Multipath modeling for deep integration
A state is added to a Kalman filter to model GPS multipath errors. The multipath states may be modeled as either a random walk model or a Gauss-Markov process. The choice of the model depends on the characteristics of the multi-path error and the GPS receiver. Adding this state to the Kalman filter to model multipath improves the navigation system's robustness when operating as a deeply integrated system when multipath is present.
1. A navigation system that operates in the presence of multipath, comprising:
a navigation processor that receives data from inertial sensors and computes a navigation solution; and
a Kalman filter that includes a multipath error model, wherein the Kalman filter receives the navigation solution and data from a global positioning satellite (GPS) receiver, and uses the navigation solution, the data from the GPS receiver, and the multipath error model to calculate an estimate that is provided to the navigation processor.
2. The system of claim 1 , wherein the multipath error model is a random walk model.
3. The system of claim 1 , wherein the multipath error model is a Gauss-Markov process.
4. A method for improving navigation system performance in the presence of multipath, comprising:
receiving data from inertial sensors and a global positioning satellite (GPS) receiver;
modeling a multipath state in a Kalman filter; and
calculating a navigation solution based on the received data and a navigation estimate that is calculated using the modeled multipath state.
5. The method of claim 4 , wherein modeling the multipath state includes using a random walk model.
6. The method of claim 4 , wherein modeling the multipath state includes using a Gauss-Markov process.
7. A method for improving navigation system performance in the presence of multipath, comprising:
receiving data from inertial sensors and a satellite based navigation system receiver;
calculating a Kalman gain using a first error covariance matrix that includes a multipath error state;
calculating a first estimate with the received data, the Kalman gain, and a state vector that includes the multipath error state; and
calculating a second estimate and a second error covariance matrix using a state transition matrix that includes the multipath error state.
8. The method of claim 7 , wherein the Kalman gain K is calculated as follows:
K n =P n − H n T ( H n P n − H n T +R n ) −1
where P is the error covariance matrix, H is a measurement matrix, and R is a measurement noise covariance matrix.
9. The method of claim 7 , wherein the multipath error state is modeled as a random walk model.
10. The method of claim 7 , wherein the multipath error state is modeled as a Gauss-Markov process.
11. The method of claim 7 , wherein the first estimate {circumflex over (X)} n is calculated as follows:
{circumflex over (x)} n ={circumflex over (x)} n − +K n ( Z n −H n {circumflex over (x)} n − )
where K is the Kalman gain, Z is a measurement vector, and H is a measurement matrix.
12. The method of claim 7 , wherein the first error covariance matrix P is calculated as follows:
P n =(1 −K n H n ) P n −
where K is the Kalman gain and H is a measurement matrix.
13. The method of claim 7 , wherein the second estimate {circumflex over (x)} n is calculated as follows:
{circumflex over (x)} n+1 − =Φ n {circumflex over (x)} n
where Φ is the state transition matrix.
14. The method of claim 7 , wherein the second error covariance matrix P is calculated as follows:
P n+1 − =Φ n P n Φ n T +Q n
where Φ is the state transition matrix and Q is the process noise covariance matrix.