Arbitrarily extended target shape and state estimation method based on b-spline function
A spline function and extended target technology, applied in radio wave measurement systems, instruments, etc., can solve problems such as inaccurate shape information and affect target state analysis, and achieve the effect of reliable information features
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[0029] 1. Introduction to basic theory
[0030] 1. Kalman filter technology
[0031] Suppose the state equation and measurement equation of a single target are expressed as:
[0032] x k+1 =Fx k +Gw k (1)
[0033] the y k =h(x k )+v k (2) Among them, x k represents the state of the target at time k, F is a one-step transition matrix, h( ) represents the observation model, w k and v k Denote the state noise and measurement noise, respectively, and the corresponding covariances are denoted as Q k and R k .
[0034] Suppose the state x of the target at time k is known k and covariance P k , the Kalman filtering steps are as follows:
[0035] (1) Predict the target state at the next moment
[0036] x k+1|k =Fx k +Gw k
[0037] (2) Predict the covariance matrix at the next moment
[0038] P k+1|k =FP k f T +GQG T
[0039] (3) Calculation gain
[0040] K k+1 =P k+1|k [S k+1|k ] -1
[0041] S k+1|k =P k+1|k +R k+1
[0042] (4) Update the status a...
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