Track fusion by optimal reduced state estimation in multi-sensor environment with limited-bandwidth communication path

US 7,719,461 B1
Filed: 08/05/2008
Issued: 05/18/2010
Est. Priority Date: 08/05/2008
Status: Active Grant

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1. A method for determining at least the location of a target, when limited communication bandwidth does not permit sharing of individual measurements from at least two sensors;

said method comprising the steps of;

sensing the target with a first sensor at a location to produce a first set of measurements;

processing said first set of measurements by optimal reduced state estimation to thereby produce a first minimal set of target track information, including a first estimated state vector, with at least an estimated location or position of the target as one of its components, as well as associated matrices, including a covariance matrix containing mean square errors of the first estimated state vector due to random and bias measurement errors, and a matrix of coefficients relating parameter uncertainty to state estimation error;

sensing the target with at least a second sensor, at a second location, different from said first location, to produce a second set of measurements;

processing said second set of measurements by optimal reduced state estimation to thereby produce at least a second minimal set of target track information, including a second estimated state vector, with at least an estimated location or position of the target as one of its components, as well as associated matrices, including a covariance matrix containing mean square errors of the second estimated state vector due to random and bias measurement errors, and a matrix of coefficients relating parameter uncertainty to state estimation error;

transmitting the first and second minimal sets of track information by way of communication paths from each sensor to a user processing site at a location remote from the location of at least one of said sensors;

selecting at the user processing site, according to its own criteria or requirements, a parameter covariance matrix, representing the physical bounds of time-varying parameters of the target which are unknown, but which are physically constrained to lie within known bounds, and which are distinct from the state variables that are being estimated; and

optimally fusing the first and second minimal sets of track information, using the selected parameter covariance matrix, to produce fused information representing at least the estimated state of the target and the associated covariance.

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Abstract

The invention, called “ORSE Track Fusion”, combines sensor tracks from dispersed sites, when limited communication bandwidth does not permit sharing of individual measurements. Since estimation errors due to maneuver biases are not independent for each sensor, optimal fusion of tracks produced by Kalman filters requires transmission of all the filter gain matrices used to update each sensor track prior to the fusion time. For this reason, prior art has resorted to suboptimal designs. ORSE Track Fusion according to aspects of the invention overcomes this disadvantage by propagating, transmitting, and fusing separately calculated covariance matrices for random and bias estimation errors. Furthermore, with ORSE, each sensor can have its own criteria in forming its track, and track fusion can be performed with different criteria at each processing site. Thus, ORSE Track Fusion has the unique flexibility to optimize track fusion simultaneously for multiple criteria to serve multiple users.

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1. A method for determining at least the location of a target, when limited communication bandwidth does not permit sharing of individual measurements from at least two sensors;
- said method comprising the steps of;
  
  sensing the target with a first sensor at a location to produce a first set of measurements;
  
  processing said first set of measurements by optimal reduced state estimation to thereby produce a first minimal set of target track information, including a first estimated state vector, with at least an estimated location or position of the target as one of its components, as well as associated matrices, including a covariance matrix containing mean square errors of the first estimated state vector due to random and bias measurement errors, and a matrix of coefficients relating parameter uncertainty to state estimation error;
  
  sensing the target with at least a second sensor, at a second location, different from said first location, to produce a second set of measurements;
  
  processing said second set of measurements by optimal reduced state estimation to thereby produce at least a second minimal set of target track information, including a second estimated state vector, with at least an estimated location or position of the target as one of its components, as well as associated matrices, including a covariance matrix containing mean square errors of the second estimated state vector due to random and bias measurement errors, and a matrix of coefficients relating parameter uncertainty to state estimation error;
  
  transmitting the first and second minimal sets of track information by way of communication paths from each sensor to a user processing site at a location remote from the location of at least one of said sensors;
  
  selecting at the user processing site, according to its own criteria or requirements, a parameter covariance matrix, representing the physical bounds of time-varying parameters of the target which are unknown, but which are physically constrained to lie within known bounds, and which are distinct from the state variables that are being estimated; and
  
  optimally fusing the first and second minimal sets of track information, using the selected parameter covariance matrix, to produce fused information representing at least the estimated state of the target and the associated covariance.
- View Dependent Claims (2, 3, 4, 5, 6, 7, 14)
- - 2. A method according to claim 1, wherein:
    - the step of transmitting the first and second minimal sets of track information by way of communication paths from each sensor includes the step of transmitting to a plurality of user processing sites.
  - 3. A method according to claim 1, wherein said step of processing measurements from each sensor comprises the step of optimal reduced state estimation including the steps of:
    - time updating by ${F_{i} = \frac{\partial Φ (T, x, λ)}{\partial x} \rangle}_{x = {\hat{x}}_{i} (k | k), λ = \hat{λ}}$ whereF_iis the dynamic matrix,φ
      
      (T,x,λ
      
      ) is a general nonlinear function,T is sampling time,x is the state vector, andλ
      
      is a parameter vector;
      
      determining the input matrix G₁by ${G_{i} = \frac{\partial Φ (T, x, λ)}{\partial λ} \rangle}_{x = {\hat{x}}_{i} (k | k), λ = \overline{λ}};$ determining the time updated state estimate by
      {circumflex over (x)}_i(k_i+1|k_i)=φ
      
      (T,{circumflex over (x)}_i(k|k), λ
      
      )determining the time updated covariance of state estimate due to measurement noise only by
      M_i(k+1|k)=F_iM_i(k|k)F_i′
      
      where ′
      
      denotes transpose;
      
      determining the time updated bias coefficients due to unmodeled dynamics by
      D_i(k+1|k)=F_iD_i(k|k)+G_idetermining the time updated bias coefficients due to sensor bias by
      E_i(k+1|k)=F_iE_i(k|k)calculating intermediate variables P_i, V_i, U_i, according to $P_{i} \overset{def}{=} M_{i} (k + 1 | k) + D_{i} (k + 1 | k) {{ΛD}_{i} (k + 1 | k)}^{'}$ $V_{i} \overset{def}{=} H_{i} E_{i} (k + 1 | k) + J_{i} and$ $U_{i} \overset{def}{=} P_{i} H_{i}^{'} + E_{i} (k + 1 | k) B_{i} V_{i}^{'};$ calculating the innovation covariance Q_iby
      Q_i=H_iP_iH_i′
      
      +V_iB_iV_i′
      
      +N_i;
      
      computing the fusion gain as
      K_i=U_i(Q_i)^−
      
      1performing measurement update of the states and associated matrices according to
      {circumflex over (x)}(k+1|k+1)={circumflex over (x)}(k+1|k)+K_i[z₁(k+1)−
      
      H_i{circumflex over (x)}_i(k+1k)] $L_{i} \overset{def}{=} I - K_{i} H_{i} where I is an identity matrix$
      M_i(k+1|k+1)=L_iM_i(k+1|k)L_i′
      
      +K_iN_iK_i′
      
      D_i(k+1|k)=L_iD_i(k+1|k)
      E_i(k+1|k+1)=E_i(k+1|k)−
      
      K_iV_i
      R_i(k+1|k+1)=M_i(k+1|k+1)+E_i(k+1|k+1)B_iE_i(k+1|k+1)′
      
      to thereby predict the limited-information-bandwidth 3-tuples {{circumflex over (x)}_i, R_i, D_i} of track information for each sensor to a current time.
  - 4. A method according to claim 1, wherein each user processing site selects its own parameter covariance matrix Λ
    - , according to its own criteria or requirements.
  - 5. A method according to claim 1, wherein said step of optimally fusing to produce fused information representing at least the state and the covariance of said target includes the steps of:
    - initializing an optimal fusion algorithm by, for the first sensor, initializing
      {{circumflex over (x)}_#, R_#, D_#}={{circumflex over (x)}₁, R₁, D₁}and combining with the second sensor according to
      Q=R_#+R₂+(D_#−
      
      D₂)Λ
      
      (D_#−
      
      D₂)′
      
      K=[R_#+D_#Λ
      
      (D_#−
      
      D₂)′
      
      ]Q^−
      
      1
      I−
      
      K=[R₂+D₂Λ
      
      (D₂−
      
      D_#)′
      
      ]Q^−
      
      1
      R=[I−
      
      K]R_#[I−
      
      K]′
      
      +KR₂K′
      
      D=[I−
      
      K]D_#+KD₂
      S=R+DΛ
      
      D′
      
      {circumflex over (x)}=[I−
      
      K]{circumflex over (x)}_#+K{circumflex over (x)}₂and yielding {{circumflex over (x)}, R, D} as the output.
  - 6. A method according to claim 1, further comprising the step of displaying said location of said target.
  - 7. A method according to claim 1, wherein said target is a vehicle.
  - 14. A method according to claim 1, wherein said step of optimally fusing as many sets of minimal track information as the number of sensors sensing said target to produce fused information representing at least the state and the covariance of said target includes the steps of:
    - initializing an optimal fusion algorithm by, for the first sensor, initializing
      {{circumflex over (x)}_#, R_#, D_#}={{circumflex over (x)}₁, R₁, D₁}combining with the i^thsensor, i=2, 3, 4, . . . according to
      Q=R_#+R_i+(D_#−
      
      D_i)Λ
      
      (D_#−
      
      D_i)
      K=[R_#+D_#Λ
      
      (D_#−
      
      D_i)′
      
      ]Q^−
      
      1
      I−
      
      K=[R_i+D_iΛ
      
      (D_i−
      
      D_#)′
      
      ]Q^−
      
      1
      R=[I−
      
      K]R_#[I−
      
      K]′
      
      +KR_iK′
      
      D=[I−
      
      K]D_#+KD_i
      S=R+DΛ
      
      D′
      
      {circumflex over (x)}=[I−
      
      K]{circumflex over (x)}_#+K{circumflex over (x)}_iresetting
      R_#=
      D_#=D
      {circumflex over (x)}_#={circumflex over (x)}and looping back to Q=R_#+R_i+(D_#−
      
      D_i)Λ
      
      (D_#−
      
      D_i)′
      
      for the remaining sensor tracks until all tracks are fused and yielding {{circumflex over (x)}, R, D} as the output.

8. A method for determining at least the location of a target, when limited communication bandwidth does not permit sharing of individual measurements from a plurality of sensors including at least two sensors;
- said method comprising the steps of;
  
  sensing the target with a first sensor at a location to produce a first set of measurements;
  
  processing said first set of measurements by optimal reduced state estimation to thereby produce a first minimal set of target track information, including a first estimated state vector, with at least an estimated location or position of the target as one of its components, as well as associated matrices, including a covariance matrix containing mean square errors of the first estimated state vector due to random and bias measurement errors, and a matrix of coefficients relating parameter uncertainty to state estimation error;
  
  sensing the target with at least a second sensor, at a second location, different from said first location, to produce a second set of measurements;
  
  processing said second set of measurements by optimal reduced state estimation to thereby produce at least a second minimal set of target track information, including a second estimated state vector, with at least an estimated location or position of the target as one of its components, as well as associated matrices, including a covariance matrix containing mean square errors of the second estimated state vector due to random and bias measurement errors, and a matrix of coefficients relating parameter uncertainty to state estimation error;
  
  transmitting the first and second minimal sets of track information by way of communication paths from each sensor to at least one user processing site at a location remote from the location of at least one of said sensors;
  
  selecting at the user processing site, according to its own criteria or requirements, a parameter covariance matrix, representing the physical bounds of time-varying parameters of the target which are unknown, but which are physically constrained to lie within known bounds, and which are distinct from the state variables that are being estimated; and
  
  optimally fusing the first and second minimal sets of track information, using the selected parameter covariance matrix, to produce fused information representing at least the estimated state of the target and the associated covariance;
  
  sensing the target with an additional sensor at a location to produce an additional set of measurements;
  
  processing said additional set of measurements by optimal reduced state estimation to thereby produce an additional minimal set of target track information, including an additional estimated state vector, with at least an estimated location or position of the target as one of its components, as well as associated matrices, including a covariance matrix containing mean square errors of the additional estimated state vector due to random and bias measurement errors, and a matrix of coefficients relating parameter uncertainty to state estimation error;
  
  transmitting the additional minimal sets of track information by way of communication paths from the additional sensor to the user processing site; and
  
  optimally fusing the first, second, and additional minimal sets of track information, using the selected parameter covariance matrix, to produce fused information representing at least the estimated state of the target and the associated covariance.
- View Dependent Claims (9, 10, 11, 12, 13)
- - 9. A method according to claim 8, wherein said steps of sensing the target, processing by optimal reduced state estimation, transmitting, and optimally fusing are repeated until the track information from all sensors sensing a target are optimally fused, using the selected parameter covariance matrix at said user processing site, to produce fused information representing at least the estimated state of the target and the associated covariance.
  - 10. A method according to claim 8, wherein said target is a vehicle.
  - 11. A method according to claim 8, wherein:
    - the step of transmitting the first and second minimal sets of track information by way of communication paths from each sensor includes the step of transmitting to a plurality of user processing sites.
  - 12. A method according to claim 8, wherein said step of processing measurements from each sensor comprises the step of optimal reduced state estimation including the steps of:
    - time updating by ${F_{i} = \frac{\partial Φ (T, x, λ)}{\partial x} \rangle}_{x = {\hat{x}}_{i} (k | k), λ = \hat{λ}}$ whereF_iis the dynamic matrix,φ
      
      (T,x,λ
      
      ) is a general nonlinear function,T is sampling time,x is the state vector, andλ
      
      is a parameter vector;
      
      determining the input matrix G₁by ${G_{i} = \frac{\partial Φ (T, x, λ)}{\partial λ} \rangle}_{x = {\hat{x}}_{i} (k | k), λ = \overline{λ}};$ determining the time updated state estimate by
      {circumflex over (x)}_i(k+1|k)=φ
      
      (T,{circumflex over (x)}_i(k|k), λ
      
      )determining the time updated covariance of state estimate due to measurement noise only by
      M_i(k+1|k)=F_iM_i(k|k)F_i′
      
      where ′
      
      denotes transpose;
      
      determining the time updated bias coefficients due to unmodeled dynamics by
      D_i(k+1|k)=F_iD_i(k|k)+G_i;
      
      determining the time updated bias coefficients due to sensor bias by
      E_i(k+1|k)=F_iE_i(k|k)calculating intermediate variables P_i, V_i, U_i, according to $P_{i} \overset{def}{=} M_{i} (k + 1 | k) + D_{i} (k + 1 | k) {{ΛD}_{i} (k + 1 | k)}^{'}$ $V_{i} \overset{def}{=} H_{i} E_{i} (k + 1 | k) + J_{i} and$ $U_{i} \overset{def}{=} P_{i} H_{i}^{'} + E_{i} (k + 1 | k) B_{i} V_{i}^{'};$ calculating the innovation covariance Q_iby
      Q_i=H_iP_iH_i′
      
      +V_iB_iV_i′
      
      +N_i;
      
      computing the fusion gain as
      K_i=U_i(Q_i)^−
      
      1performing measurement update of the states and associated matrices according to
      {circumflex over (x)}_i(k+1|k+1)={circumflex over (x)}_i(k+1|k)+K_i[z_i(k+1)−
      
      H_i{circumflex over (x)}_i(k+1|k)] $L_{i} \overset{def}{=} I - K_{i} H_{i} where I is an identity matrix$
      M_i(k_i+1|k_i+1)=L_iM_i(k₁+1|k)L_i′
      
      +K_iN_iK_i′
      
      D_i(k_i+1|k_i+1)=L_iD_i(k_i+1|k)
      E_i(k_i+1|k_i+1)=E_i(k_i+1|k_i)−
      
      K_iV_i
      R_i(k_i+1|k_i+1)=M_i(k_i+1|k_i+1)+E_i(k_i+1|k_i+1)B_iE_i(k_i+1|k_i+1) to thereby predict the limited-information-bandwidth 3-tuples {{circumflex over (x)}_i, R_i, D_i} of track information for each sensor to a current time.
  - 13. A method according to claim 8, wherein each user processing site selects its own parameter covariance matrix Λ
    - , according to its own criteria or requirements.

15. A method for determining the location of a target, said method comprising the steps of:
- sensing the target with a first sensor to produce a first set of measurements;
  
  processing the first set of measurements by optimal reduced state estimation to produce a first minimal set of target track information;
  
  sensing the target with at least a second sensor to produce at least a second set of measurements;
  
  processing the at least second set of measurements by optimal reduced state estimation to produce at least a second minimal set of target track information; and
  
  optimally fusing the first and at least second minimal sets of track information, using a selected parameter covariance matrix representing the physical bounds of the target, to produce fused information representing at least the estimated state of the target and the associated covariance.
- View Dependent Claims (16, 17)
- - 16. The method according to claim 15, wherein the first minimal set of target track information includes a first estimated state vector, a covariance matrix containing mean square errors of the first estimated state vector, and a matrix of coefficients relating parameter uncertainty to state estimation error, and the at least second minimal set of target track information includes at least a second estimated state vector, a covariance matrix containing mean square errors of the at least second estimated state vector, and a matrix of coefficients relating parameter uncertainty to state estimation error.
  - 17. The method according to claim 15, wherein prior to the optimally fusing step, further comprising the steps of:
    - transmitting the first and at least second minimal sets of track information from each sensor to a user processing site; and
      
      selecting at the user processing site the parameter covariance matrix.

18. A system for determining the location of a target, said system comprising:
- a first sensor for sensing the target to produce a first set of measurements;
  
  at least a second sensor for sensing the target to produce at least a second set of measurements;
  
  a processor for processing said first set of measurements by optimal reduced state estimation to produce a first minimal set of target track information;
  
  processors for processing each of the first and second sets of measurements by optimal reduced state estimation to produce minimal sets of target track information; and
  
  a processor for optimally fusing the first and at least second minimal sets of track information, using a selected parameter covariance matrix representing the physical bounds of the target, to produce fused information representing at least the estimated state of the target and the associated covariance.
- View Dependent Claims (19, 20)
- - 19. The system according to claim 18, wherein the first minimal set of target track information includes a first estimated state vector, a covariance matrix containing mean square errors of the first estimated state vector, and a matrix of coefficients relating parameter uncertainty to state estimation error, and the at least second minimal set of target track information includes at least a second estimated state vector, a covariance matrix containing mean square errors of the at least second estimated state vector, and a matrix of coefficients relating parameter uncertainty to state estimation error.
  - 20. The system according to claim 18, further comprising a network for transmitting the first and at least second minimal sets of track information from each sensor to a user processing site, the user processing site including the processor for optimally fusing the first and at least second minimal sets of track information.

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Current Assignee
Lockheed Martin Corporation (Martin Marietta Corporation)
Original Assignee
Lockheed Martin Corporation (Martin Marietta Corporation)
Inventors
Reifler, Frank J., Mookerjee, Purusottam
Primary Examiner(s)
Sotomayor; John B

Application Number

US12/186,227
Time in Patent Office

651 Days
Field of Search

342/59, 342/90, 342 95- 97, 342107-109, 342113-115, 342/133, 342/135, 342139-140, 342145-148, 342/162, 342/189, 342194-195
US Class Current

342/95
CPC Class Codes

G01S 13/726   Multiple target tracking

G01S 13/87   Combinations of radar syste...

G01S 7/003   Transmission of data betwee...

Track fusion by optimal reduced state estimation in multi-sensor environment with limited-bandwidth communication path

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Track fusion by optimal reduced state estimation in multi-sensor environment with limited-bandwidth communication path

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