1. 1 Multisensor Data Fusion 1. The Filtering Approach: F 1 (s) F 2 (s) F k (s) x n1n1 n2n2 nknk z y1y1 y2y2 ykyk (1) (2) (3) 2. The Compensation Approach: S1S1 S2S2 n1n1 n2n2 Filter z y x x xy1y1 + - (4)+ (5)

2. 2 Goals of Optimization (5) 1. Unbiasedness: 2. Minimal variance: (6) a

3. 3 Kalman Filter Built-in to the Commercial Navigation Measurement System

4. 4 GPS+SINS Integration SensorsSINS Kalman Filter GPS (8) (7)State Space Equations of SINS Errors:

5. 5 Mathematical Formulation of the Kalman Filtering Problem Measurement:(9) (10) where: (11) Let: Filtration error: (12) Prediction:

6. 6 Main Requirements: 1. Zero-bias (see (5)): 2. Minimal Variance: (14) (13) Prediction error (derived from (10) and (12)) : (15) Covariance matrix of prediction error : (16) Estimation of the prediction based on the measurement results (measurement update): (17) (18)

7. 7 From (13) it follows: (19) (20) From (13) and (20) it follows:(21) Substituting (21) in (17), we obtain: (22) Determination of the Kalman Gain K from requirement (14) (23) (25) Substituting (11) in (25), we obtain: (26)

8. 8 (27) Condition of optimality: (29) Differentiation of the traces of matrices: (28) (30) (31) Taking in account (30) and (31), expression (27) can be simplified: (32) Basic expression for Kalman Filtering are: (12), (16), (22), (31), (32).

9. 9 Time-dependant Kalman Filter Algorithm P(0),X(0),  n, H n,Q n,R n. Initial data: y[n] Measurements z -1 1 (16)(12) (31) (32)(22) 7

10. 10 Discrete Stationary Kalman Filter (33) (34) Command in MATLAB for discrete models (3): [kest, K, P, M, Z]=kalman(‘sys’,Q,R) (35)

11. 11 Block Diagram of Discrete Kalman Filter

12. 12 Example: fusion of the dead reckon and radio-navigation systems RNS DRS FK w1w1 w2w2 v w ynyn (1) (2) (3)

13. 13 Multisensor Data Fusion The Filtering Approach: F 1 (s) F 2 (s) F k (s) x n1n1 n2n2 nknk z y1y1 y2y2 ykyk (1) (2) (3)

14. 14 Optimal Filtration in Scalar Case. W(s)F(s) x n I(s)=1 e y (4) (6a) (5) Wiener-Hopf Equation: (7) (6)

15. 15 Wiener Factorization: Wiener Separation: Optimal Filter: (8) (9) (10) Example: (11) (12) (13)

16. 16 Optimal Fusion of 2 sensors. F (s) F 1 (s) xn n1n1 z y y1y1 W(s) W 1 (s) ε (1) (2) (3) i (4) (5) (6)

17. 17 Wiener-Hopf equation: (7) (9) (8) Example: fusion of Doppler and barometric speed sensors: Barometric: Doppler: where: (10) (11) (12)

18. 18 General Block Diagram of the Information Processing in the ACS. Sources of Infor- mation (sensors) PPSP&ASToIReceiver BITE Sources of Infor- mation (sensors)

19. 19 Computer Network Architecture of Boeing-787 CCR CDN Remote Data Concentrators

20. 20 Transmission of Information 1. Coding of Signals. Hamming’s distance: 1 st word 001101 2 nd word 100100 H d =3 Grey Code. Truth Table: Encoding: Decoding: 0 11 1 00 1 0 x y Example: 3-digit word 0011117 1010116 1111015 0110014 0101103 1100102 1001001 0000000 Grey Bin.Dec. Max H d = 1.

21. 21 Angle-Code Converter BINARY ENCODER GRAY ENCODER

22. 22 2. Modulation of Signals Com. Ch. CSG LPF ymym ymym