EE 570: Location and Navigation INS/GPS Integration Aly El-Osery 1 Stephen Bruder 2 1 Electrical Engineering Department, New Mexico Tech Socorro, New Mexico, USA 2 Electrical and Computer Engineering Department, Embry-Riddle Aeronautical Univesity Prescott, Arizona, USA April 15, 2014 Aly El-Osery, Stephen Bruder (NMT,ERAU) EE 570: Location and Navigation April 15, 2014 1 / 14
Open-Loop Integration True PVA + errors Aiding errors - INS errors Aiding Sensors + Filter INS + + Inertial errors est. True PVA + errors Correct INS Output Aly El-Osery, Stephen Bruder (NMT,ERAU) EE 570: Location and Navigation April 15, 2014 2 / 14
Closed-Loop Integration If error estimates are fedback to correct the INS mechanization, a reset of the state estimates becomes necessary. Aiding Sensors + Filter INS INS Correction Correct INS Output Aly El-Osery, Stephen Bruder (NMT,ERAU) EE 570: Location and Navigation April 15, 2014 3 / 14
Loosely Coupled Integration GNSS Receiver Simple GNSS Ranging Processor PV + GNSS KF PV INS Filter Optional PVA INS Correction Cascade KF therefore integration KF BW must be less than that of GNSS KF (e.g. update interval of 10s) Minimum of 4 satellites required Correct INS Output Aly El-Osery, Stephen Bruder (NMT,ERAU) EE 570: Location and Navigation April 15, 2014 4 / 14
Tightly Coupled Integration GNSS Receiver GNSS Ranging Processor ρ, ρ ˆρ, ˆρ Filter INS derived psuedo-range and -rates INS INS Correction No cascade KF KF BW must be kept less than the GNSS tracking loop Does not require 4 satellites Correct INS Output Aly El-Osery, Stephen Bruder (NMT,ERAU) EE 570: Location and Navigation April 15, 2014 5 / 14
Tightly Coupled Integration Optional GNSS Receiver GNSS Ranging Processor ρ, ρ ˆρ, ˆρ Filter INS derived psuedo-range and -rates INS INS Correction No cascade KF KF BW must be kept less than the GNSS tracking loop Does not require 4 satellites Correct INS Output Aly El-Osery, Stephen Bruder (NMT,ERAU) EE 570: Location and Navigation April 15, 2014 5 / 14
ECEF INS/GNSS Loosely Coupled z e k = r GPS ˆ r eb e (1) v GPS ˆ v eb e H = 0 3 3 0 3 3 I 3 3 0 3 3 0 3 3 (2) 0 3 3 I 3 3 0 3 3 0 3 3 0 3 3 Theoretically, the lever arm from the INS to the GNSS antenna needs to be included, but in practice, the coupling of the attitude errors and gyro biases into the measurement through the lever arm is week. Aly El-Osery, Stephen Bruder (NMT,ERAU) EE 570: Location and Navigation April 15, 2014 6 / 14
INS Derived Psuedo-Range and -Rates The computed INS psuedo-range and rates with respect to the jth satellite, ˆρ j and ˆρ j ˆρ j = [ r es,j e ˆ r eb e ]T [ r es,j e ˆ r eb e ]+δˆρ rc,j (3) ˆρ j = u T j [ v e s,j ˆ v e eb ]T +δ ˆρ rc,j (4) where u j = re es,j ˆ r e eb r e es,j ˆ r e eb (5) Aly El-Osery, Stephen Bruder (NMT,ERAU) EE 570: Location and Navigation April 15, 2014 7 / 14
ECEF INS/GNSS Tightly Coupled Pseudo-ranges are used instead of XYZ. ( ) zρ z = z ρ (6) where z ρ = (ρ gps,1 ˆρ 1,ρ gps,2 ˆρ 2,...,ρ gps,n ˆρ n ) (7) z ρ = ( ρ gps,1 ˆρ 1, ρ gps,2 ˆρ 2,..., ρ gps,n ˆρ n ) (8) ( x(t) = δψ ) T eb e δ v eb e δ r eb e ba bg δρ rc δ ρ rc (9) ρ gps,j, and ρ gps,j and ˆρ j, and ˆρ j are the psuedo-ranges and rates obtained from the GNSS and INS, respectively, for the jth satellite. These equations are none linear and an EKF needs to be used. δρ rc and δ ρ rc are the clock bias and drift. Aly El-Osery, Stephen Bruder (NMT,ERAU) EE 570: Location and Navigation April 15, 2014 8 / 14
Tightly Coupled Linearized Measurement Matrix 0 1 3 0 1 3 u T 1 0 1 3 0 1 3 1 0 1 3 0 1 3 0 1 3 u T 2 0 1 3 0 1 3 1 0 1 3....... 0 1 3 0 1 3 u T n 0 1 3 0 1 3 1 0 1 3 H = 0 1 3 u T 1 0 1 3 0 1 3 0 1 3 0 1 3 1 0 1 3 u T 2 0 1 3 0 1 3 0 1 3 0 1 3 1....... 0 1 3 u T n 0 1 3 0 1 3 0 1 3 0 1 3 1 (10) Aly El-Osery, Stephen Bruder (NMT,ERAU) EE 570: Location and Navigation April 15, 2014 9 / 14
Deeply Coupled In deeply coupled GPS/INS integration the integration architecture utlizes the INS to aid in the tracking loops, allows fast aquistion, performance improvement with low signal-to-noise environments, and more resistance to jamming. Aly El-Osery, Stephen Bruder (NMT,ERAU) EE 570: Location and Navigation April 15, 2014 10 / 14
Deeply Coupled Signal samples from front-end I 0, Q 0 Correlators one for each sat. I E, Q E I P, Q P I L, Q L Pre- Filters Error state vec one per sat. Error Cov one per sat. Master Filter I c Q c Carrier NCO Code NCO C E C P C L Early, prompt, and late reference code generator INS PVA Reference Oscillator Receiver Clock LOS Projection Pseudorange & Pseudorange Rates IMU Aly El-Osery, Stephen Bruder (NMT,ERAU) EE 570: Location and Navigation April 15, 2014 11 / 14
Observability Are the states observable given a certain set of measurements? The system is observable if the observability matrix O(k) = H(k n+1) H(k n 2)Φ(k n+1). H(k)Φ(k 1)...Φ(k n+1) (11) where n is the number of states, has a rank of n. The rank of O is a binary indicator and does not provide a measure of how close the system is to being unobservable, hence, is prone to numerical ill-conditioning. Aly El-Osery, Stephen Bruder (NMT,ERAU) EE 570: Location and Navigation April 15, 2014 12 / 14
A Better Observability Measure In addition to the computation of the rank of O(k), compute the Singular Value Decomposition (SVD) of O(k) as O = UΣV (12) and observe the diagonal values of the matrix Σ. Using this approach it is possible to monitor the variations in the system observability due to changes in system dynamics. Aly El-Osery, Stephen Bruder (NMT,ERAU) EE 570: Location and Navigation April 15, 2014 13 / 14
Corrupt/Missing Data In Many cases the data from the aiding sensor may get corrupt and even not available. In those cases we can t use those measurements in the Kalman filter. Therefore 1 Set the Kalman gain to zero, or 2 Do not run the state or error covariance update steps. Aly El-Osery, Stephen Bruder (NMT,ERAU) EE 570: Location and Navigation April 15, 2014 14 / 14