two antenna baselines by solving the multimodal posterior probability function with an assumption of Gaussian distribution of measured arrival times at an observation, as

16. The interferometer according to claim 15, wherein the χ

² goodness of fit factor is determined according to

17. The interferometer according to claim 16, wherein the stored instructions are further configured for determining the net probability of each possible sequence of modes as the product of a relative probability derived from the χ

² and determining the mode sequence probability

18. The interferometer according to claim 10, wherein the stored instructions are further configured for setting an initial threshold by simulating motion and sampling data with a Monte Carlo method, adjusting the threshold until known correct motion parameters occur with the highest probability weight.