One way to create an extended Kalman filter without using Matlab's built-in `extendedKalmanFilter`

function is by implementing the prediction and correction steps manually.

Firstly, define your system model and measurement model, which can be represented by state transition function `f`

and observation function `h`

. The state transition and observation model are:

main.m55 chars3 lines

where `x_k`

is the state at time step `k`

, `u_k`

is the control input, `z_k`

is the measurement at time step `k`

, `w_k`

and `v_k`

are process and measurement noise respectively.

Next, initialize the initial state estimate `x_0`

, the initial state covariance matrix P_0, and the process noise and measurement noise covariance matrices `Q`

and `R`

.

Then, for each time step, perform the following steps:

- Prediction step: Use the system model to predict the state estimate at time
`k`

:

main.m82 chars3 lines

where `F_k-1`

is the Jacobian matrix of `f`

at `x_k-1`

and `u_k-1`

.

- Correction step: Use the measurement model to correct the state estimate at time
`k`

:

main.m145 chars4 lines

where `H_k`

is the Jacobian matrix of `h`

at `x_k_pred`

.

Repeat these steps for each time step.

Note that matrix multiplication is used extensively in both prediction and correction steps.

Here's an example implementation in Matlab:

main.m1167 chars30 lines

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